Component Groups Of Quotients Of J(0)(N)

Let f be a newform of weight 2 on Gamma (0)(N), and let A(f) be the corresponding optimal Abelian variety quotient of J(0)(N). We describe an algorithm to compute the order of the component group of A(f) at primes p that exactly divide N. We give a table of orders of component groups for all f of level N less than or equal to 127 and five examples in which the component group is very large, as predicted by the Birch and Swinnerton-Dyer conjecture.