[was@modular was]$ [was@modular was]$ Magma V2.8-4      Sun Feb 24 2002 01:45:06 on modular  [Seed = 2716145245]
Type ? for help.  Type <Ctrl>-D to quit.

Loading startup file "/home/was/magma/local/emacs.m"

Loading "/home/was/magma/local/init.m"
> M := MS("11A");
> f := qEigenform(M,80);
> [p : p in [1..39] |IsPrime(p) and (Coefficient(f,p)^2-(p+1)^2) mod 6 eq 0];

>> [p : p in [1..39] |IsPrime(p) and (Coefficient(f,p)^2-(p+1)^2) mod 6 eq 0];
                                                                  ^
Runtime error in 'mod': Bad argument types
Argument types given: FldRatElt, FldRatElt
> [p : p in [1..39] |IsPrime(p) and (Integers()!Coefficient(f,p)^2-(p+1)^2) mod 6 eq 0];
[ 7, 13, 29 ]
> A := MS(77);
> iA := A!!M;
> IntersectionGroup(iA,NS(CS(A));

>> IntersectionGroup(iA,NS(CS(A));
                                 ^
User error: bad syntax
> IntersectionGroup(iA,NS(CS(A)));
Abelian Group isomorphic to Z/2 + Z/2 + Z/6 + Z/6
Defined on 4 generators
Relations:
2*$.1 = 0
2*$.2 = 0
6*$.3 = 0
6*$.4 = 0
> [p : p in [1..39] |IsPrime(p) and (Integers()!Coefficient(f,p)^2-(p+1)^2) mod 9 eq 0];
[ 13, 29 ]
> M13 := MS(11*13);
> iM := M13!!M;
> iM;
Modular symbols space of level 143, weight 2, and dimension 4
> IntersectionGroup(iM,NS(CS(M13)));
Abelian Group isomorphic to Z/2 + Z/2 + Z/18 + Z/18
Defined on 4 generators
Relations:
2*$.1 = 0
2*$.2 = 0
18*$.3 = 0
18*$.4 = 0
> D := DC(NS(CS(M13)));

>> D := DC(NS(CS(M13)));
          ^
Runtime error in 'Decomposition': Bad argument types
Argument types given: ModSym
> D := DC(NS(CS(M13)),10);
> D;
[
Modular symbols space of level 143, weight 2, and dimension 2,
Modular symbols space of level 143, weight 2, and dimension 8,
Modular symbols space of level 143, weight 2, and dimension 12
]
> IntersectionGroup(iM,D[1]);
Abelian Group isomorphic to Z/2 + Z/2
Defined on 2 generators
Relations:
2*$.1 = 0
2*$.2 = 0
> IntersectionGroup(iM,D[2]);
Abelian Group isomorphic to Z/9 + Z/9
Defined on 2 generators
Relations:
9*$.1 = 0
9*$.2 = 0
> IntersectionGroup(iM,D[3]);
Abelian Group isomorphic to Z/2 + Z/2
Defined on 2 generators
Relations:
2*$.1 = 0
2*$.2 = 0
> LRatio(D[2],1);
1/7
> Coefficient(f,13)-(13+1);
-10
> Coefficient(f,13)+(13+1);
18
> [p : p in [1..39] |IsPrime(p) and (Integers()!Coefficient(f,p)^2-(p+1)^2) mod 13 eq 0];
[ 11, 31 ]
> M11 := MS(11*11);
> iM := M13!!M;
> iM := M11!!M;
> IntersectionGroup(iM,NS(CS(M11)));
Abelian Group isomorphic to Z/24 + Z/24
Defined on 2 generators
Relations:
24*$.1 = 0
24*$.2 = 0
> M11 := MS(11*31,2,+1);
> M31 := MS(11*31,2,+1);
> M := MS("11A",2,+1);

>> M := MS("11A",2,+1);
          ^
Runtime error in 'ModularSymbols': Bad argument types
Argument types given: MonStgElt, RngIntElt, RngIntElt
>  M := MS("11A",+1);
> iM := M31!!M;
> IntersectionGroup(iM,NS(CS(M31)));
Abelian Group isomorphic to Z/195
Defined on 1 generator
Relations:
195*$.1 = 0
> factor(195);
[ <3, 1>, <5, 1>, <13, 1> ]
1
> [p : p in [1..39] |IsPrime(p) and (Integers()!Coefficient(f,p)+(p+1) mod 13 eq 0];

