On Eisenstein ideals and the cuspidal group of $J_0(N)$

Abstract

Let ${\mathcal{C}}_N$ be the cuspidal subgroup of the Jacobian $J_0(N)$ for a square-free integer $N>6$. For any Eisenstein maximal ideal $\mathfrak{m}$ of the Hecke ring of level $N$, we show that ${\mathcal{C}}_N[\mathfrak{m}]\ne 0$. To prove this, we calculate the index of an Eisenstein ideal $\mathcal{I}$ contained in $\mathfrak{m}$ by computing the order of a cuspidal divisor annihilated by $\mathcal{I}$.

comments are welcome

References in corpus (2)

• Non-optimal levels of a reducible mod l modular representation
• The index of an Eisenstein ideal and multiplicity one

Cited by in corpus (1)

• Non-optimal levels of a reducible mod l modular representation