📝 SummarXiv

Abstract

Let N be a positive integer and let f be a newform of weight 2 on \Gamma_0(N). In earlier joint work with K. Ribet and W. Stein, we introduced the notions of the modular number and the congruence number of the quotient abelian variety A_f of J_0(N) associated to the newform f. These invariants are analogs of the notions of the modular degree and congruence primes respectively associated to elliptic curves. We show that if p is a prime such that every maximal ideal of the Hecke algebra of characteristic p that contains the annihilator ideal of f satisfies multiplicity one, then the modular number and the congruence number have the same p-adic valuation.