unknown terminal "dumb"
[was@form finding_modular_forms]$ [was@form finding_modular_forms]$ Magma V2.7-1      Mon Jan 22 2001 22:42:56 on form     [Seed = 2680754903]
Type ? for help.  Type <Ctrl>-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
> eps := DirichletCharacter(189);

>> eps := DirichletCharacter(189);
                            ^
Runtime error in 'DirichletCharacter': Bad argument types
Argument types given: RngIntElt
> G<a,b> := DirichletGroup(189);
> G;
Group of Dirichlet characters of modulus 189 over Rational Field
> factor(189);
[ <3, 3>, <7, 1> ]
1
> Conductor(a);
3
> eps := a;
> G := DirichletGroup(189);
> G.1;
$.1
> G.2;
$.2
> Conductor(G.1);
3
> Conductor(G.2);
7
> eps := G.1;
> eps;
$.1
> time M := ModularSymbols(eps, 7, GF(7), +1);

>> time M := ModularSymbols(eps, 7, GF(7), +1);
                           ^
Runtime error in 'ModularSymbols': Bad argument types
Argument types given: GrpDrchElt, RngIntElt, FldFin, RngIntElt
> time M := ModularSymbols(eps, 7, +1, GF(7));

>> time M := ModularSymbols(eps, 7, +1, GF(7));
                           ^
Runtime error in 'ModularSymbols': Bad argument types
Argument types given: GrpDrchElt, RngIntElt, RngIntElt, FldFin
> BaseRing(eps);
Rational Field
> BaseExtend(eps,GF(7));
$.1
> eps_mod7 := BaseExtend(eps,GF(7));
> eps_mod7;
$.1
> // alternative ---->  G := DirichletGroup(189, GF(7));
>  time M := ModularSymbols(eps, 7, +1);
Time: 55.880
> M;
Full Modular symbols space of level 189, weight 7,
character $.1, and dimension 144
> R<x>:=PolynomialRing(GF(7));
> I := [<79,x>, <107,x>, <139,x>];
> time V:=Kernel(I,M);

[Interrupted]
>  time M := ModularSymbols(eps_mod7, 7, +1);
Time: 6.579
> R<x>:=PolynomialRing(GF(7));
> time V:=Kernel(I,M);
Time: 2.780
> V;
Modular symbols space of level 189, weight 7, character $.1, and dimension 6
> fcp(Tn(V,3));

[Interrupted]
> fcp(DualHeckeOperator(V,3));
[
<x, 6>
]
1
> fcp(DualHeckeOperator(V,5));
[
<x^2 + 4, 3>
]
1
> fcp(DualHeckeOperator(V,7));
[
<x, 6>
]
1
> for [p : p in [2..97] | IsPrime(p)] do p, fcp(DualHeckeOperator(V,7)); end for;

>> for [p : p in [2..97] | IsPrime(p)] do p, fcp(DualHeckeOperator(V,7)); end 
       ^
User error: bad syntax
> for p in [p : p in [2..97] | IsPrime(p)] do p, fcp(DualHeckeOperator(V,7)); end for;
2 [
<x, 6>
]
1
3 [
<x, 6>
]
1
5 [
<x, 6>
]
1
7 [
<x, 6>
]
1
11 [
<x, 6>
]
1
13 [
<x, 6>
]
1
17 [
<x, 6>
]
1
19 [
<x, 6>
]
1
23 [
<x, 6>
]
1
29 [
<x, 6>
]
1
31 [
<x, 6>
]
1
37 [
<x, 6>
]
1
41 [
<x, 6>
]
1
43 [
<x, 6>
]
1
47 [
<x, 6>
]
1
53 [
<x, 6>
]
1
59 [
<x, 6>
]
1
61 [
<x, 6>
]
1
67 [
<x, 6>
]
1
71 [
<x, 6>
]
1
73 [
<x, 6>
]
1
79 [
<x, 6>
]
1
83 [
<x, 6>
]
1
89 [
<x, 6>
]
1
97 [
<x, 6>
]
1
> 
for p in [p : p in [2..97] | IsPrime(p)] do p, fcp(DualHeckeOperator(V,p)); end for;
> 2 [
<x^2 + 4, 3>
]
1
3 [
<x, 6>
]
1
5 [
<x^2 + 4, 3>
]
1
7 [
<x, 6>
]
1
11 [
<x^2 + 4, 3>
]
1
13 [
<x + 3, 4>,
<x + 4, 2>
]
1
17 [
<x^2 + 1, 3>
]
1
19 [
<x + 1, 4>,
<x + 6, 2>
]
1
23 [
<x^2 + 1, 3>
]
1
29 [
<x^2 + 4, 3>
]
1
31 [
<x + 2, 4>,
<x + 5, 2>
]
1
37 [
<x + 4, 6>
]
1
41 [
<x^2 + 2, 3>
]
1
43 [
<x + 6, 6>
]
1
47 [
<x^2 + 2, 3>
]
1
53 [
<x^2 + 4, 3>
]
1
59 [
<x^2 + 2, 3>
]
1
61 [
<x + 3, 4>,
<x + 4, 2>
]
1
67 [
<x + 6, 6>
]
1
71 [
<x^2 + 1, 3>
]
1
73 [
<x + 3, 4>,
<x + 4, 2>
]
1
79 [
<x, 6>
]
1
83 [
<x^2 + 2, 3>
]
1
89 [
<x^2 + 2, 3>
]
1
97 [
<x + 1, 4>,
<x + 6, 2>
]
1
> fcp(DualHeckeOperator(V,151))
> ;
[
<x, 6>
]
1
> fcp(DualHeckeOperator(V,227));
[
<x, 6>
]
1
>  fcp(DualHeckeOperator(V,241));
[
<x, 6>
]
1
>  fcp(DualHeckeOperator(V,277));
[
<x, 6>
]
1
> time C:=CuspidalSubspace(M);
Time: 0.190
> time N:=NewSubspace(C);

