:=PolynomialRing(GF(3));
> I:=[<2,x-ellap(E,2)>,<3,x-ellap(E,3)>,<5,x-ellap(E,5)>];
> time M := [MS(e[i],2,+1) : i in [1..#e]];
Time: 63.620
> Mnz:=[m : m in M | Dimension(m) ne 0];
> Mnz;
[
Full Modular symbols space of level 2849, weight 2, and dimension 308,
Full Modular symbols space of level 2849, weight 2, character $.1*$.2, and dimension 304,
Full Modular symbols space of level 2849, weight 2, character $.3, and dimension 308,
Full Modular symbols space of level 2849, weight 2, character $.1*$.2*$.3, and dimension 304
]
> time K1:=Kernel(I,Mnz[1]);
Time: 1.700
> K1;
Modular symbols space of level 2849, weight 2, and dimension 1
> SetVerbose("ModularForm",0);
> time K2:=Kernel(I,Mnz[2]);
Time: 3.580
> K2;
Modular symbols space of level 2849, weight 2, character $.1*$.2, and dimension 2
> DirichletCharacter(Mnz[2]);
$.1*$.2
> qEigenform(K1,40);
q + 2*q^2 + 2*q^3 + 2*q^4 + q^5 + q^6 + q^7 + q^9 + 2*q^10 + 2*q^11 + q^12 + q^13 + 2*q^14 + 2*q^15 + 2*q^16 + q^17 + 2*q^18 + 2*q^20 + 2*q^21 + q^22 + 2*q^25 + 2*q^26 + 2*q^27 + 2*q^28 + q^30 + q^31 + q^32 + q^33 + 2*q^34 + q^35 + 2*q^36 + O(q^37)
> DualHeckeOperator(K2,13);DualHeckeOperator(K2,13);
[1 0]
[0 1]
> DualHeckeOperator(K2,31);
[1 1]
[0 1]
> qEigenform(K1,40);
q + 2*q^2 + 2*q^3 + 2*q^4 + q^5 + q^6 + q^7 + q^9 + 2*q^10 + 2*q^11 + q^12 + q^13 + 2*q^14 + 2*q^15 + 2*q^16 + q^17 + 2*q^18 + 2*q^20 + 2*q^21 + q^22 + 2*q^25 + 2*q^26 + 2*q^27 + 2*q^28 + q^30 + q^31 + q^32 + q^33 + 2*q^34 + q^35 + 2*q^36 + 2*q^37 + 2*q^39 + O(q^40)
> DualHeckeOperator(K2,31);
[0 0]
[0 0]
> I:=[ : p in [2,3,5,13,17,19,23,29,31]];
> time K1:=Kernel(I,Mnz[1]);
Time: 1.369
> K1;
Modular symbols space of level 2849, weight 2, and dimension 1
> time K2:=Kernel(I,Mnz[2]);
Time: 1.679
> K2;
Modular symbols space of level 2849, weight 2, character $.1*$.2, and dimension 0
> time K3:=Kernel(I,Mnz[3]);
Time: 3.890
> K3;
Modular symbols space of level 2849, weight 2, character $.3, and dimension 0
> time K4:=Kernel(I,Mnz[4]);
Time: 2.800
> K4;
Modular symbols space of level 2849, weight 2, character $.1*$.2*$.3, and dimension 0
> #Mnz;
4
> Mnz[1];
Full Modular symbols space of level 2849, weight 2, and dimension 308
>