> M:=ModularSymbols(503);
> D:=NewformDecomposition(CuspidalSubspace(M));
> D:=SortDecomposition(D);
> E:=D[1]; F:=D[2]; G:=D[3];
> qEigenform(E,8);
q + q^2 + q^3 - q^4 - 2*q^5 + q^6 - 3*q^7 + O(q^8)
> qEigenform(F,8);
q + q^2 + 3*q^3 - q^4 - 2*q^5 + 3*q^6 + 3*q^7 + O(q^8)
> qEigenform(G,8);
q - q^2 + q^3 - q^4 - 4*q^5 - q^6 - 3*q^7 + O(q^8)
> IntersectionGroup(E,F);
Abelian Group of order 1
> IntersectionGroup(E,G);
Abelian Group of order 1
> IntersectionGroup(F,G);
Abelian Group of order 1
> IntersectionGroup(E,F+G);
Abelian Group isomorphic to Z/2 + Z/2