[Interrupted]
> Restrict(eps_mod7,27);
$.1
> Restrict(eps_mod7,9*7);
$.1
> Restrict(eps_mod7,7);

>> Restrict(eps_mod7,7);
           ^
Runtime error in 'Restrict': Conductor of argument 1 does not divide argument 2.
> Restrict(eps_mod7,3*7);
$.1
> I1 := [<13, x+3>, <79,x>, <107,x>, <139,x>];
> I1 := [<13, x+3>, <79,x>, <107,x>, <139,x>];
> I2 := [<13, x+4>, <79,x>, <107,x>, <139,x>];
> I1;
[
<13, x + 3>,
<79, x>,
<107, x>,
<139, x>
]
> I2;
[
<13, x + 4>,
<79, x>,
<107, x>,
<139, x>
]
> time V1:=Kernel(I1,M);
Time: 0.629
> time V2:=Kernel(I2,M);
Time: 0.540
> V1;
Modular symbols space of level 189, weight 7, character $.1, and dimension 4
> V2;
Modular symbols space of level 189, weight 7, character $.1, and dimension 2
> for p in [p : p in [2..29] | IsPrime(p)] do p, fcp(DualHeckeOperator(V1,p)); end for;
2 [
<x^2 + 4, 2>
]
1
3 [
<x, 4>
]
1
5 [
<x^2 + 4, 2>
]
1
7 [
<x, 4>
]
1
11 [
<x^2 + 4, 2>
]
1
13 [
<x + 3, 4>
]
1
17 [
<x^2 + 1, 2>
]
1
19 [
<x + 1, 4>
]
1
23 [
<x^2 + 1, 2>
]
1
29 [
<x^2 + 4, 2>
]
1
> for p in [p : p in [2..29] | IsPrime(p)] do p, fcp(DualHeckeOperator(V2,p)); end for;
2 [
<x^2 + 4, 1>
]
1
3 [
<x, 2>
]
1
5 [
<x^2 + 4, 1>
]
1
7 [
<x, 2>
]
1
11 [
<x^2 + 4, 1>
]
1
13 [
<x + 4, 2>
]
1
17 [
<x^2 + 1, 1>
]
1
19 [
<x + 6, 2>
]
1
23 [
<x^2 + 1, 1>
]
1
29 [
<x^2 + 4, 1>
]
1
> time M27 := ModularSymbols(Restrict(eps_mod7,27), 7, +1);
Time: 0.769
> time D:=Decomposition(M27,13);
Time: 0.280
> D;
[
Modular symbols space of level 27, weight 7, character $.1, and dimension 6,
Modular symbols space of level 27, weight 7, character $.1, and dimension 1,
Modular symbols space of level 27, weight 7, character $.1, and dimension 1,
Modular symbols space of level 27, weight 7, character $.1, and dimension 4,
Modular symbols space of level 27, weight 7, character $.1, and dimension 2,
Modular symbols space of level 27, weight 7, character $.1, and dimension 2,
Modular symbols space of level 27, weight 7, character $.1, and dimension 2
]
>  I := [<79,x>, <107,x>, <139,x>];
> V27 := Kernel(I,M27);
> V27;
Modular symbols space of level 27, weight 7, character $.1, and dimension 0
> time M63 := ModularSymbols(Restrict(eps_mod7,9*7), 7, +1);
Time: 2.130
> time M63 := ModularSymbols(Restrict(eps_mod7,9*7), 7, +1);
Time: 2.160
> V63 := Kernel(I,M63);
> V63;
Modular symbols space of level 63, weight 7, character $.1, and dimension 0
>  time M := ModularSymbols(eps, 7, +1);
Time: 55.330
> time T2:=DualHeckeOperator(M,2);
Time: 3.200
> fcp(T2);

