\\ showing how to use gp-pari's modular symbol routines.
\\ at present these are not as developed as what's available in Sage/MAGMA.
\\ nevertheless one can play with them
\\ Gamma_0(11), weight 2
M = msinit(11,2);
\\ compute T2 on this space
T2 = mshecke(M,2);
\\ find eigenvalues
a2 = factor(charpoly(T2));
\\ find eigenvectors
ev = mateigen(T2);
\\ take first eigenvector, which is cuspidal
ev1 = ev[,1];
\\ compute the eigenvalue of the HO T
eigval(T) = (T*ev1)[2];
\\ do a bunch
\\ forprime(p=2,97,print(p, " : ", eigval(mshecke(M,p))));
\\ compare with elliptic curve
E=ellinit("11a1"); \\ Cremona label
\\ do a bunch
\\ forprime(p=2,97,print(p, " : ", eigval(mshecke(M,p))," ",ellap(E,p)))