[was@modular manjul]$ [was@modular manjul]$ Magma V2.8-10 Sat Mar 30 2002 16:14:15 on modular [Seed = 3766154770] Type ? for help. Type -D to quit. Loading startup file "/home/was/magma/local/emacs.m" Loading "/home/was/magma/local/init.m" > Attach("eigenrep.m"); > G := DirichletGroup(420); eps := c;M := ModularForms(eps,2); S := CuspidalSubspace(M); > > M; Space of modular forms on Gamma_1(420) with character all conjugates of [c], weight 2, and dimension 107 over Integer Ring. > Conductor(c); 5 > > S; Space of modular forms on Gamma_1(420) with character all conjugates of [c], weight 2, and dimension 84 over Integer Ring. > EisensteinSeries(M); [* 1/24 + q + q^2 + 4*q^3 + q^4 + 6*q^5 + 4*q^6 + 8*q^7 + O(q^8), 1/12 + q + 3*q^2 + q^3 + 7*q^4 + 6*q^5 + 3*q^6 + 8*q^7 + O(q^8), 1/8 + q + 3*q^2 + 4*q^3 + 3*q^4 + 6*q^5 + 12*q^6 + 8*q^7 + O(q^8), 1/6 + q + 3*q^2 + 4*q^3 + 7*q^4 + q^5 + 12*q^6 + 8*q^7 + O(q^8), 5/24 + q + 3*q^2 + 4*q^3 + 7*q^4 + 6*q^5 + 6*q^6 + 8*q^7 + O(q^8), 1/4 + q + 3*q^2 + 4*q^3 + 7*q^4 + 6*q^5 + 12*q^6 + q^7 + O(q^8), 3/8 + q + 3*q^2 + 4*q^3 + 7*q^4 + 6*q^5 + 12*q^6 + 8*q^7 + O(q^8), 11/24 + q + 3*q^2 + 4*q^3 + 7*q^4 + 6*q^5 + 12*q^6 + 8*q^7 + O(q^8), 13/24 + q + 3*q^2 + 4*q^3 + 7*q^4 + 6*q^5 + 12*q^6 + 8*q^7 + O(q^8), 7/12 + q + 3*q^2 + 4*q^3 + 7*q^4 + 6*q^5 + 12*q^6 + 8*q^7 + O(q^8), 19/24 + q + 3*q^2 + 4*q^3 + 7*q^4 + 6*q^5 + 12*q^6 + 8*q^7 + O(q^8), 5/6 + q + 3*q^2 + 4*q^3 + 7*q^4 + 6*q^5 + 12*q^6 + 8*q^7 + O(q^8), 9/8 + q + 3*q^2 + 4*q^3 + 7*q^4 + 6*q^5 + 12*q^6 + 8*q^7 + O(q^8), 29/24 + q + 3*q^2 + 4*q^3 + 7*q^4 + 6*q^5 + 12*q^6 + 8*q^7 + O(q^8), 17/12 + q + 3*q^2 + 4*q^3 + 7*q^4 + 6*q^5 + 12*q^6 + 8*q^7 + O(q^8), 41/24 + q + 3*q^2 + 4*q^3 + 7*q^4 + 6*q^5 + 12*q^6 + 8*q^7 + O(q^8), 59/24 + q + 3*q^2 + 4*q^3 + 7*q^4 + 6*q^5 + 12*q^6 + 8*q^7 + O(q^8), 23/8 + q + 3*q^2 + 4*q^3 + 7*q^4 + 6*q^5 + 12*q^6 + 8*q^7 + O(q^8), 83/24 + q + 3*q^2 + 4*q^3 + 7*q^4 + 6*q^5 + 12*q^6 + 8*q^7 + O(q^8), 13/3 + q + 3*q^2 + 4*q^3 + 7*q^4 + 6*q^5 + 12*q^6 + 8*q^7 + O(q^8), 139/24 + q + 3*q^2 + 4*q^3 + 7*q^4 + 6*q^5 + 12*q^6 + 8*q^7 + O(q^8), 209/24 + q + 3*q^2 + 4*q^3 + 7*q^4 + 6*q^5 + 12*q^6 + 8*q^7 + O(q^8), 419/24 + q + 3*q^2 + 4*q^3 + 7*q^4 + 6*q^5 + 12*q^6 + 8*q^7 + O(q^8) *] > S; Space of modular forms on Gamma_1(420) with character all conjugates of [c], weight 2, and dimension 84 over Integer Ring. > Basis(S); [ q + O(q^8), q^2 + O(q^8), q^3 + O(q^8), q^4 + O(q^8), q^5 + O(q^8), q^6 + O(q^8), q^7 + O(q^8), O(q^8), O(q^8), O(q^8), O(q^8), O(q^8), O(q^8), O(q^8), O(q^8), O(q^8), O(q^8), O(q^8), O(q^8), O(q^8), O(q^8), O(q^8), O(q^8), O(q^8), O(q^8), O(q^8), O(q^8), O(q^8), O(q^8), O(q^8), O(q^8), O(q^8), O(q^8), O(q^8), O(q^8), O(q^8), O(q^8), O(q^8), O(q^8), O(q^8), O(q^8), O(q^8), O(q^8), O(q^8), O(q^8), O(q^8), O(q^8), O(q^8), O(q^8), O(q^8), O(q^8), O(q^8), O(q^8), O(q^8), O(q^8), O(q^8), O(q^8), O(q^8), O(q^8), O(q^8), O(q^8), O(q^8), O(q^8), O(q^8), O(q^8), O(q^8), O(q^8), O(q^8), O(q^8), O(q^8), O(q^8), O(q^8), O(q^8), O(q^8), O(q^8), O(q^8), O(q^8), O(q^8), O(q^8), O(q^8), O(q^8), O(q^8), O(q^8), O(q^8) ] > SetPrecision(S,100); >> SetDefaultPrecision(S,100); ^ User error: Identifier 'SetDefaultPrecision' has not been declared or assigned > SetPrecision(S,100); > Basis(S); [ q + 16*q^87 + 22*q^89 + 48*q^91 - 12*q^93 + 5*q^95 - 26*q^97 + 60*q^99 + O(q^100), q^2 + 55*q^80 + 80*q^82 - 62*q^84 - 87*q^86 - 43*q^88 - 13*q^90 - 25*q^92 - 8*q^94 + 29*q^96 + 26*q^98 + O(q^100), q^3 + 14*q^87 + 17*q^89 + 43*q^91 - 8*q^93 + 10*q^95 - 25*q^97 + 55*q^99 + O(q^100), q^4 + 2*q^78 + 45*q^80 + 60*q^82 - 42*q^84 - 60*q^86 - 24*q^88 - 9*q^90 - 29*q^92 - q^94 + 19*q^96 + 13*q^98 + O(q^100), q^5 + q^89 + 2*q^91 + q^95 - 2*q^97 + 2*q^99 + O(q^100), q^6 + q^78 + 12*q^80 + 12*q^82 - 6*q^84 - 10*q^86 - q^88 - 12*q^92 + 2*q^94 + q^96 - q^98 + O(q^100), q^7 + 4*q^87 + 6*q^89 + 18*q^91 - 8*q^93 + 10*q^95 - 10*q^97 + 24*q^99 + O(q^100), q^8 + q^78 + 33*q^80 + 45*q^82 - 32*q^84 - 45*q^86 - 20*q^88 - 7*q^90 - 21*q^92 - 2*q^94 + 15*q^96 + 10*q^98 + O(q^100), q^9 + 11*q^87 + 14*q^89 + 31*q^91 - 6*q^93 + 6*q^95 - 18*q^97 + 40*q^99 + O(q^100), q^10 + 40*q^80 + 56*q^82 - 42*q^84 - 60*q^86 - 28*q^88 - 9*q^90 - 22*q^92 - 4*q^94 + 20*q^96 + 16*q^98 + O(q^100), q^11 + 2*q^87 + 2*q^89 + 4*q^91 - q^95 - 2*q^97 + 3*q^99 + O(q^100), q^12 + 4*q^78 + 63*q^80 + 83*q^82 - 60*q^84 - 87*q^86 - 38*q^88 - 15*q^90 - 36*q^92 - 4*q^94 + 29*q^96 + 21*q^98 + O(q^100), q^13 + 18*q^87 + 21*q^89 + 56*q^91 - 8*q^93 + 15*q^95 - 31*q^97 + 74*q^99 + O(q^100), q^14 + 77*q^80 + 108*q^82 - 83*q^84 - 119*q^86 - 56*q^88 - 17*q^90 - 35*q^92 - 12*q^94 + 39*q^96 + 35*q^98 + O(q^100), q^15 + 2*q^89 + 6*q^91 + 2*q^95 - 4*q^97 + 6*q^99 + O(q^100), q^16 + q^78 + 13*q^80 + 15*q^82 - 9*q^84 - 14*q^86 - 4*q^88 - 2*q^90 - 11*q^92 + q^94 + 3*q^96 + q^98 + O(q^100), q^17 + 14*q^87 + 17*q^89 + 45*q^91 - 4*q^93 + 9*q^95 - 26*q^97 + 60*q^99 + O(q^100), q^18 + 4*q^78 + 12*q^80 + 7*q^82 + 5*q^88 - 2*q^90 - 15*q^92 + 6*q^94 - 6*q^98 + O(q^100), q^19 + 14*q^87 + 15*q^89 + 40*q^91 - 6*q^93 + 9*q^95 - 23*q^97 + 53*q^99 + O(q^100), q^20 + 66*q^80 + 95*q^82 - 74*q^84 - 105*q^86 - 50*q^88 - 16*q^90 - 30*q^92 - 10*q^94 + 35*q^96 + 31*q^98 + O(q^100), q^21 - 4*q^91 + O(q^100), q^22 + 37*q^80 + 53*q^82 - 40*q^84 - 57*q^86 - 26*q^88 - 8*q^90 - 20*q^92 - 5*q^94 + 19*q^96 + 16*q^98 + O(q^100), q^23 - 2*q^89 - 2*q^91 + 2*q^93 - q^95 - 3*q^99 + O(q^100), q^24 + 3*q^78 + 61*q^80 + 82*q^82 - 59*q^84 - 85*q^86 - 37*q^88 - 14*q^90 - 35*q^92 - 4*q^94 + 28*q^96 + 21*q^98 + O(q^100), q^25 + 3*q^87 + 2*q^89 + 5*q^91 - 2*q^95 - 3*q^97 + 5*q^99 + O(q^100), q^26 + 68*q^80 + 97*q^82 - 74*q^84 - 107*q^86 - 50*q^88 - 15*q^90 - 32*q^92 - 9*q^94 + 34*q^96 + 31*q^98 + O(q^100), q^27 + 9*q^87 + 12*q^89 + 28*q^91 - 8*q^93 + 6*q^95 - 16*q^97 + 36*q^99 + O(q^100), q^28 + 18*q^80 + 27*q^82 - 21*q^84 - 30*q^86 - 14*q^88 - 6*q^90 - 7*q^92 - 2*q^94 + 10*q^96 + 8*q^98 + O(q^100), q^29 + 9*q^87 + 12*q^89 + 29*q^91 - 6*q^93 + 3*q^95 - 16*q^97 + 36*q^99 + O(q^100), q^30 + 68*q^80 + 97*q^82 - 75*q^84 - 108*q^86 - 52*q^88 - 16*q^90 - 31*q^92 - 10*q^94 + 36*q^96 + 32*q^98 + O(q^100), q^31 + 5*q^87 + 8*q^89 + 16*q^91 - 6*q^93 + q^95 - 8*q^97 + 18*q^99 + O(q^100), q^32 + 3*q^78 + 17*q^80 + 19*q^82 - 11*q^84 - 15*q^86 - 4*q^88 - 3*q^90 - 15*q^92 + 2*q^94 + 5*q^96 + O(q^100), q^33 + 18*q^87 + 23*q^89 + 54*q^91 - 14*q^93 + 11*q^95 - 30*q^97 + 70*q^99 + O(q^100), q^34 + 3*q^78 + 41*q^80 + 54*q^82 - 38*q^84 - 56*q^86 - 23*q^88 - 10*q^90 - 24*q^92 - 2*q^94 + 18*q^96 + 13*q^98 + O(q^100), q^35 + 19*q^87 + 22*q^89 + 59*q^91 - 12*q^93 + 19*q^95 - 33*q^97 + 77*q^99 + O(q^100), q^36 + 2*q^78 + 46*q^80 + 61*q^82 - 42*q^84 - 62*q^86 - 26*q^88 - 10*q^90 - 29*q^92 - 2*q^94 + 20*q^96 + 14*q^98 + O(q^100), q^37 + 9*q^87 + 12*q^89 + 28*q^91 - 7*q^93 + 6*q^95 - 15*q^97 + 36*q^99 + O(q^100), q^38 + 4*q^78 + 9*q^80 + 5*q^82 + 2*q^84 + 3*q^86 + 8*q^88 - q^90 - 15*q^92 + 5*q^94 - q^96 - 7*q^98 + O(q^100), q^39 + 14*q^87 + 18*q^89 + 43*q^91 - 6*q^93 + 9*q^95 - 25*q^97 + 58*q^99 + O(q^100), q^40 + 2*q^78 + 79*q^80 + 110*q^82 - 83*q^84 - 117*q^86 - 54*q^88 - 18*q^90 - 39*q^92 - 8*q^94 + 39*q^96 + 33*q^98 + O(q^100), q^41 + 11*q^87 + 14*q^89 + 35*q^91 - 6*q^93 + 9*q^95 - 20*q^97 + 46*q^99 + O(q^100), q^42 + 26*q^80 + 38*q^82 - 30*q^84 - 42*q^86 - 20*q^88 - 8*q^90 - 10*q^92 - 4*q^94 + 14*q^96 + 14*q^98 + O(q^100), q^43 + 2*q^87 + 3*q^89 + 8*q^91 + q^93 + q^95 - 5*q^97 + 10*q^99 + O(q^100), q^44 + 61*q^80 + 87*q^82 - 66*q^84 - 94*q^86 - 44*q^88 - 13*q^90 - 30*q^92 - 7*q^94 + 31*q^96 + 27*q^98 + O(q^100), q^45 + q^89 + 2*q^91 + q^95 - 2*q^97 + 2*q^99 + O(q^100), q^46 + 4*q^78 + 34*q^80 + 41*q^82 - 26*q^84 - 39*q^86 - 13*q^88 - 7*q^90 - 24*q^92 + q^94 + 12*q^96 + 6*q^98 + O(q^100), q^47 + 14*q^87 + 15*q^89 + 41*q^91 - 6*q^93 + 10*q^95 - 23*q^97 + 55*q^99 + O(q^100), q^48 + q^78 + 17*q^80 + 21*q^82 - 15*q^84 - 21*q^86 - 9*q^88 - 4*q^90 - 10*q^92 + 7*q^96 + 5*q^98 + O(q^100), q^49 + 20*q^87 + 24*q^89 + 60*q^91 - 12*q^93 + 16*q^95 - 34*q^97 + 80*q^99 + O(q^100), q^50 + 67*q^80 + 97*q^82 - 74*q^84 - 105*q^86 - 50*q^88 - 15*q^90 - 32*q^92 - 10*q^94 + 35*q^96 + 31*q^98 + O(q^100), q^51 + 14*q^87 + 16*q^89 + 37*q^91 - 6*q^93 + 7*q^95 - 21*q^97 + 49*q^99 + O(q^100), q^52 + 3*q^78 + 45*q^80 + 58*q^82 - 40*q^84 - 57*q^86 - 23*q^88 - 10*q^90 - 28*q^92 - q^94 + 19*q^96 + 12*q^98 + O(q^100), q^53 - 2*q^89 - 2*q^91 + 3*q^93 + 2*q^97 - 3*q^99 + O(q^100), q^54 + 4*q^78 + 31*q^80 + 36*q^82 - 22*q^84 - 33*q^86 - 10*q^88 - 7*q^90 - 23*q^92 + 2*q^94 + 10*q^96 + 4*q^98 + O(q^100), q^55 + 16*q^87 + 21*q^89 + 50*q^91 - 12*q^93 + 9*q^95 - 28*q^97 + 66*q^99 + O(q^100), q^56 + 61*q^80 + 86*q^82 - 66*q^84 - 95*q^86 - 44*q^88 - 13*q^90 - 29*q^92 - 8*q^94 + 31*q^96 + 27*q^98 + O(q^100), q^57 + 13*q^87 + 16*q^89 + 40*q^91 - 6*q^93 + 9*q^95 - 23*q^97 + 52*q^99 + O(q^100), q^58 + 4*q^78 + 32*q^80 + 39*q^82 - 25*q^84 - 36*q^86 - 12*q^88 - 7*q^90 - 23*q^92 + q^94 + 12*q^96 + 5*q^98 + O(q^100), q^59 + 12*q^87 + 15*q^89 + 37*q^91 - 6*q^93 + 6*q^95 - 21*q^97 + 49*q^99 + O(q^100), q^60 + 4*q^78 + 76*q^80 + 