[Interrupt twice in half a second; exiting]

Total time: 560.420 seconds
[was@form finding_modular_forms]$ 
[was@form finding_modular_forms]$ 
[was@form finding_modular_forms]$ exit
exit

Process magma finished
unknown terminal "dumb"
[was@form finding_modular_forms]$ [was@form finding_modular_forms]$ Magma V2.7-1      Mon Jan 22 2001 23:21:33 on form     [Seed = 3683459487]
Type ? for help.  Type <Ctrl>-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
> G<a,b> := DirichletGroup(189);
> eps := a;
> time M := ModularSymbols(eps, 7, +1);
Time: 55.509
> G<a,b> := DirichletGroup(189, CyclotomicField(6));
> eps := a;
> eps := a*b^5;
> Conductor(eps);
63
> Conductor(b);
7
> Conductor(a);
9
> Conductor(a^3);
3
> Order(a);
6
> eps := a^3*b^5;
> Conductor(eps);
21
> IsEven(eps);
true
>  time M := ModularSymbols(eps, 2, +1);
Time: 0.520
> load "some_code";
Loading "some_code"
> KernelIntersection(2);
Time: 0.000

KernelIntersection(
k: 2
)
Kernel(
I: [ <79, x>, <107, x>, <139, x>, <151, x> ],
M: Full Modular symbols space of level 27, weight 2, character ...
)
In file "/home/was/modsym/decomp.m", line 455, column 18:
>>    fT := Evaluate(f, DualHeckeOperator(M,p));
                    ^
Runtime error in 'Evaluate': Bad argument types
Argument types given: RngUPolElt, ModMatFldElt
>  KernelIntersection(3);
Time: 0.230
Time: 0.289
Modular symbols space of level 27, weight 3, character $.1, and dimension 2
> load "some_code";
Loading "some_code"
> KernelIntersection(3);
Time: 0.229
Time: 0.899
Modular symbols space of level 27, weight 3, character $.1, and dimension 2
> V:=$1;
> V;
Modular symbols space of level 27, weight 3, character $.1, and dimension 2
> for p in [p : p in [2..29] | IsPrime(p)] do p, fcp(DualHeckeOperator(V,p)); end for;
2 [
<x^2 + 2, 1>
]
1
3 [
<x, 2>
]
1
5 [
<x^2 + 2, 1>
]
1
7 [
<x + 2, 2>
]
1
11 [
<x^2 + 1, 1>
]
1
13 [
<x + 3, 2>
]
1
17 [
<x^2 + 2, 1>
]
1
19 [
<x + 2, 2>
]
1
23 [
<x^2 + 4, 1>
]
1
29 [
<x^2 + 4, 1>
]
1
> qEigenform(V,29);
q + a*q^2 + 2*q^4 + 6*a*q^5 + 5*q^7 + 6*a*q^8 + 2*q^10 + 2*a*q^11 + 4*q^13 + 5*a*q^14 + 3*q^16 + 6*a*q^17 + 5*q^19 + 5*a*q^20 + 3*q^22 + 3*a*q^23 + 2*q^25 + 4*a*q^26 + 3*q^28 + O(q^29)
> f:=qEigenform(V,97);
q + a*q^2 + 2*q^4 + 6*a*q^5 + 5*q^7 + 6*a*q^8 + 2*q^10 + 2*a*q^11 + 4*q^13 + 5*a*q^14 + 3*q^16 + 6*a*q^17 + 5*q^19 + 5*a*q^20 + 3*q^22 + 3*a*q^23 + 2*q^25 + 4*a*q^26 + 3*q^28 + 3*a*q^29 + 6*q^31 + 6*a*q^32 + 2*q^34 + 2*a*q^35 + 6*q^37 + 5*a*q^38 + 5*q^40 + 6*a*q^41 + q^43 + 4*a*q^44 + q^46 + 5*a*q^47 + 4*q^49 + 2*a*q^50 + q^52 + 5*a*q^53 + 4*q^55 + 2*a*q^56 + q^58 + 4*a*q^59 + q^61 + 6*a*q^62 + 3*a*q^65 + 4*q^67 + 5*a*q^68 + 3*q^70 + 5*a*q^71 + 2*q^73 + 6*a*q^74 + 3*q^76 + 3*a*q^77 + 4*a*q^80 + 2*q^82 + a*q^83 + 5*q^85 + a*q^86 + 4*q^88 + 2*a*q^89 + 6*q^91 + 6*a*q^92 + 4*q^94 + 2*a*q^95 + O(q^97)
> Parent($1);
Power series ring in q over Univariate Quotient Polynomial Algebra in a over GF(7)
with modulus a^2 + 2
> for k in [k : k in [3..11] |IsOdd(k)] do k,KernelIntersection(k); end for;
Time: 0.220
Time: 0.909
3 Modular symbols space of level 27, weight 3, character $.1, and dimension 2
Time: 0.470
Time: 0.170
5 Modular symbols space of level 27, weight 5, character $.1, and dimension 0
Time: 0.740
Time: 0.289
7 Modular symbols space of level 27, weight 7, character $.1, and dimension 0
Time: 1.039
Time: 1.590
9 Modular symbols space of level 27, weight 9, character $.1, and dimension 2
Time: 1.290
Time: 1.889
11 Modular symbols space of level 27, weight 11, character $.1, and dimension 2
> V9:=KernelIntersection(9);
Time: 1.030
Time: 1.630
> qEigenform(V9,29);
q + a*q^2 + 2*q^4 + 6*a*q^5 + 5*q^7 + 6*a*q^8 + 2*q^10 + 2*a*q^11 + 4*q^13 + 5*a*q^14 + 3*q^16 + 6*a*q^17 + 5*q^19 + 5*a*q^20 + 3*q^22 + 3*a*q^23 + 2*q^25 + 4*a*q^26 + 3*q^28 + O(q^29)
> V11:=KernelIntersection(11);
Time: 1.329


