On Eisenstein ideals and the cuspidal group of J 0(N)

Abstract

Let CN be the cuspidal subgroup of the Jacobian J0(N) for a square-free integer N > 6. For any Eisenstein maximal ideal m of the Hecke ring of level N, we show that CN[m] ≠ 0. To prove this, we calculate the index of an Eisenstein ideal I contained in m by computing the order of the cuspidal divisor annihilated by I. © 2016, Hebrew University of Jerusalem