103*q^82 - 75*q^84 - 108*q^86 - 48*q^88 - 18*q^90 - 41*q^92 - 6*q^94 + 36*q^96 + 28*q^98 + O(q^100), q^61 + 2*q^87 + 2*q^89 + 3*q^91 - q^95 - 2*q^97 + 4*q^99 + O(q^100), q^62 + 4*q^78 + 8*q^80 + 4*q^82 + 2*q^84 + 3*q^86 + 8*q^88 - q^90 - 13*q^92 + 5*q^94 - q^96 - 7*q^98 + O(q^100), q^63 + 6*q^87 + 10*q^89 + 22*q^91 - 8*q^93 + 4*q^95 - 12*q^97 + 30*q^99 + O(q^100), q^64 + 30*q^80 + 44*q^82 - 33*q^84 - 48*q^86 - 23*q^88 - 7*q^90 - 15*q^92 - 4*q^94 + 16*q^96 + 14*q^98 + O(q^100), q^65 + 5*q^87 + 4*q^89 + 15*q^91 + 5*q^95 - 9*q^97 + 21*q^99 + O(q^100), q^66 + 21*q^80 + 29*q^82 - 21*q^84 - 31*q^86 - 14*q^88 - 4*q^90 - 12*q^92 - 2*q^94 + 10*q^96 + 8*q^98 + O(q^100), q^67 + 8*q^87 + 9*q^89 + 22*q^91 - 3*q^93 + 3*q^95 - 13*q^97 + 28*q^99 + O(q^100), q^68 + 3*q^78 + 24*q^80 + 29*q^82 - 19*q^84 - 27*q^86 - 9*q^88 - 5*q^90 - 17*q^92 + q^94 + 9*q^96 + 4*q^98 + O(q^100), q^69 + 9*q^87 + 11*q^89 + 25*q^91 - 6*q^93 + 5*q^95 - 14*q^97 + 32*q^99 + O(q^100), q^70 + 8*q^80 + 11*q^82 - 9*q^84 - 12*q^86 - 6*q^88 - 2*q^90 - 3*q^92 - 2*q^94 + 4*q^96 + 4*q^98 + O(q^100), q^71 + 5*q^87 + 8*q^89 + 16*q^91 - 6*q^93 - 8*q^97 + 19*q^99 + O(q^100), q^72 + 3*q^78 + 21*q^80 + 24*q^82 - 15*q^84 - 21*q^86 - 7*q^88 - 5*q^90 - 15*q^92 + 2*q^94 + 7*q^96 + 3*q^98 + O(q^100), q^73 + 18*q^87 + 22*q^89 + 54*q^91 - 10*q^93 + 12*q^95 - 30*q^97 + 70*q^99 + O(q^100), q^74 + 67*q^80 + 96*q^82 - 74*q^84 - 105*q^86 - 50*q^88 - 15*q^90 - 31*q^92 - 9*q^94 + 35*q^96 + 31*q^98 + O(q^100), q^75 + 18*q^87 + 23*q^89 + 54*q^91 - 12*q^93 + 11*q^95 - 30*q^97 + 70*q^99 + O(q^100), q^76 + 62*q^80 + 88*q^82 - 66*q^84 - 95*q^86 - 44*q^88 - 13*q^90 - 31*q^92 - 7*q^94 + 31*q^96 + 27*q^98 + O(q^100), q^77 + 20*q^87 + 24*q^89 + 61*q^91 - 12*q^93 + 16*q^95 - 34*q^97 + 80*q^99 + O(q^100), 5*q^78 + 80*q^80 + 106*q^82 - 75*q^84 - 108*q^86 - 45*q^88 - 18*q^90 - 46*q^92 - 4*q^94 + 36*q^96 + 26*q^98 + O(q^100), q^79 + 20*q^87 + 26*q^89 + 61*q^91 - 12*q^93 + 13*q^95 - 34*q^97 + 80*q^99 + O(q^100), 81*q^80 + 117*q^82 - 90*q^84 - 129*q^86 - 62*q^88 - 19*q^90 - 36*q^92 - 12*q^94 + 43*q^96 + 39*q^98 + O(q^100), q^81 + 14*q^87 + 16*q^89 + 38*q^91 - 6*q^93 + 7*q^95 - 21*q^97 + 49*q^99 + O(q^100), q^83 + 14*q^87 + 17*q^89 + 44*q^91 - 8*q^93 + 12*q^95 - 24*q^97 + 59*q^99 + O(q^100), q^85 + 3*q^87 + 4*q^89 + 11*q^91 + 2*q^95 - 7*q^97 + 15*q^99 + O(q^100), 21*q^87 + 26*q^89 + 63*q^91 - 12*q^93 + 13*q^95 - 35*q^97 + 83*q^99 + O(q^100) ] > N := Newforms(S); > N; [* [* q + 1/6*(-a + 4)*q^3 + 1/6*(a + 8)*q^5 + 1/6*(-a + 4)*q^7 - q^9 + 4*q^11 + 1/3*(a - 4)*q^13 + 1/3*(-a + 7)*q^15 + 1/3*(-a + 4)*q^17 + 2*q^19 - q^21 + (-a + 4)*q^23 + 1/3*(2*a + 1)*q^25 + 1/6*(a - 4)*q^27 - 6*q^29 + 6*q^31 + 1/3*(-2*a + 8)*q^33 + 1/3*(-a + 7)*q^35 + 1/3*(2*a - 8)*q^37 + 2*q^39 + 1/3*(-2*a + 8)*q^43 + 1/6*(-a - 8)*q^45 + 1/3*(-2*a + 8)*q^47 - q^49 - 2*q^51 + 1/3*(-a + 4)*q^53 + 1/3*(2*a + 16)*q^55 + 1/3*(-a + 4)*q^57 - 4*q^59 - 2*q^61 + 1/6*(a - 4)*q^63 + 1/3*(2*a - 14)*q^65 + (2*a - 8)*q^67 - 6*q^69 - 8*q^71 + 1/3*(7*a - 28)*q^73 + 1/2*(-a + 12)*q^75 + 1/3*(-2*a + 8)*q^77 - 16*q^79 + q^81 + 1/3*(8*a - 32)*q^83 + 1/3*(-2*a + 14)*q^85 + (a - 4)*q^87 - 16*q^89 + 2*q^91 + (-a + 4)*q^93 + 1/3*(a + 8)*q^95 + 1/3*(7*a - 28)*q^97 - 4*q^99 + O(q^100), q + 1/6*(-b + 4)*q^3 + 1/6*(b + 8)*q^5 + 1/6*(-b + 4)*q^7 - q^9 + 4*q^11 + 1/3*(b - 4)*q^13 + 1/3*(-b + 7)*q^15 + 1/3*(-b + 4)*q^17 + 2*q^19 - q^21 + (-b + 4)*q^23 + 1/3*(2*b + 1)*q^25 + 1/6*(b - 4)*q^27 - 6*q^29 + 6*q^31 + 1/3*(-2*b + 8)*q^33 + 1/3*(-b + 7)*q^35 + 1/3*(2*b - 8)*q^37 + 2*q^39 + 1/3*(-2*b + 8)*q^43 + 1/6*(-b - 8)*q^45 + 1/3*(-2*b + 8)*q^47 - q^49 - 2*q^51 + 1/3*(-b + 4)*q^53 + 1/3*(2*b + 16)*q^55 + 1/3*(-b + 4)*q^57 - 4*q^59 - 2*q^61 + 1/6*(b - 4)*q^63 + 1/3*(2*b - 14)*q^65 + (2*b - 8)*q^67 - 6*q^69 - 8*q^71 + 1/3*(7*b - 28)*q^73 + 1/2*(-b + 12)*q^75 + 1/3*(-2*b + 8)*q^77 - 16*q^79 + q^81 + 1/3*(8*b - 32)*q^83 + 1/3*(-2*b + 14)*q^85 + (b - 4)*q^87 - 16*q^89 + 2*q^91 + (-b + 4)*q^93 + 1/3*(b + 8)*q^95 + 1/3*(7*b - 28)*q^97 - 4*q^99 + O(q^100) *], [* q + 1/6*(a + 4)*q^3 + 1/6*(-a - 16)*q^5 + 1/6*(a + 4)*q^7 - q^9 - 4*q^11 + (a + 4)*q^13 + 1/3*(-a - 1)*q^15 + 1/3*(a + 4)*q^17 - 6*q^19 - q^21 + 1/3*(-a - 4)*q^23 + 1/3*(2*a + 17)*q^25 + 1/6*(-a - 4)*q^27 - 6*q^29 - 2*q^31 + 1/3*(-2*a - 8)*q^33 + 1/3*(-a - 1)*q^35 + 1/3*(-2*a - 8)*q^37 - 6*q^39 + 8*q^41 + 1/3*(2*a + 8)*q^43 + 1/6*(a + 16)*q^45 + 1/3*(2*a + 8)*q^47 - q^49 - 2*q^51 + (-a - 4)*q^53 + 1/3*(2*a + 32)*q^55 + (-a - 4)*q^57 - 4*q^59 + 14*q^61 + 1/6*(-a - 4)*q^63 + (-2*a - 2)*q^65 + 1/3*(2*a + 8)*q^67 + 2*q^69 + 1/3*(5*a + 20)*q^73 + 1/2*(a - 4)*q^75 + 1/3*(-2*a - 8)*q^77 + q^81 + 1/3*(8*a + 32)*q^83 + 1/3*(-2*a - 2)*q^85 + (-a - 4)*q^87 - 8*q^89 - 6*q^91 + 1/3*(-a - 4)*q^93 + (a + 16)*q^95 + 1/3*(5*a + 20)*q^97 + 4*q^99 + O(q^100), q + 1/6*(b + 4)*q^3 + 1/6*(-b - 16)*q^5 + 1/6*(b + 4)*q^7 - q^9 - 4*q^11 + (b + 4)*q^13 + 1/3*(-b - 1)*q^15 + 1/3*(b + 4)*q^17 - 6*q^19 - q^21 + 1/3*(-b - 4)*q^23 + 1/3*(2*b + 17)*q^25 + 1/6*(-b - 4)*q^27 - 6*q^29 - 2*q^31 + 1/3*(-2*b - 8)*q^33 + 1/3*(-b - 1)*q^35 + 1/3*(-2*b - 8)*q^37 - 6*q^39 + 8*q^41 + 1/3*(2*b + 8)*q^43 + 1/6*(b + 16)*q^45 + 1/3*(2*b + 8)*q^47 - q^49 - 2*q^51 + (-b - 4)*q^53 + 1/3*(2*b + 32)*q^55 + (-b - 4)*q^57 - 4*q^59 + 14*q^61 + 1/6*(-b - 4)*q^63 + (-2*b - 2)*q^65 + 1/3*(2*b + 8)*q^67 + 2*q^69 + 1/3*(5*b + 20)*q^73 + 1/2*(b - 4)*q^75 + 1/3*(-2*b - 8)*q^77 + q^81 + 1/3*(8*b + 32)*q^83 + 1/3*(-2*b - 2)*q^85 + (-b - 4)*q^87 - 8*q^89 - 6*q^91 + 1/3*(-b - 4)*q^93 + (b + 16)*q^95 + 1/3*(5*b + 20)*q^97 + 4*q^99 + O(q^100) *] *] > f := S.4; > f; q^4 + 2*q^78 + 45*q^80 + 60*q^82 - 42*q^84 - 60*q^86 - 24*q^88 - 9*q^90 - 29*q^92 - q^94 + 19*q^96 + 13*q^98 + O(q^100) > w, E := EigenDecomp(S,f,70); Magma: Internal error Please mail this entire run [**WITH THE FOLLOWING LINES**] to magma-bugs@maths.usyd.edu.au Version date: Tue Mar 12 19:47:33 EST 2002 Initial seed: 3766154770 Time to this point: 60.81 division by zero in gdiv > w, E := EigenDecomp(S,f,70); Magma: Internal error Please mail this entire run [**WITH THE FOLLOWING LINES**] to magma-bugs@maths.usyd.edu.au Version date: Tue Mar 12 19:47:33 EST 2002 Initial seed: 3766154770 Time to this point: 79.66 division by zero in gdiv > w, E := EigenDecomp(S,f,100); Magma: Internal error Please mail this entire run [**WITH THE FOLLOWING LINES**] to magma-bugs@maths.usyd.edu.au Version date: Tue Mar 12 19:47:33 EST 2002 Initial seed: 3766154770 Time to this point: 96.73 division by zero in gdiv > w, E := EigenDecomp(S,f,100); In file "/home/was/people/manjul/eigenrep.m", line 8, column 4: >> return EigenDecomp(M, PowerSeries(f,prec), prec); ^ User error: bad syntax >> w, E := EigenDecomp(S,f,100); ^ User error: Identifier 'EigenDecomp' has not been declared or assigned > > w, E := EigenDecomp(S,f,100); Magma: Internal error Please mail this entire run [**WITH THE FOLLOWING LINES**] to magma-bugs@maths.usyd.edu.au Version date: Tue Mar 12 19:47:33 EST 2002 Initial seed: 3766154770 Time to this point: 114 division by zero in gdiv > > w, E := EigenDecomp(S,f,100); 1 2 3 Magma: Internal error Please mail this entire run [**WITH THE FOLLOWING LINES**] to magma-bugs@maths.usyd.edu.au Version date: Tue Mar 12 19:47:33 EST 2002 Initial seed: 3766154770 Time to this point: 138.33 division by zero in gdiv > > w, E := EigenDecomp(S,f,100); 1 2 3 3.500000000000000000000000000 Magma: Internal error Please mail this entire run [**WITH THE FOLLOWING LINES**] to magma-bugs@maths.usyd.edu.au Version date: Tue Mar 12 19:47:33 EST 2002 Initial seed: 3766154770 Time to this point: 155.67 division by zero in gdiv > > w, E := EigenDecomp(S,f,100); 1 2 3 3.500000000000000000000000000 [0 1 1.0000000000000000000000000000000000000*i -1.0000000000000000000000000000000000000*i -1 + 0.E-38*i -2/1 + 1.0000000000000000000000000000000000000*i 1 + 0.E-38*i -2.0000000000000000000000000000000000000*i -1.0000000000000000000000000000000000000*i -1 + 0.E-38*i -1 - 2.0000000000000000000000000000000000000*i 2/1 + 0.E-38*i 1.0000000000000000000000000000000000000*i 6.0000000000000000000000000000000000000*i 2/1 + 0.E-38*i 1 + 2.0000000000000000000000000000000000000*i 1 + 0.E-38*i -2.0000000000000000000000000000000000000*i 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3.9999999999999999999999999999999999999*i 0 -3.9183145016431808470000000000000000000 E-39 - 3.9999999999999999999999999999999999999*i 0 12] Magma: Internal error Please mail this entire run [**WITH THE FOLLOWING LINES**] to magma-bugs@maths.usyd.edu.au Version date: Tue Mar 12 19:47:33 EST 2002 Initial seed: 3766154770 Time to this point: 233.32 division by zero in gdiv > AssertAttribute(FldPr,"Precision",150); > time w, E := EigenDecomp(S,f,95); 1 2 3 3.500000000000000000000000000 [0 1 1.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000*i -1.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000*i -1 + 0.E-163*i -2/1 + 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3.999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999*i 0 2.