>> nt(f,p)+(p+1) mod 13 eq 0];
                            ^
User error: bad syntax
> [p : p in [1..39] |IsPrime(p) and (Integers()!Coefficient(f,p)+(p+1)) mod 13 eq 0];
[ 11, 31 ]
>  D := DC(NS(CS(M31)),10);
> D;
[
Modular symbols space of level 341, weight 2, and dimension 2,
Modular symbols space of level 341, weight 2, and dimension 4,
Modular symbols space of level 341, weight 2, and dimension 8,
Modular symbols space of level 341, weight 2, and dimension 11
]
> for A in D do IntersectionGroup(A,iM); end for;
Abelian Group isomorphic to Z/5
Defined on 1 generator
Relations:
5*$.1 = 0
Abelian Group of order 1
Abelian Group of order 1
Abelian Group isomorphic to Z/39
Defined on 1 generator
Relations:
39*$.1 = 0
> LRatio(D[4],1);
1024
> LRatio(D[1],1);
0
> [p : p in [1..39] |IsPrime(p) and (Integers()!Coefficient(f,p)+(p+1)) mod 17 eq 0];
[]
> f := qEigenform(M,80);
> [p : p in [1..79] |IsPrime(p) and (Integers()!Coefficient(f,p)+(p+1)) mod 17 eq 0];
[ 41 ]
> 11*41;
451
> M41 := MS(11*41,2,+1);
> iM := M41!!M;
> IntersectionGroup(iM,NS(CS(M41)));
Abelian Group isomorphic to Z/2 + Z/170
Defined on 2 generators
Relations:
2*$.1 = 0
170*$.2 = 0
> D := DC(NS(CS(M31)),10);
> D;
[
Modular symbols space of level 341, weight 2, and dimension 2,
Modular symbols space of level 341, weight 2, and dimension 4,
Modular symbols space of level 341, weight 2, and dimension 8,
Modular symbols space of level 341, weight 2, and dimension 11
]
> 
D := DC(NS(CS(M41)),10);
> > for A in D do IntersectionGroup(A,iM); end for;
Abelian Group isomorphic to Z/2
Defined on 1 generator
Relations:
2*$.1 = 0
Abelian Group of order 1
Abelian Group isomorphic to Z/5
Defined on 1 generator
Relations:
5*$.1 = 0
Abelian Group isomorphic to Z/17
Defined on 1 generator
Relations:
17*$.1 = 0
Abelian Group isomorphic to Z/2
Defined on 1 generator
Relations:
2*$.1 = 0
> LRatio(D[3],1);
0
> D;
[
Modular symbols space of level 451, weight 2, and dimension 1,
Modular symbols space of level 451, weight 2, and dimension 5,
Modular symbols space of level 451, weight 2, and dimension 5,
Modular symbols space of level 451, weight 2, and dimension 10,
Modular symbols space of level 451, weight 2, and dimension 12
]
> LRatio(D[4],1);
32768/7
> factor($1);
[ <2, 15>, <7, -1> ]
> factor(451);
[ <11, 1>, <41, 1> ]
1
> M11_4 := MS(11,4,+1);
> M11_4 := ModularForms(11,4);
> Newforms(CS(M11_4));
[* [*
q + a*q^2 + (-4*a + 3)*q^3 + (2*a - 6)*q^4 + (8*a - 7)*q^5 + (-5*a - 8)*q^6 + (-4*a + 14)*q^7 + O(q^8),
q + b*q^2 + (-4*b + 3)*q^3 + (2*b - 6)*q^4 + (8*b - 7)*q^5 + (-5*b - 8)*q^6 + (-4*b + 14)*q^7 + O(q^8)
*] *]
> f := $1[1][1]
> ;
> f;
q + a*q^2 + (-4*a + 3)*q^3 + (2*a - 6)*q^4 + (8*a - 7)*q^5 + (-5*a - 8)*q^6 + (-4*a + 14)*q^7 + O(q^8)
> Reductions(f,3);
[* [*
q + q^2 + 2*q^3 + 2*q^4 + q^5 + 2*q^6 + q^7 + O(q^8)
*] *]
> g := $1[1];
> g;
[*
q + q^2 + 2*q^3 + 2*q^4 + q^5 + 2*q^6 + q^7 + O(q^8)
*]
> g := $1[1];
> f := Newforms("11A")[1];
> f;
q - 2*q^2 - q^3 + 2*q^4 + q^5 + 2*q^6 - 2*q^7 + O(q^8)
> Reductions(f,3);
[* [*
q + q^2 + 2*q^3 + 2*q^4 + q^5 + 2*q^6 + q^7 + O(q^8)
*] *]
> g;
q + q^2 + 2*q^3 + 2*q^4 + q^5 + 2*q^6 + q^7 + O(q^8)
> MS11_4 := MS(11,4,+1);
> D11_4 := DC(CS(NS(MS11_4)));

