unknown terminal "dumb" [was@form was]$ [was@form was]$ Magma V2.7-1 Tue Jan 23 2001 00:27:57 on form [Seed = 1731300692] Type ? for help. Type -D to quit. Loading startup file "/home/was/modsym/init-magma.m" C IndexGamma0 R ellap idxG0 CS MS S factormod modcharpoly DC ND Tn factorpadic padiccharpoly ES NS Z fcp qexp F Q charpoly fn x > M:=MS(37); > VectorSpace(M); Full Vector space of degree 5 over Rational Field Mapping from: Full Vector space of degree 5 over Rational Field to ModSym: M given by a rule [no inverse] Mapping from: ModSym: M to Full Vector space of degree 5 over Rational Field given by a rule [no inverse] > V, f:= VectorSpace(M); > f(V.1); {-1/29, 0} > V, f, g:= VectorSpace(M); > g(M.1); (1 0 0 0 0) > DualVectorSpace(M); Full Vector space of degree 5 over Rational Field > D:=Decomposition(M,23 : Proof:=false); > D; [ Modular symbols space of level 37, weight 2, and dimension 1, Modular symbols space of level 37, weight 2, and dimension 2, Modular symbols space of level 37, weight 2, and dimension 2 ] > VectorSpace(D[1]); Vector space of degree 5, dimension 1 over Rational Field User basis: (0 0 0 1 3) Mapping from: Vector space of degree 5, dimension 1 over Rational Field to Modular symbols space of level 37, weight 2, and dimension 1 given by a rule [no inverse] Mapping from: Modular symbols space of level 37, weight 2, and dimension 1 to Vector space of degree 5, dimension 1 over Rational Field given by a rule [no inverse] > DualVectorSpace(D[1]); Vector space of degree 5, dimension 1 over Rational Field User basis: (0 0 0 0 1) > f(V.5); {oo, 0} > Vd:=DualVectorSpace(D[1]); > V:=VectorSpace(D[1]); > InnerProduct(Vd.1,V.1); 3 > Vd.1; (0 0 0 0 1) > V.1; (0 0 0 1 3) > IntegralRepresentation(D[1]); Lattice of rank 1 and degree 5 Basis: (0 0 0 1 3) >Lattice(D[1]); Lattice(D[1]); Lattice of rank 1 and degree 5 Basis: (0 0 0 1 3) Mapping from: Lattice of rank 1 and degree 5 to Modular symbols space of level 37, weight 2, and dimension 1 given by a rule [no inverse] > DualLattice(D[1]); Lattice of rank 1 and degree 5 Basis: (0 0 0 0 1) Mapping from: Lattice of rank 1 and degree 5 to Modular symbols space of level 37, weight 2, and dimension 1 given by a rule [no inverse] > > > > > > ///////////////////// coset reps. > The SECRET MAGIC FUNCTIONS are P1Classes and P1Reduce. > See modsym/core.m for example real-world usage. > P1Reduce; Intrinsic 'P1Reduce' Signatures: ( v, L) -> RngIntElt, RngIntResElt The index in L of the normalization of v, and the appropriate scalar > P1Classes; Intrinsic 