Time: 1.919
> > > qEigenform(V11,29);
q + a*q^2 + q^4 + a*q^5 + 3*a*q^8 + 6*q^10 + 4*a*q^11 + 3*q^13 + 6*q^16 + 2*a*q^17 + 4*q^19 + a*q^20 + 3*q^22 + 3*a*q^23 + q^25 + 3*a*q^26 + O(q^29)
>  for k in [k : k in [12..20] |IsOdd(k)] do k,KernelIntersection(k); end for;
Time: 1.650
Time: 2.279
13 Modular symbols space of level 27, weight 13, character $.1, and dimension 2
Time: 1.999
Time: 2.769
15 Modular symbols space of level 27, weight 15, character $.1, and dimension 2
Time: 2.310
Time: 1.430
17 Modular symbols space of level 27, weight 17, character $.1, and dimension 0
Time: 2.700
Time: 3.700
19 Modular symbols space of level 27, weight 19, character $.1, and dimension 2
> Parent(qEigenform(V11,29));
Power series ring in q over Univariate Quotient Polynomial Algebra in a over GF(7)
with modulus a^2 + 1
> f:=qEigenform(V,97);
> f;
q + a*q^2 + 2*q^4 + 6*a*q^5 + 5*q^7 + 6*a*q^8 + 2*q^10 + 2*a*q^11 + 4*q^13 + 5*a*q^14 + 3*q^16 + 6*a*q^17 + 5*q^19 + 5*a*q^20 + 3*q^22 + 3*a*q^23 + 2*q^25 + 4*a*q^26 + 3*q^28 + 3*a*q^29 + 6*q^31 + 6*a*q^32 + 2*q^34 + 2*a*q^35 + 6*q^37 + 5*a*q^38 + 5*q^40 + 6*a*q^41 + q^43 + 4*a*q^44 + q^46 + 5*a*q^47 + 4*q^49 + 2*a*q^50 + q^52 + 5*a*q^53 + 4*q^55 + 2*a*q^56 + q^58 + 4*a*q^59 + q^61 + 6*a*q^62 + 3*a*q^65 + 4*q^67 + 5*a*q^68 + 3*q^70 + 5*a*q^71 + 2*q^73 + 6*a*q^74 + 3*q^76 + 3*a*q^77 + 4*a*q^80 + 2*q^82 + a*q^83 + 5*q^85 + a*q^86 + 4*q^88 + 2*a*q^89 + 6*q^91 + 6*a*q^92 + 4*q^94 + 2*a*q^95 + O(q^97)
nn> Parent(f);
Power series ring in q over Univariate Quotient Polynomial Algebra in a over GF(7)
with modulus a^2 + 2
> F<s>:=GF(49);
> MinimalPolynomial(s);
x^2 + 6*x + 3
> S<t>:=Polynomial(F);

