Magma V2.7-0      Tue May 16 2000 03:33:26 on etale    [Seed = 3285859173]
Type ? for help.  Type <Ctrl>-D to quit.

> E := ModularSymbols("54B");  // could count points on curve instead
> EllipticCurve(E);
Elliptic Curve defined by y^2 + x*y + y = x^3 - x^2 + x - 1 over Rational Field
> f := qEigenform(E,24);   
> f;
q + q^2 + q^4 - 3*q^5 - q^7 + q^8 - 3*q^10 + 3*q^11 - 4*q^13 - q^14 + q^16 + 2*q^19 - 3*q^20 + 3*q^22 + 6*q^23 + O(q^24)
> ModularDegree(E);  // homology computation
2
> CongruenceModulus(E);   // computes reduced basis of q-expansions.
6
> F := ModularSymbols("27A");
> g := qEigenform(F,24);      // direct verification.
> R<q> := Parent(g);
> g + Evaluate(g,q^2) - f;
-3*q^4 + 3*q^5 - 3*q^8 + 3*q^10 - 3*q^11 + 9*q^13 + 3*q^16 - 9*q^19 + 3*q^20 - 3*q^22 - 6*q^23 + O(q^24)