'P1Classes' Signatures: ( N) -> SetIndx An indexed set of distinct normalized representatives for the set of equivalence classes of P^1(Z/NZ) > p1:=P1Classes(40); {@ (0 1), (1 1), (2 1), ( 1 27), (4 1), (5 1), (2 7), ( 1 23), (8 1), (1 9), (10 1), ( 1 11), (4 7), ( 1 37), (2 3), (5 3), (8 3), ( 1 33), (2 9), ( 1 19), (20 1), ( 1 21), ( 2 11), (1 7), (8 7), ( 5 13), ( 2 17), (1 3), (4 3), ( 1 29), (10 3), ( 1 31), (8 9), ( 1 17), ( 2 13), (5 7), (4 9), ( 1 13), ( 2 19), ( 1 39), (1 0), (1 2), (1 4), (1 5), (1 6), (1 8), ( 1 10), ( 1 12), ( 1 14), ( 1 15), ( 1 16), ( 1 18), ( 1 20), ( 1 22), ( 1 24), ( 1 25), ( 1 26), ( 1 28), ( 1 30), ( 1 32), ( 1 34), ( 1 35), ( 1 36), ( 1 38), (2 5), ( 2 15), (4 5), (5 2), (5 4), (5 6), (5 8), (8 5) @} > p1:=P1Classes(40); > P1Reduce; Intrinsic 'P1Reduce' Signatures: ( v, L) -> RngIntElt, RngIntResElt The index in L of the normalization of v, and the appropriate scalar > P1Reduce([1,2],p1); >> P1Reduce([1,2],p1); ^ Runtime error in 'P1Reduce': Bad argument types Argument types given: SeqEnum[RngIntElt], SetIndx[ModTupRngElt] > P1Reduce(Parent(p1[1])![1,2],p1); 42 1 > P1Reduce(Parent(p1[1])![37,56],p1); 46 37 > p1[46]; (1 8) > Parent(p1[1])![37,56] > ; (37 16) > Parent(p1[1])![37,56]*37 > ; ( 9 32) > p1[46]*37; (37 16) > > > > > M; Full Modular symbols space of level 37, weight 2, and dimension 5 > Basis(M); [ {-1/29, 0}, {-1/22, 0}, {-1/12, 0}, {-1/18, 0}, {oo, 0} ] > x:=M.2; > x; {-1/22, 0} > ManinSymbol(x); [ <1, ( 1 22)> ] > y:=M!<1,[Cusps()!Infinity(), 1/13]>; >> y:=M!<1,[Cusps()!Infinity(), 1/13]>; ^ Runtime error in [ ... ]: Could not find a valid universe > y:=M!<1,[Cusps()| Infinity(), 1/13]>; > y; {-1/12, 0} + {oo, 0} > y; {-1/12, 0} + {oo, 0} > ManinSymbol(y); [ <1, ( 1 12)>, <1, (1 0)> ] > M:=ModularSymbols(99); > M; Full Modular symbols space of level 99, weight 2, and dimension 25 > time N:=NewformDecomposition(CuspidalSubspace(M) : Proof := false); Time: 2.500 > N; p[ Modular symbols space of level 99, weight 2, and dimension 2, Modular symbols space of level 99, weight 2, and dimension 2, Modular symbols space of level 99, weight 2, and dimension 2, Modular symbols space of level 99, weight 2, and dimension 2, Modular symbols space of level 99, weight 2, and dimension 4, Modular symbols space of level 99, weight 2, and dimension 6 ] > AssociatedNewSpace(N[1]); Modular symbols space of level 99, weight 2, and dimension 2 > AssociatedNewSpace(N[5]); Modular symbols space of level 33, weight 2, and dimension 2 > qEigenform(N[1],11); q + 2*q^2 + 2*q^4 - q^5 - 2*q^7 - 