>> D11_4 := DC(CS(NS(MS11_4)));
                    ^
Runtime error in 'NewSubspace': Argument 1 must be contained in the cuspidal subspace.
>  D11_4 := DC(NS(CS(MS11_4)));

>>  D11_4 := DC(NS(CS(MS11_4)));
               ^
Runtime error in 'Decomposition': Bad argument types
Argument types given: ModSym
>  D11_4 := ND(NS(CS(MS11_4)));
> D11_4;
[
Modular symbols space of level 11, weight 4, and dimension 2
]
> LRatio(D11_4,1);

>> LRatio(D11_4,1);
         ^
Runtime error in 'LRatio': Bad argument types
Argument types given: SeqEnum[ModSym], RngIntElt
> LRatio(D11_4[1],1);
968/61
> LRatio(D11_4[1],2);

>> LRatio(D11_4[1],2);
         ^
Runtime error in 'LRatio': The sign of argument 1 is +1, so it is only possible to compute L(A,j) for j odd.
> factor(968);
[ p<2, 3>, <11, 2> ]
1
> LRatio(MS("11A"),1);
1/5
> f;
q - 2*q^2 - q^3 + 2*q^4 + q^5 + 2*q^6 - 2*q^7 + O(q^8)
> [p : p in [1..79] |IsPrime(p) and (Integers()!Coefficient(f,p)+(p+1)) mod 3 eq 0];
[ 3, 7, 13, 29, 31, 53, 71, 73 ]
> M77_4 := ModularForms(11,4);
> N77_4 := Newforms(M77_4);
> N77_4;
[* [*
q + a*q^2 + (-4*a + 3)*q^3 + (2*a - 6)*q^4 + (8*a - 7)*q^5 + (-5*a - 8)*q^6 + (-4*a + 14)*q^7 + O(q^8),
q + b*q^2 + (-4*b + 3)*q^3 + (2*b - 6)*q^4 + (8*b - 7)*q^5 + (-5*b - 8)*q^6 + (-4*b + 14)*q^7 + O(q^8)
*] *]
> h := $1[1][1];
> h;
q + a*q^2 + (-4*a + 3)*q^3 + (2*a - 6)*q^4 + (8*a - 7)*q^5 + (-5*a - 8)*q^6 + (-4*a + 14)*q^7 + O(q^8)
> Reductions(h,3);
[* [*
q + q^2 + 2*q^3 + 2*q^4 + q^5 + 2*q^6 + q^7 + O(q^8)
*] *]
> h := $1[1][1];
> Level(h);
11
> Level(N77_4[1][1]);
11
> M77_4;
Space of modular forms on Gamma_0(11) of weight 4 and dimension 4 over Integer Ring.
> NS(M77_4);
Space of modular forms on Gamma_0(11) of weight 4 and dimension 2 over Integer Ring.
> Newforms(NS(M77_4));
[* [*
q + a*q^2 + (-4*a + 3)*q^3 + (2*a - 6)*q^4 + (8*a - 7)*q^5 + (-5*a - 8)*q^6 + (-4*a + 14)*q^7 + O(q^8),
q + b*q^2 + (-4*b + 3)*q^3 + (2*b - 6)*q^4 + (8*b - 7)*q^5 + (-5*b - 8)*q^6 + (-4*b + 14)*q^7 + O(q^8)
*] *]
> M77_4 := ModularForms(77,4);
> N77_4 := Newforms(M77_4);
> N77_4;
[* [*
q + 3*q^2 + 4*q^3 + q^4 + 12*q^5 + 12*q^6 + 7*q^7 + O(q^8)
*], [*
q + a*q^2 - 2*q^3 + (-2*a - 1)*q^4 + (-3*a - 5)*q^5 - 2*a*q^6 + 7*q^7 + O(q^8),
q + b*q^2 - 2*q^3 + (-2*b - 1)*q^4 + (-3*b - 5)*q^5 - 2*b*q^6 + 7*q^7 + O(q^8)
*], [*
q + a*q^2 + 1/4*(-a^3 + 21*a + 12)*q^3 + (a^2 - 8)*q^4 + 1/2*(-a^3 + a^2 + 20*a - 12)*q^5 + 1/2*(a^3 - 3*a^2 - 14*a + 56)*q^6 - 7*q^7 + O(q^8),