>> S<t>:=Polynomial(F);
                   ^
Runtime error in 'Polynomial': Bad argument types
Argument types given: FldFin
>  S<t>:=PolynomialRing(F);
> Roots(t^2+2);
[ <s^20, 1>, <s^44, 1> ]
> Z:=BaseRing(Parent(f));
> Z;
Univariate Quotient Polynomial Algebra in a over Finite field of size 7
with modulus a^2 + 2
> coefff:=Eltseq(f);
> coefff;
> coefff;
[
1,
s^20,
0,
2,
6*s^20,
0,
5,
6*s^20,
0,
2,
2*s^20,
0,
4,
5*s^20,
0,
3,
6*s^20,
0,
5,
5*s^20,
0,
3,
3*s^20,
0,
2,
4*s^20,
0,
3,
3*s^20,
0,
6,
6*s^20,
0,
2,
2*s^20,
0,
6,
5*s^20,
0,
5,
6*s^20,
0,
1,
4*s^20,
0,
1,
5*s^20,
0,
4,
2*s^20,
0,
1,
5*s^20,
0,
4,
2*s^20,
0,
1,
4*s^20,
0,
1,
6*s^20,
0,
0,
3*s^20,
0,
4,
5*s^20,
0,
3,
5*s^20,
0,
2,
6*s^20,
0,
3,
3*s^20,
0,
0,
4*s^20,
0,
2,
s^20,
0,
5,
s^20,
0,
4,
2*s^20,
0,
6,
6*s^20,
0,
4,
2*s^20
]
> c:=[
1,
s^20,
0,
2,
6*s^20,
0,
5,
6*s^20,
0,
2,
2*s^20,
0,
4,
5*s^20,
0,
3,
6*s^20,
0,
5,
5*s^20,
0,
3,
3*s^20,
0,
2,
4*s^20,
0,
3,
3*s^20,
0,
6,
6*s^20,
0,
2,
2*s^20,
0,
6,
5*s^20,
0,
5,
6*s^20,
0,
1,
4*s^20,
0,
1,
5*s^20,
0,
4,
2*s^20,
0,
1,
5*s^20,
0,
4,
2*s^20,
0,
1,
4*s^20,
0,
1,
6*s^20,
0,
0,
3*s^20,
0,
4,
5*s^20,
0,
3,
5*s^20,
0,
2,
6*s^20,
0,
3,
3*s^20,
0,
0,
4*s^20,
0,
2,
s^20,
0,
5,
s^20,
0,
4,
2*s^20,
0,
6,
6*s^20,
0,
4,
2*s^20
];
> > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > 
> 
> c;
[ 1, s^20, 0, 2, s^44, 0, 5, s^44, 0, 2, s^36, 0, 4, s^12, 0, 3, s^44, 0, 5, s^12, 0, 3, s^28, 0, 2, s^4, 0, 3, s^28, 0, 6, s^44, 0, 2, s^36, 0, 6, s^12, 0, 5, s^44, 0, 1, s^4, 0, 1, s^12, 0, 4, s^36, 0, 1, s^12, 0, 4, s^36, 0, 1, s^4, 0, 1, s^44, 0, 0, s^28, 0, 4, s^12, 0, 3, s^12, 0, 2, s^44, 0, 3, s^28, 0, 0, s^4, 0, 2, s^20, 0, 5, s^20, 0, 4, s^36, 0, 6, s^44, 0, 4, s^36 ]
> G;
Group of Dirichlet characters of modulus 27 over Rational Field
> G:=DirichletGroup(27, F);
> G;
Group of Dirichlet characters of modulus 27 over Finite field of size 7^2
> E:=Elements(G);
> #E;
6
> Evaluate(E[1],2);
1
> Evaluate(E[2],2);
3
> Evaluate(E[3],2);
2
> Evaluate(E[4],2);
6
> Evaluate(E[5],2);
4
> GCD(18,48);
6
> Parent( Evaluate(E[5],2));
Finite field of size 7^2
> Eltseq( Evaluate(E[5],2));
[ 4, 0 ]
> GCD(EulerPhi(3^4),48);
6
> GCD(EulerPhi(3^3*7),48);
12
> Order(s^20);
12
> G:=DirichletGroup(27*7, F);
> E:=Elements(G);
> Evaluate(E[1],2);
1
> Evaluate(E[2],2);
3
> Evaluate(E[3],2);
2
> #E;
36
> s^(-20)
> ;
s^28
> [i : i in [1..#E] | Evaluate(E[i],2) eq s^28 ];
[]
>