2*q^10 + O(q^11) > M:=ModularSymbols(99,2,+1); > time N:=NewformDecomposition(CuspidalSubspace(M) : Proof := false); Time: 1.709 > N:=SortDecomposition(N); >> N:=SortDecomposition(N); ^ Runtime error in 'SortDecomposition': Each element of argument 1 must be new. > time N:=NewformDecomposition(NS(CuspidalSubspace(M)) : Proof := false); Time: 0.130 > N; [ Modular symbols space of level 99, weight 2, and dimension 1, Modular symbols space of level 99, weight 2, and dimension 1, Modular symbols space of level 99, weight 2, and dimension 1, Modular symbols space of level 99, weight 2, and dimension 1 ] > M:=ModularSymbols( 123,2,+1); > time N:=NewformDecomposition(CuspidalSubspace(M) : Proof := false); Time: 1.459 > N; [ Modular symbols space of level 123, weight 2, and dimension 1, Modular symbols space of level 123, weight 2, and dimension 1, Modular symbols space of level 123, weight 2, and dimension 2, Modular symbols space of level 123, weight 2, and dimension 3, Modular symbols space of level 123, weight 2, and dimension 6 ] > A:=N[4]; > qEigenform(A,11); q + a*q^2 - q^3 + (a^2 - 2)*q^4 + (-a^2 + a + 4)*q^5 - a*q^6 + (-a^2 - a + 4)*q^7 + (a^2 - 2)*q^8 + q^9 + 2*q^10 + O(q^11) > Parent($1); Power series ring in q over Univariate Quotient Polynomial Algebra in a over Rational Field with modulus a^3 - a^2 - 4*a + 2 > QpNewforms(A,2,11); [ q - (501637 + O(2^20))*q^2 - q^3 + (314135 + O(2^20))*q^4 + (116403*2 + O(2^20))*q^5 + (501637 + O(2^20))*q^6 + (11719*2^4 + O(2^20))*q^7 + (314135 + O(2^20))*q^8 + q^9 + 2*q^10 + O(q^11) ] > QpBarNewforms(A,2,11); [* q - (501637 + O(2^20))*q^2 - q^3 + (314135 + O(2^20))*q^4 + (116403*2 + O(2^20))*q^5 + (501637 + O(2^20))*q^6 + (11719*2^4 + O(2^20))*q^7 + (314135 + O(2^20))*q^8 + q^9 + 2*q^10 + O(q^11), q + a1*q^2 - q^3 + ((250819*2 + O(2^20))*a1 + (58201*2^2 + O(2^20)))*q^4 + (-(501637 + O(2^20))*a1 - 116401*2 + O(2^20))*q^5 - a1*q^6 + (-(501639 + O(2^20))*a1 - 116401*2 + O(2^20))*q^7 + ((250819*2 + O(2^20))*a1 + (58201*2^2 + O(2^20)))*q^8 + q^9 + 2*q^10 + O(q^11) *] > QpNewforms(NS(CS(M)),5,11); [ q - q^3 - 2*q^4 - 2*q^5 - 4*q^7 + q^9 + O(q^11), q - 2*q^2 + q^3 + 2*q^4 - 4*q^5 - 2*q^6 - 2*q^7 + q^9 + 8*q^10 + O(q^11) ] > QpBarNewforms(NS(CS(M)),5,11); [* q - q^3 - 2*q^4 - 2*q^5 - 4*q^7 + q^9 + O(q^11), q - 2*q^2 + q^3 + 2*q^4 - 4*q^5 - 2*q^6 - 2*q^7 + q^9 + 8*q^10 + O(q^11), q + a1*q^2 + q^3 + (-a1 + 2)*q^5 + a1*q^6 + (a1 - 2)*q^7 - 2*a1*q^8 + q^9 + (2*a1 - 2)*q^10 + O(q^11), q + a2*q^2 - q^3 + (a2^2 - 2)*q^4 + (-a2^2 + a2 + 4)*q^5 - a2*q^6 + (-a2^2 - a2 + 4)*q^7 + (a2^2 - 2)*q^8 + q^9 + 2*q^10 + O(q^11) *] > Parent($1[4]); Power series ring in q over Univariate Quotient Polynomial Algebra in a2 over 5-adic Field with modulus a2^3 - a2^2 - 4*a2 + 2 > QpNewforms(NS(CS(M)),3,11); [ q - q^3 - 2*q^4 - 2*q^5 - 4*q^7 + q^9 + O(q^11), q - 2*q^2 + q^3 + 2*q^4 - 4*q^5 - 2*q^6 - 2*q^7 + q^9 + 8*q^10 + O(q^11) ] > QpNewforms(NS(CS(M)),7,11); [ q - q^3 - 2*q^4 - 2*q^5 - 4*q^7 + q^9 + O(q^11), q - 2*q^2 + q^3 + 2*q^4 - 4*q^5 - 2*q^6 - 2*q^7 + q^9 + 8*q^10 + O(q^11), q + (4609765579368303 + O(7^20))*q^2 + q^3 - (4609765579368301 + O(7^20))*q^5 + (4609765579368303 + O(7^20))*q^6 + (4609765579368301 + O(7^20))*q^7 - (9219531158736606 + O(7^20))*q^8 + q^9 + (9219531158736604 + O(7^20))*q^10 + O(q^11), q - (4609765579368303 + O(7^20))*q^2 + q^3 + (4609765579368305 + O(7^20))*q^5 - (4609765579368303 + O(7^20))*q^6 - (4609765579368305 + O(7^20))*q^7 + (9219531158736606 + O(7^20))*q^8 + q^9 - (9219531158736608 + O(7^20))*q^10 + O(q^11) ] > QpNewforms(NS(CS(M)),11,11); [ q - q^3 - 2*q^4 - 2*q^5 - 4*q^7 + q^9 + O(q^11), q - 2*q^2 + q^3 + 2*q^4 - 4*q^5 - 2*q^6 - 2*q^7 + q^9 + 8*q^10 + O(q^11), q - (153576613270149266926 + O(11^20))*q^2 - q^3 - (41524740197543309216 + O(11^20))*q^4 - (112051873072605957708 + O(11^20))*q^5 + (153576613270149266926 + O(11^20))*q^6 + (195101353467692576144 + O(11^20))*q^7 - (41524740197543309216 + O(11^20))*q^8 + q^9 + 2*q^10 + O(q^11) ] > QpNewforms(NS(CS(M)),13,11); [ q - q^3 - 2*q^4 - 2*q^5 - 4*q^7 + q^9 + O(q^11), q - 2*q^2 + q^3 + 2*q^4 - 4*q^5 - 2*q^6 - 2*q^7 + q^9 + 8*q^10 + O(q^11) ] > QpNewforms(NS(CS(M)),2,11); [ q - q^3 - 2*q^4 - 2*q^5 - 4*q^7 + q^9 + O(q^11), q - 2*q^2 + q^3 + 2*q^4 - 4*q^5 - 2*q^6 - 2*q^7 + q^9 + 8*q^10 + O(q^11), q + (621139010588222429002458 + O(17^20))*q^2 + q^3 - (621139010588222429002456 + O(17^20))*q^5 + (621139010588222429002458 + O(17^20))*q^6 + (621139010588222429002456 + O(17^20))*q^7 - (1242278021176444858004916 + O(17^20))*q^8 + q^9 + (1242278021176444858004914 + O(17^20))*q^10 + O(q^11), q - (621139010588222429002458 + O(17^20))*q^2 + q^3 + (621139010588222429002460 + O(17^20))*q^5 - (621139010588222429002458 + O(17^20))*q^6 - (621139010588222429002460 + O(17^20))*q^7 + (1242278021176444858004916 + O(17^20))*q^8 + q^9 - (1242278021176444858004918 + O(17^20))*q^10 + O(q^11), q + (1401064556980839276469010 + O(17^20))*q^2 - q^3 + (1440047152771975741417324 + O(17^20))*q^4 - (38982595791136464948312 + O(17^20))*q^5 - (1401064556980839276469010 + O(17^20))*q^6 + (1223119696894757504515269 + O(17^20))*q^7 + (1440047152771975741417324 + O(17^20))*q^8 + q^9 + 2*q^10 + O(q^11) ] > M:=MS(1,50,+1); > QpNewforms(NS(CS(M)),2,11); [ q + (57*2^13 + O(2^20))*q^2 - (55375*2^2 + O(2^19))*q^3 + (49*2^26 + O(2^33))*q^4 - (521437*2 + O(2^21))*q^5 - (23*2^15 + O(2^22))*q^6 - (57391*2^3 + O(2^20))*q^7 + O(2^33)*q^8 - (1973043 + O(2^22))*q^9 - (53*2^14 + O(2^21))*q^10 + O(q^11), q + (1053*2^8 + O(2^20))*q^2 + (59089*2^2 + O(2^19))*q^3 - (1207*2^16 + O(2^28))*q^4 - (169437*2 + O(2^21))*q^5 - (1619*2^10 + O(2^22))*q^6 - (35855*2^3 + O(2^20))*q^7 + (69*2^24 + O(2^32))*q^8 + (968909 + O(2^22))*q^9 + (503*2^9 + O(2^21))*q^10 + O(q^11), q + (12759*2^4 + O(2^20))*q^2 + (50609*2^2 + O(2^19))*q^3 + (657*2^8 + O(2^24))*q^4 - (484573*2 + O(2^21))*q^5 - (5977*2^6 + O(2^22))*q^6 + (60881*2^3 + O(2^20))*q^7 - (5945*2^12 + O(2^28))*q^8 - (1465139 + O(2^22))*q^9 - (667*2^5 + O(2^21))*q^10 + O(q^11) ] > QpBarNewforms(NS(CS(M)),2,11); [* q + (57*2^13 + O(2^20))*q^2 - (55375*2^2 + O(2^19))*q^3 + (49*2^26 + O(2^33))*q^4 - (521437*2 + O(2^21))*q^5 - (23*2^15 + O(2^22))*q^6 - (57391*2^3 + O(2^20))*q^7 + O(2^33)*q^8 - (1973043 + O(2^22))*q^9 - (53*2^14 + O(2^21))*q^10 + O(q^11), q + (1053*2^8 + O(2^20))*q^2 + (59089*2^2 + O(2^19))*q^3 - (1207*2^16 + O(2^28))*q^4 - (169437*2 + O(2^21))*q^5 - (1619*2^10 + O(2^22))*q^6 - (35855*2^3 + O(2^20))*q^7 + (69*2^24 + O(2^32))*q^8 + (968909 + O(2^22))*q^9 + (503*2^9 + O(2^21))*q^10 + O(q^11), q + (12759*2^4 + O(2^20))*q^2 + (50609*2^2 + O(2^19))*q^3 + (657*2^8 + O(2^24))*q^4 - (484573*2 + O(2^21))*q^5 - (5977*2^6 + O(2^22))*q^6 + (60881*2^3 + O(2^20))*q^7 - (5945*2^12 + O(2^28))*q^8 - (1465139 + O(2^22))*q^9 - (667*2^5 + O(2^21))*q^10 + O(q^11) *] > > > > > > > M:=MS(40); > StarInvolution(M); [ 1 0 0 0 0 0 0 0 0 0 0 0 0] [ 0 0 0 0 1 0 0 0 0 0 0 0 0] [ 0 0 0 0 1 0 0 -1 1 0 0 -1 -1] [ 0 0 0 1 0 0 0 0 0 0 0 0 0] [ 0 1 0 0 0 0 0 0 0 0 0 0 0] [ 0 1 0 0 -1 1 0 0 0 0 0 0 0] [ 0 1 0 0 -1 0 1 0 0 0 0 0 0] [ 0 1 -1 0 0 0 0 0 1 -1 0 0 -1] [ 0 0 0 0 0 0 0 0 1 0 0 0 0] [ 0 0 0 0 0 0 0 0 0 0 0 1 0] [ 0 0 0 0 0 0 0 0 0 0 1 0 0] [ 0 0 0 0 0 0 0 0 0 1 0 0 0] [ 0 0 0 0 0 0 0 0 0 0 0 0 1] > M:=MS(123); > time N:=NewformDecomposition(CuspidalSubspace(M) : Proof := false); Time: 2.129 > N; [ Modular symbols space of level 123, weight 2, and dimension 2, Modular symbols space of level 123, weight 2, and dimension 2, Modular symbols space of level 123, weight 2, and dimension 4, Modular symbols space of level 123, weight 2, and dimension 6, Modular symbols space of level 123, weight 2, and dimension 12 ] > A:=N[3]; > StarInvolution(A); [ 0 0 -1 1] [ 0 -1 0 