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 + 0.E-164*i 0 0 0 -1.157686848193407058000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 E-163 - 9.999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999*i 0 -4.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 - 2.999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999*i 0 4.630747392773628234000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 E-164 + 3.999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999*i 0 0 0 1.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 + 0.E-164*i 0 -1.852298957295715808000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 E-163 - 15.99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999*i 0 2.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 + 3.999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999*i 0 6.946121089160442352000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 E-164 + 5.999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999*i 0 -8.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 + 0.E-164*i 0 -6.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 + 0.E-164*i 0 2.315373696386814117000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 E-164 + 1.999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999*i 0] Magma: Internal error Please mail this entire run [**WITH THE FOLLOWING LINES**] to magma-bugs@maths.usyd.edu.au Version date: Tue Mar 12 19:47:33 EST 2002 Initial seed: 3766154770 Time to this point: 254.67 division by zero in gdiv > EigenDecomp; > > > > > Intrinsic 'EigenDecomp' Signatures: In file "/home/was/people/manjul/eigenrep.m", line 89, column 60: >> A := MatrixAlgebra(ComplexField(),n)!(&cat[[b[i] : i in P] : b in B]); ^ Runtime error: Undefined reference 'P' in package "/home/was/people/manjul/eigenrep.m" > M; Space of modular forms on Gamma_1(420) with character all conjugates of [c], weight 2, and dimension 107 over Integer Ring. > MQ := BaseExtend(M,RationalField()); > SQ := BaseExtend(S,RationalField()); > SetPrecision(SQ,90); > Basis(SQ); [ q + 16*q^87 + 22*q^89 + O(q^90), q^2 + 55*q^80 + 80*q^82 - 62*q^84 - 87*q^86 - 43*q^88 + O(q^90), q^3 + 14*q^87 + 17*q^89 + O(q^90), q^4 + 2*q^78 + 45*q^80 + 60*q^82 - 42*q^84 - 60*q^86 - 24*q^88 + O(q^90), q^5 + q^89 + O(q^90), q^6 + q^78 + 12*q^80 + 12*q^82 - 6*q^84 - 10*q^86 - q^88 + O(q^90), q^7 + 4*q^87 + 6*q^89 + O(q^90), q^8 + q^78 + 33*q^80 + 45*q^82 - 32*q^84 - 45*q^86 - 20*q^88 + O(q^90), q^9 + 11*q^87 + 14*q^89 + O(q^90), q^10 + 40*q^80 + 56*q^82 - 42*q^84 - 60*q^86 - 28*q^88 + O(q^90), q^11 + 2*q^87 + 2*q^89 + O(q^90), q^12 + 4*q^78 + 63*q^80 + 83*q^82 - 60*q^84 - 87*q^86 - 38*q^88 + O(q^90), q^13 + 18*q^87 + 21*q^89 + O(q^90), q^14 + 77*q^80 + 108*q^82 - 83*q^84 - 119*q^86 - 56*q^88 + O(q^90), q^15 + 2*q^89 + O(q^90), q^16 + q^78 + 13*q^80 + 15*q^82 - 9*q^84 - 14*q^86 - 4*q^88 + O(q^90), q^17 + 14*q^87 + 17*q^89 + O(q^90), q^18 + 4*q^78 + 12*q^80 + 7*q^82 + 5*q^88 + O(q^90), q^19 + 14*q^87 + 15*q^89 + O(q^90), q^20 + 66*q^80 + 95*q^82 - 74*q^84 - 105*q^86 - 50*q^88 + O(q^90), q^21 + O(q^90), q^22 + 37*q^80 + 53*q^82 - 40*q^84 - 57*q^86 - 26*q^88 + O(q^90), q^23 - 2*q^89 + O(q^90), q^24 + 3*q^78 + 61*q^80 + 82*q^82 - 59*q^84 - 85*q^86 - 37*q^88 + O(q^90), q^25 + 3*q^87 + 2*q^89 + O(q^90), q^26 + 68*q^80 + 97*q^82 - 74*q^84 - 107*q^86 - 50*q^88 + O(q^90), q^27 + 9*q^87 + 12*q^89 + O(q^90), q^28 + 18*q^80 + 27*q^82 - 21*q^84 - 30*q^86 - 14*q^88 + O(q^90), q^29 + 9*q^87 + 12*q^89 + O(q^90), q^30 + 68*q^80 + 97*q^82 - 75*q^84 - 108*q^86 - 52*q^88 + O(q^90), q^31 + 5*q^87 + 8*q^89 + O(q^90), q^32 + 3*q^78 + 17*q^80 + 19*q^82 - 11*q^84 - 15*q^86 - 4*q^88 + O(q^90), q^33 + 18*q^87 + 23*q^89 + O(q^90), q^34 + 3*q^78 + 41*q^80 + 54*q^82 - 38*q^84 - 56*q^86 - 23*q^88 + O(q^90), q^35 + 19*q^87 + 22*q^89 + O(q^90), q^36 + 2*q^78 + 46*q^80 + 61*q^82 - 42*q^84 - 62*q^86 - 26*q^88 + O(q^90), q^37 + 9*q^87 + 12*q^89 + O(q^90), q^38 + 4*q^78 + 9*q^80 + 5*q^82 + 2*q^84 + 3*q^86 + 8*q^88 + O(q^90), q^39 + 14*q^87 + 18*q^89 + O(q^90), q^40 + 2*q^78 + 79*q^80 + 110*q^82 - 83*q^84 - 117*q^86 - 54*q^88 + O(q^90), q^41 + 11*q^87 + 14*q^89 + O(q^90), q^42 + 26*q^80 + 38*q^82 - 30*q^84 - 42*q^86 - 20*q^88 + O(q^90), q^43 + 2*q^87 + 3*q^89 + O(q^90), q^44 + 61*q^80 + 87*q^82 - 66*q^84 - 94*q^86 - 44*q^88 + O(q^90), q^45 + q^89 + O(q^90), q^46 + 4*q^78 + 34*q^80 + 41*q^82 - 26*q^84 - 39*q^86 - 13*q^88 + O(q^90), q^47 + 14*q^87 + 15*q^89 + O(q^90), q^48 + q^78 + 17*q^80 + 21*q^82 - 15*q^84 - 21*q^86 - 9*q^88 + O(q^90), q^49 + 20*q^87 + 24*q^89 + O(q^90), q^50 + 67*q^80 + 97*q^82 - 74*q^84 - 105*q^86 - 50*q^88 + O(q^90), q^51 + 14*q^87 + 16*q^89 + O(q^90), q^52 + 3*q^78 + 45*q^80 + 58*q^82 - 40*q^84 - 57*q^86 - 23*q^88 + O(q^90), q^53 - 2*q^89 + O(q^90), q^54 + 4*q^78 + 31*q^80 + 36*q^82 - 22*q^84 - 33*q^86 - 10*q^88 + O(q^90), q^55 + 16*q^87 + 21*q^89 + O(q^90), q^56 + 61*q^80 + 86*q^82 - 66*q^84 - 95*q^86 - 44*q^88 + O(q^90), q^57 + 13*q^87 + 16*q^89 + O(q^90), q^58 + 4*q^78 + 32*q^80 + 39*q^82 - 25*q^84 - 36*q^86 - 12*q^88 + O(q^90), q^59 + 12*q^87 + 15*q^89 + O(q^90), q^60 + 4*q^78 + 76*q^80 + 103*q^82 - 75*q^84 - 108*q^86 - 48*q^88 + O(q^90), q^61 + 2*q^87 + 2*q^89 + O(q^90), q^62 + 4*q^78 + 8*q^80 + 4*q^82 + 2*q^84 + 3*q^86 + 8*q^88 + O(q^90), q^63 + 6*q^87 + 10*q^89 + O(q^90), q^64 + 30*q^80 + 44*q^82 - 33*q^84 - 48*q^86 - 23*q^88 + O(q^90), q^65 + 5*q^87 + 4*q^89 + O(q^90), q^66 + 21*q^80 + 29*q^82 - 21*q^84 - 31*q^86 - 14*q^88 + O(q^90), q^67 + 8*q^87 + 9*q^89 + O(q^90), q^68 + 3*q^78 + 24*q^80 + 29*q^82 - 19*q^84 - 27*q^86 - 9*q^88 + O(q^90), q^69 + 9*q^87 + 11*q^89 + O(q^90), q^70 + 8*q^80 + 11*q^82 - 9*q^84 - 12*q^86 - 6*q^88 + O(q^90), q^71 + 5*q^87 + 8*q^89 + O(q^90), q^72 + 3*q^78 + 21*q^80 + 24*q^82 - 15*q^84 - 21*q^86 - 7*q^88 + O(q^90), q^73 + 18*q^87 + 22*q^89 + O(q^90), q^74 + 67*q^80 + 96*q^82 - 74*q^84 - 105*q^86 - 50*q^88 + O(q^90), q^75 + 18*q^87 + 23*q^89 + O(q^90), q^76 + 62*q^80 + 88*q^82 - 66*q^84 - 95*q^86 - 44*q^88 + O(q^90), q^77 + 20*q^87 + 24*q^89 + O(q^90), 5*q^78 + 80*q^80 + 106*q^82 - 75*q^84 - 108*q^86 - 45*q^88 + O(q^90), q^79 + 20*q^87 + 26*q^89 + O(q^90), 81*q^80 + 117*q^82 - 90*q^84 - 129*q^86 - 62*q^88 + O(q^90), q^81 + 14*q^87 + 16*q^89 + O(q^90), q^83 + 14*q^87 + 17*q^89 + O(q^90), q^85 + 3*q^87 + 4*q^89 + O(q^90), 21*q^87 + 26*q^89 + O(q^90) ] > f := S.5; > g := S.84; > g; 21*q^87 + 26*q^89 + 63*q^91 - 12*q^93 + 13*q^95 - 35*q^97 + 83*q^99 + O(q^100) > PowerSeries(g,200); 21*q^87 + 26*q^89 + 63*q^91 - 12*q^93 + 13*q^95 - 35*q^97 + 83*q^99 + 24*q^103 + 56*q^105 + 9*q^107 - 26*q^109 - 126*q^111 + 62*q^113 - 60*q^115 - 33*q^117 + 16*q^119 - 19*q^123 - 90*q^125 - 74*q^127 - 64*q^129 - 46*q^131 - 27*q^133 - 9*q^135 - 41*q^137 - 4*q^139 - 15*q^141 - 139*q^143 - 30*q^145 - 2*q^147 + 22*q^149 + 57*q^151 + 31*q^153 + 10*q^155 + 123*q^157 - 62*q^159 - 48*q^161 + 30*q^163 + 85*q^165 + 132*q^167 - 47*q^169 + 48*q^171 + 73*q^173 - 41*q^175 - 63*q^177 - 5*q^179 + 20*q^181 + 84*q^183 + 89*q^185 + 81*q^187 + 42*q^189 - 53*q^191 - 47*q^193 - 55*q^195 + 74*q^197 + 30*q^199 + O(q^200) > g; 21*q^87 + 26*q^89 + 63*q^91 - 12*q^93 + 13*q^95 - 35*q^97 + 83*q^99 + O(q^100) > Valuation(g); >> Valuation(g); ^ Runtime error in 'Valuation': Bad argument types Argument types given: ModFrmElt > Eltseq(PowerSeries(g,100)); [ 21, 0, 26, 0, 63, 0, -12, 0, 13, 0, -35, 0, 83 ] 87 1 > _,a := Eltseq(PowerSeries(g,100)); > a; 87 > Coefficient(f,5); 1 > Coefficient(f,6); 0 > f; q^5 + q^89 + 2*q^91 + q^95 - 2*q^97 + 2*q^99 + O(q^100) > ; > time w, E := EigenDecomp(S,f,95); Pivots = [ 2, 3, 4, 5, 6, 7, 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-3.473060544580221176000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 E-164 + 5.999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999*i 0 0.E-163 - 6.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000*i 0 0.E-163 + 6.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000*i 0 0.E-163 + 6.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000*i 0.E-163 - 6.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000*i -6.946121089160442352000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 E-164 + 5.999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999*i -6.946121089160442352000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 E-164 - 5.999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999*i] Magma: Internal error Please mail this entire run [**WITH THE FOLLOWING LINES**] to magma-bugs@maths.usyd.edu.au Version date: Tue Mar 12 19:47:33 EST 2002 Initial seed: 3766154770 Time to this point: 295.48 division by zero in gdiv > quit; Total time: 295.880 seconds [was@modular manjul]$ me Magma V2.8-10 Sat Mar 30 2002 16:54:30 on modular [Seed = 1456234007] Type ? for help. Type -D to quit. Loading startup file "/home/was/magma/local/emacs.m" Loading "/home/was/magma/local/init.m" > G := DirichletGroup(420); eps := c;M := ModularForms(eps,2); S := CuspidalSubspace(M); > time w, E := EigenDecomp(S,f,95); >> time w, E := EigenDecomp(S,f,95); ^ User error: Identifier 'f' has not been