q + b*q^2 + 1/4*(-b^3 + 21*b + 12)*q^3 + (b^2 - 8)*q^4 + 1/2*(-b^3 + b^2 + 20*b - 12)*q^5 + 1/2*(b^3 - 3*b^2 - 14*b + 56)*q^6 - 7*q^7 + O(q^8),
q + c*q^2 + 1/4*(-c^3 + 21*c + 12)*q^3 + (c^2 - 8)*q^4 + 1/2*(-c^3 + c^2 + 20*c - 12)*q^5 + 1/2*(c^3 - 3*c^2 - 14*c + 56)*q^6 - 7*q^7 + O(q^8),
q + d*q^2 + 1/4*(-d^3 + 21*d + 12)*q^3 + (d^2 - 8)*q^4 + 1/2*(-d^3 + d^2 + 20*d - 12)*q^5 + 1/2*(d^3 - 3*d^2 - 14*d + 56)*q^6 - 7*q^7 + O(q^8)
*], [*
q + a*q^2 + 1/5*(a^3 - 2*a^2 - 22*a + 21)*q^3 + (a^2 - 8)*q^4 + 1/5*(-2*a^3 - a^2 + 24*a - 47)*q^5 + 1/5*(-6*a^3 - 3*a^2 + 77*a - 66)*q^6 - 7*q^7 + O(q^8),
q + b*q^2 + 1/5*(b^3 - 2*b^2 - 22*b + 21)*q^3 + (b^2 - 8)*q^4 + 1/5*(-2*b^3 - b^2 + 24*b - 47)*q^5 + 1/5*(-6*b^3 - 3*b^2 + 77*b - 66)*q^6 - 7*q^7 + O(q^8),
q + c*q^2 + 1/5*(c^3 - 2*c^2 - 22*c + 21)*q^3 + (c^2 - 8)*q^4 + 1/5*(-2*c^3 - c^2 + 24*c - 47)*q^5 + 1/5*(-6*c^3 - 3*c^2 + 77*c - 66)*q^6 - 7*q^7 + O(q^8),
q + d*q^2 + 1/5*(d^3 - 2*d^2 - 22*d + 21)*q^3 + (d^2 - 8)*q^4 + 1/5*(-2*d^3 - d^2 + 24*d - 47)*q^5 + 1/5*(-6*d^3 - 3*d^2 + 77*d - 66)*q^6 - 7*q^7 + O(q^8)
*], [*
q + a*q^2 + 1/8*(-a^4 + a^3 + 34*a^2 - 34*a - 152)*q^3 + (a^2 - 8)*q^4 + 1/2*(a^3 + a^2 - 26*a - 36)*q^5 + (-a^3 - 2*a^2 + 27*a + 44)*q^6 + 7*q^7 + O(q^8),
q + b*q^2 + 1/8*(-b^4 + b^3 + 34*b^2 - 34*b - 152)*q^3 + (b^2 - 8)*q^4 + 1/2*(b^3 + b^2 - 26*b - 36)*q^5 + (-b^3 - 2*b^2 + 27*b + 44)*q^6 + 7*q^7 + O(q^8),
q + c*q^2 + 1/8*(-c^4 + c^3 + 34*c^2 - 34*c - 152)*q^3 + (c^2 - 8)*q^4 + 1/2*(c^3 + c^2 - 26*c - 36)*q^5 + (-c^3 - 2*c^2 + 27*c + 44)*q^6 + 7*q^7 + O(q^8),
q + d*q^2 + 1/8*(-d^4 + d^3 + 34*d^2 - 34*d - 152)*q^3 + (d^2 - 8)*q^4 + 1/2*(d^3 + d^2 - 26*d - 36)*q^5 + (-d^3 - 2*d^2 + 27*d + 44)*q^6 + 7*q^7 + O(q^8),
q + e*q^2 + 1/8*(-e^4 + e^3 + 34*e^2 - 34*e - 152)*q^3 + (e^2 - 8)*q^4 + 1/2*(e^3 + e^2 - 26*e - 36)*q^5 + (-e^3 - 2*e^2 + 27*e + 44)*q^6 + 7*q^7 + O(q^8)
*] *]
> NS(M77_4);
Space of modular forms on Gamma_0(77) of weight 4 and dimension 16 over Integer Ring.
> N77_4 := Newforms(CS(NS(M77_4)));
> N77_4 := Newforms(M77_4);
> N77_4 := Newforms(CS(NS(M77_4)));
> N77_4;
[* [*
q + 3*q^2 + 4*q^3 + q^4 + 12*q^5 + 12*q^6 + 7*q^7 + O(q^8)
*], [*
q + a*q^2 - 2*q^3 + (-2*a - 1)*q^4 + (-3*a - 5)*q^5 - 2*a*q^6 + 7*q^7 + O(q^8),
q + b*q^2 - 2*q^3 + (-2*b - 1)*q^4 + (-3*b - 5)*q^5 - 2*b*q^6 + 7*q^7 + O(q^8)
*], [*
q + a*q^2 + 1/4*(-a^3 + 21*a + 12)*q^3 + (a^2 - 8)*q^4 + 1/2*(-a^3 + a^2 + 20*a - 12)*q^5 + 1/2*(a^3 - 3*a^2 - 14*a + 56)*q^6 - 7*q^7 + O(q^8),