1] [-1 0 0 1] [ 0 0 0 1] > S:=$1; > Kernel(S-1); Vector space of degree 4, dimension 2 over Rational Field Echelonized basis: ( 1 0 -1 0) ( 0 0 0 1) > A.1 + A.3; {-1/33, 0} + -1*{-1/42, 0} + {-1/45, 0} + {-1/60, 0} + -1*{-1/72, 0} + {-1/84, 0} + -1*{-1/87, 0} + {-1/90, 0} + -1*{-1/93, 0} + -1*{-1/114, 0} > Basis(A); [ {-1/33, 0} + -1*{-1/42, 0} + {-1/45, 0} + -1*{-1/72, 0} + {-1/78, 0} + -1*{-1/87, 0} + {-1/90, 0} + -1*{-1/114, 0}, {-1/51, 0} + -1*{-1/54, 0} + {-1/57, 0} + -1*{-1/78, 0} + {-1/84, 0} + -1*{-1/90, 0} + {-1/99, 0} + -1*{-1/102, 0} + {-1/105, 0} + -1*{-1/111, 0} + {-1/114, 0} + -1*{-1/120, 0}, {-1/60, 0} + -1*{-1/78, 0} + {-1/84, 0} + -1*{-1/93, 0}, {-1/66, 0} + -1*{-1/69, 0} + {-1/72, 0} + -1*{-1/82, 0} + {-1/84, 0} + -1*{-1/96, 0} + {-1/99, 0} + -1*{-1/120, 0} + -1*{1/3, 14/41} ] > A.4; {-1/66, 0} + -1*{-1/69, 0} + {-1/72, 0} + -1*{-1/82, 0} + {-1/84, 0} + -1*{-1/96, 0} + {-1/99, 0} + -1*{-1/120, 0} + -1*{1/3, 14/41} > A.4*S; >> A.4*S; ^ Runtime error in '*': Arguments have incompatible dimensions. > A.4*StarInvolution(M); {-1/66, 0} + -1*{-1/69, 0} + {-1/72, 0} + -1*{-1/82, 0} + {-1/84, 0} + -1*{-1/96, 0} + {-1/99, 0} + -1*{-1/120, 0} + -1*{1/3, 14/41} > // A.4 is in M! > A![ 1,0,-1, 0]; >> A![ 1,0,-1, 0]; ^ Runtime error in '!': Argument 2 is not coercible into the vector space of argument 1. > M; Full Modular symbols space of level 123, weight 2, and dimension 29 > S:=CS(M); > S; Modular symbols space of level 123, weight 2, and dimension 26 > Basis(S); [ {-1/21, 0} + -1*{-1/120, 0}, {-1/33, 0} + -1*{-1/120, 0}, {-1/42, 0} + -1*{-1/120, 0}, {-1/45, 0} + -1*{-1/120, 0}, {-1/48, 0} + -1*{-1/120, 0}, {-1/51, 0} + -1*{-1/120, 0}, {-1/54, 0} + -1*{-1/120, 0}, {-1/57, 0} + -1*{-1/120, 0}, {-1/60, 0} + -1*{-1/120, 0}, {-1/66, 0} + -1*{-1/120, 0}, {-1/69, 0} + -1*{-1/120, 0}, {-1/72, 0} + -1*{-1/120, 0}, {-1/78, 0} + -1*{-1/120, 0}, {-1/82, 0} + -1*{-1/120, 0} + {1/3, 14/41}, {-1/84, 0} + -1*{-1/120, 0}, {-1/87, 0} + -1*{-1/120, 0}, {-1/90, 0} + -1*{-1/120, 0}, {-1/93, 0} + -1*{-1/120, 0}, {-1/96, 0} + -1*{-1/120, 0}, {-1/99, 0} + -1*{-1/120, 0}, {-1/102, 0} + -1*{-1/120, 0}, {-1/105, 0} + -1*{-1/120, 0}, {-1/108, 0} + -1*{-1/120, 0}, {-1/111, 0} + -1*{-1/120, 0}, {-1/114, 0} + -1*{-1/120, 0}, {-1/117, 0} + -1*{-1/120, 0} ] > IntersectionPairing(S.1,S.2); 0 > IntersectionPairing(S.1,S.3); >> IntersectionPairing(S.1,S.3); ^ User error: bad syntax > > IntersectionPairing(S.1,S.3); 1 > IntersectionPairing(S.3,S.1); -1 > quit; Total time: 14.450 seconds [was@form was]$ exit exit Process magma finished