declared or assigned > f := S.5; > > time w, E := EigenDecomp(S,f,95); >> time w, E := EigenDecomp(S,f,95); ^ User error: Identifier 'EigenDecomp' has not been declared or assigned > Attach("eigenrep.m"); > > time w, E := EigenDecomp(S,f,95); Pivots = [ 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 84, 86, 88 ] A = [1 0 0 0 1 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 1 1 1] [1.0000000000000000000000000000000000000*i 1 0 0 -1.0000000000000000000000000000000000000*i 1 0 0 -4.0000000000000000000000000000000000000*i 1 0 0 0 0 4.0000000000000000000000000000000000000*i 1 0 0 0 0 0 0 0 0 0.E-38 - 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Magma: Internal error Please mail this entire run [**WITH THE FOLLOWING LINES**] to magma-bugs@maths.usyd.edu.au Version date: Tue Mar 12 19:47:33 EST 2002 Initial seed: 1456234007 Time to this point: 106.13 division by zero in gdiv > f; q^5 + O(q^8) > S.5; q^5 + O(q^8) > G := DirichletGroup(420); eps := c;M := ModularForms(eps,2); S := CuspidalSubspace(M); [Interrupt twice in half a second; exiting] Total time: 106.860 seconds [was@modular manjul]$ [was@modular manjul]$ [was@modular manjul]$ [was@modular manjul]$ [was@modular manjul]$ me Magma V2.8-10 Sat Mar 30 2002 16:59:39 on modular [Seed = 2028106084] Type ? for help. Type -D to quit. Loading startup file "/home/was/magma/local/emacs.m" Loading "/home/was/magma/local/init.m" > G := DirichletGroup(37); > eps := G.1; > M := ModularForms(eps,2); > M; Space of modular forms on Gamma_1(37) with character all conjugates of [$.1], weight 2, and dimension 4 over Integer Ring. > f := M.2; > f; q - q^4 + q^5 + q^6 + 4*q^7 + O(q^8) > EigenDecomp(M,f,10); >> EigenDecomp(M,f,10); ^ User error: Identifier 'EigenDecomp' has not been declared or assigned > Attach("eigenrep.m"); > EigenDecomp(M,f,10); WARNING: Precision is probably too low. Pivots = [ 1, 2, 3, 4 ] A = [0 0 -25 0] [1 1 5 1] [-2.0000000000000000000000000000000000000*i 2.0000000000000000000000000000000000000*i -5 1] [-1 + 0.E-38*i -1 + 0.E-38*i 20 4/1] now compute inverse! [ 0.39999999999999999999999999999999999999 - 0.049999999999999999999999999999999999999*i, 0.40000000000000000000000000000000000000 + 0.049999999999999999999999999999999999999*i, 0, 0.200000000000000000000000000000000000000000000000000000000 + 0.E-49*i ] [ q + -2.0000000000000000000000000000000000000*i*q^2 + (-1 + 0.E-38*i)*q^3 + (-2/1 + 0.E-38*i)*q^4 + 2.0000000000000000000000000000000000000*i*q^5 + 2.0000000000000000000000000000000000000*i*q^6 + 3/1*q^7 - 2*q^9 + O(q^10), q + 2.0000000000000000000000000000000000000*i*q^2 + (-1 + 0.E-38*i)*q^3 + (-2/1 + 0.E-38*i)*q^4 + -2.0000000000000000000000000000000000000*i*q^5 + -2.0000000000000000000000000000000000000*i*q^6 + 3/1*q^7 - 2*q^9 + O(q^10), -25 + 5*q - 5*q^2 + 20*q^3 + 15*q^4 - 20*q^5 - 20*q^6 + 40*q^7 - 25*q^8 + 65*q^9 + O(q^10), q + q^2 + 4/1*q^3 + 3/1*q^4 + 4/1*q^5 + 4/1*q^6 + 8/1*q^7 + 5/1*q^8 + 13*q^9 + O(q^10) ] > w, E := EigenDecomp(M,f,10); WARNING: Precision is probably too low. Pivots = [ 1, 2, 3, 4 ] A = [0 0 -25 0] [1 1 5 1] [-2.0000000000000000000000000000000000000*i 2.0000000000000000000000000000000000000*i -5 1] [-1 + 0.E-38*i -1 + 0.E-38*i 20 4/1] now compute inverse! > w; [ 0.39999999999999999999999999999999999999 - 0.049999999999999999999999999999999999999*i, 0.40000000000000000000000000000000000000 + 0.049999999999999999999999999999999999999*i, 0, 0.200000000000000000000000000000000000000000000000000000000 + 0.E-49*i ] > E; [ q + -2.0000000000000000000000000000000000000*i*q^2 + (-1 + 0.E-38*i)*q^3 + (-2/1 + 0.E-38*i)*q^4 + 2.0000000000000000000000000000000000000*i*q^5 + 2.0000000000000000000000000000000000000*i*q^6 + 3/1*q^7 - 2*q^9 + O(q^10), q + 2.0000000000000000000000000000000000000*i*q^2 + (-1 + 0.E-38*i)*q^3 + (-2/1 + 0.E-38*i)*q^4 + -2.0000000000000000000000000000000000000*i*q^5 + -2.0000000000000000000000000000000000000*i*q^6 + 3/1*q^7 - 2*q^9 + O(q^10), -25 + 5*q - 5*q^2 + 20*q^3 + 15*q^4 - 20*q^5 - 20*q^6 + 40*q^7 - 25*q^8 + 65*q^9 + O(q^10), q + q^2 + 4/1*q^3 + 3/1*q^4 + 4/1*q^5 + 4/1*q^6 + 8/1*q^7 + 5/1*q^8 + 13*q^9 + O(q^10) ] > w[1]*E[1]+w[2]*E[2]+w[3]*E[3]+w[4]*E[4]; (0.99999999999999999999999999999999999999 + 0.E-40*i)*q + ( 0.E-39 + 8.8162076286971569060000000000000000000 E-39*i)*q^2 + (-1.0000000000000000000000000000000000000 + 1.4693679381161928170000000000000000000 E-39*i)*q^4 + (1.0000000000000000000000000000000000000 - 8.8162076286971569060000000000000000000 E-39*i)*q^5 + (1.0000000000000000000000000000000000000 - 8.8162076286971569060000000000000000000 E-39*i)*q^6 + (3.9999999999999999999999999999999999999 + 0.E-39*i)*q^7 + (1.00000000000000000000000000000000000000000000000000000000 + 0.E-48*i)*q^8 + (1.00000000000000000000000000000000000000470197740 + 0.E-39*i)*q^9 + O(q^10) > f; q - q^4 + q^5 + q^6 + 4*q^7 + O(q^8) > PowerSeries(f)-(w[1]*E[1]+w[2]*E[2]+w[3]*E[3]+w[4]*E[4]); (2.9387358762323856350000000000000000000 E-39 + 0.E-40*i)*q + ( 0.E-39 - 8.8162076286971569060000000000000000000 E-39*i)*q^2 + ( 0.E-38 - 1.4693679381161928170000000000000000000 E-39*i)*q^4 + (5.8774717595852596658395627920000000000 E-40 + 8.8162076286971569060000000000000000000 E-39*i)*q^5 + (5.8774717595852596658395627920000000000 E-40 + 8.8162076286971569060000000000000000000 E-39*i)*q^6 + (1.1754943504929542540000000000000000000 E-38 + 0.E-39*i)*q^7 + O(q^8) > w; [ 0.39999999999999999999999999999999999999 - 0.049999999999999999999999999999999999999*i, 0.40000000000000000000000000000000000000 + 0.049999999999999999999999999999999999999*i, 0, 0.200000000000000000000000000000000000000000000000000000000 + 0.E-49*i ] > G := DirichletGroup(420); eps := c;M := ModularForms(eps,2); S := CuspidalSubspace(M); > time w, E := EigenDecomp(S,S.5,88); WARNING: Precision is probably too low. 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3.9999999999999999999999999999999999999*i, 0, -5.8774717524647712700000000000000000000 E-39 - 5.9999999999999999999999999999999999999*i ] Magma: Internal error Please mail this entire run [**WITH THE FOLLOWING LINES**] to magma-bugs@maths.usyd.edu.au Version date: Tue Mar 12 19:47:33 EST 2002 Initial seed: 2028106084 Time to this point: 39.35 division by zero in gdiv > load "bugreport"; Loading "bugreport" In file "bugreport", line 2, column 122: >> 0000000000*i, -1.0000000000000000000000000000000000000*i, -1 + 0.E-38*i, - ^ User error: Real literal has no digits after decimal point > load "bugreport"; Loading "bugreport" In file "bugreport", line 2, column 25927: >> 80000000000000000000 E-38*i, 2.9387358762323856350000000000000000000 E-39 - ^ User error: bad syntax > load "bugreport"; Loading "bugreport" In file "bugreport", line 2, column 28017: >> 56350000000000000000000 *10^(-39) - 1.0000000000000000000000000000000000000 ^ User error: Real literal has no digits after decimal point > time w, E := EigenDecomp(S,S.5,88); WARNING: Precision is probably too low. Time: 23.410 > EchelonForm(w); Magma: Internal error Please mail this entire run [**WITH THE FOLLOWING LINES**] to magma-bugs@maths.usyd.edu.au Version date: Tue Mar 12 19:47:33 EST 2002 Initial seed: 2028106084 Time to this point: 63.94 division by zero in gdiv > InputForm(w); >> InputForm(w); ^ User error: Identifier 'InputForm' has not been declared or assigned > print 1 : Magma; 1 > print 10^(-20)*1.0 : Magma; 9.999999999999999999999999999E-21 > 9.999999999999999999999999999E-21+1; 1.00000000000000000000999999999999999999999999999903330235 > print w : Magma; KMatrixSpace(ComplexField(), 84, 88) ! 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3.9999999999999999999999999999999999999*i, 0, -3.9183145016431808470000000000000000000 E-39 - 5.9999999999999999999999999999999999999*i ] > load "bugreport"; Loading "bugreport" > load "bugreport"; Loading "bugreport" Magma: Internal error Please mail this entire run [**WITH THE FOLLOWING LINES**] to magma-bugs@maths.usyd.edu.au Version date: Tue Mar 12 19:47:33 EST 2002 Initial seed: 2028106084 Time to this point: 65.76 division by zero in gdiv > time w, E := EigenDecomp(M,M.5,1000); [Interrupt twice in half a second; exiting] Total time: 169.269 seconds [was@modular manjul]$ me Magma V2.8-10 Sat Mar 30 2002 17:34:34 on modular [Seed = 3612202749] Type ? for help. Type -D to quit. Loading startup file "/home/was/magma/local/emacs.m" Loading "/home/was/magma/local/init.m" > G := DirichletGroup(420); eps := c;M := ModularForms(eps,2); S := CuspidalSubspace(M); > time w, E := EigenDecomp(M,M.5,110); >> time w, E := EigenDecomp(M,M.5,110); ^ User error: Identifier 'EigenDecomp' has not been declared or assigned > Attach("eigenrep.m"); > > time w, E := EigenDecomp(M,M.5,110); WARNING: Precision is probably too low. 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Magma: Internal error Please mail this entire run [**WITH THE FOLLOWING LINES**] to magma-bugs@maths.usyd.edu.au Version date: Tue Mar 12 19:47:33 EST 2002 Initial seed: 3612202749 Time to this point: 103.81 division by zero in gdiv >