q + b*q^2 + 1/4*(-b^3 + 21*b + 12)*q^3 + (b^2 - 8)*q^4 + 1/2*(-b^3 + b^2 + 20*b - 12)*q^5 + 1/2*(b^3 - 3*b^2 - 14*b + 56)*q^6 - 7*q^7 + O(q^8),
q + c*q^2 + 1/4*(-c^3 + 21*c + 12)*q^3 + (c^2 - 8)*q^4 + 1/2*(-c^3 + c^2 + 20*c - 12)*q^5 + 1/2*(c^3 - 3*c^2 - 14*c + 56)*q^6 - 7*q^7 + O(q^8),
q + d*q^2 + 1/4*(-d^3 + 21*d + 12)*q^3 + (d^2 - 8)*q^4 + 1/2*(-d^3 + d^2 + 20*d - 12)*q^5 + 1/2*(d^3 - 3*d^2 - 14*d + 56)*q^6 - 7*q^7 + O(q^8)
*], [*
q + a*q^2 + 1/5*(a^3 - 2*a^2 - 22*a + 21)*q^3 + (a^2 - 8)*q^4 + 1/5*(-2*a^3 - a^2 + 24*a - 47)*q^5 + 1/5*(-6*a^3 - 3*a^2 + 77*a - 66)*q^6 - 7*q^7 + O(q^8),
q + b*q^2 + 1/5*(b^3 - 2*b^2 - 22*b + 21)*q^3 + (b^2 - 8)*q^4 + 1/5*(-2*b^3 - b^2 + 24*b - 47)*q^5 + 1/5*(-6*b^3 - 3*b^2 + 77*b - 66)*q^6 - 7*q^7 + O(q^8),
q + c*q^2 + 1/5*(c^3 - 2*c^2 - 22*c + 21)*q^3 + (c^2 - 8)*q^4 + 1/5*(-2*c^3 - c^2 + 24*c - 47)*q^5 + 1/5*(-6*c^3 - 3*c^2 + 77*c - 66)*q^6 - 7*q^7 + O(q^8),
q + d*q^2 + 1/5*(d^3 - 2*d^2 - 22*d + 21)*q^3 + (d^2 - 8)*q^4 + 1/5*(-2*d^3 - d^2 + 24*d - 47)*q^5 + 1/5*(-6*d^3 - 3*d^2 + 77*d - 66)*q^6 - 7*q^7 + O(q^8)
*], [*
q + a*q^2 + 1/8*(-a^4 + a^3 + 34*a^2 - 34*a - 152)*q^3 + (a^2 - 8)*q^4 + 1/2*(a^3 + a^2 - 26*a - 36)*q^5 + (-a^3 - 2*a^2 + 27*a + 44)*q^6 + 7*q^7 + O(q^8),
q + b*q^2 + 1/8*(-b^4 + b^3 + 34*b^2 - 34*b - 152)*q^3 + (b^2 - 8)*q^4 + 1/2*(b^3 + b^2 - 26*b - 36)*q^5 + (-b^3 - 2*b^2 + 27*b + 44)*q^6 + 7*q^7 + O(q^8),
q + c*q^2 + 1/8*(-c^4 + c^3 + 34*c^2 - 34*c - 152)*q^3 + (c^2 - 8)*q^4 + 1/2*(c^3 + c^2 - 26*c - 36)*q^5 + (-c^3 - 2*c^2 + 27*c + 44)*q^6 + 7*q^7 + O(q^8),
q + d*q^2 + 1/8*(-d^4 + d^3 + 34*d^2 - 34*d - 152)*q^3 + (d^2 - 8)*q^4 + 1/2*(d^3 + d^2 - 26*d - 36)*q^5 + (-d^3 - 2*d^2 + 27*d + 44)*q^6 + 7*q^7 + O(q^8),
q + e*q^2 + 1/8*(-e^4 + e^3 + 34*e^2 - 34*e - 152)*q^3 + (e^2 - 8)*q^4 + 1/2*(e^3 + e^2 - 26*e - 36)*q^5 + (-e^3 - 2*e^2 + 27*e + 44)*q^6 + 7*q^7 + O(q^8)
*] *]
> g;
q + q^2 + 2*q^3 + 2*q^4 + q^5 + 2*q^6 + q^7 + O(q^8)
> Reductions(N77_4[1][1],3);
[* [*
q + q^3 + q^4 + q^7 + O(q^8)
*] *]
> Reductions(N77_4[2][1],3);
[* [*
q + $.1*q^2 + q^3 + $.1^7*q^4 + q^5 + $.1*q^6 + q^7 + O(q^8),
q + $.1^3*q^2 + q^3 + $.1^5*q^4 + q^5 + $.1^3*q^6 + q^7 + O(q^8)
*] *]
> Reductions(N77_4[3][1],3);
[* [*
q + q^2 + 2*q^3 + 2*q^4 + q^5 + 2*q^6 + 2*q^7 + O(q^8)
*] *]
> g;
q + q^2 + 2*q^3 + 2*q^4 + q^5 + 2*q^6 + q^7 + O(q^8)
> q := Parent(PowerSeries($1));
> SetPrecision(M77_4,20);
> Reductions(N77_4[3][1],3);
[* [*
q + q^2 + 2*q^3 + 2*q^4 + q^5 + 2*q^6 + 2*q^7 + O(q^8)
*] *]
> SetPrecision(N77_4[3][1],20);

>> SetPrecision(N77_4[3][1],20);
               ^
Runtime error in 'SetPrecision': Bad argument types
Argument types given: ModFrmElt, RngIntElt
> PowerSeries(Reductions(N77_4[3][1],3)[1][1],20);
q + q^2 + 2*q^3 + 2*q^4 + q^5 + 2*q^6 + 2*q^7 + q^9 + q^10 + q^11 + q^12 + q^13 + 2*q^14 + 2*q^15 + 2*q^16 + q^17 + q^18 + O(q^20)
> h;
q + q^2 + 2*q^3 + 2*q^4 + q^5 + 2*q^6 + q^7 + O(q^8)
> g;
q + q^2 + 2*q^3 + 2*q^4 + q^5 + 2*q^6 + q^7 + O(q^8)
> PowerSeries(h,20);
q + q^2 + 2*q^3 + 2*q^4 + q^5 + 2*q^6 + q^7 + q^9 + q^10 + q^11 + q^12 + q^13 + q^14 + 2*q^15 + 2*q^16 + q^17 + q^18 + O(q^20)
> f := Newform(EC("389A"));

>> f := Newform(EC("389A"));
               ^
Runtime error in 'Newform': Bad argument types
Argument types given: CrvEll
> f := Newforms(EC("389A"));

>> f := Newforms(EC("389A"));
                ^
Runtime error in 'Newforms': Bad argument types
Argument types given: CrvEll
> f := ModularForm(EC("389A"));
> f;
q - 2*q^2 - 2*q^3 + 2*q^4 - 3*q^5 + 4*q^6 - 5*q^7 + O(q^8)
> -2+(2+1);
1
> -2+(3+1);
2
> -3+(5+1);
3
> f := ModularForm(EC("433A"));
> f;
q - q^2 - 2*q^3 - q^4 - 4*q^5 + 2*q^6 - 3*q^7 + O(q^8)
> -1+(2+1);
2
> f := ModularForm(EC("563A"));
> f;
q - q^2 - q^3 - q^4 - 4*q^5 + q^6 - 5*q^7 + O(q^8)
> f := ModularForm(EC("571B"));
> f;
q - 2*q^2 - 2*q^3 + 2*q^4 - 2*q^5 + 4*q^6 - 4*q^7 + O(q^8)
> -1+(4);
3
> 389*5;
1945
> f := ModularForm(EC("389A"));
> [p : p in [1..79] |IsPrime(p) and (Integers()!Coefficient(f,p)+(p+1)) mod 9 eq 0];
[ 31, 59, 61, 67 ]
>