Non-optimal levels of a reducible mod l modular representation

Abstract

Let $\ell \ge 5$ be a prime and let $N$ be a square-free integer prime to $\ell$. For each prime $p$ dividing $N$, let $a_p$ be either $1$ or $-1$. We give sufficient criteria for the existence of a newform $f$ of weight 2 for ${\Gamma }_0(N)$ such that the mod $\ell$ Galois representation attached to $f$ is reducible and $U_{p}f=a_{p}f$ for primes $p$ dividing $N$. The main techniques used are level raising methods based on an exact sequence due to Ribet.

References in corpus (3)

• A torsion Jacquet--Langlands correspondence
• The index of an Eisenstein ideal and multiplicity one
• On Eisenstein ideals and the cuspidal group of $J_0(N)$

Cited by in corpus (3)

• The index of an Eisenstein ideal and multiplicity one
• On Eisenstein ideals and the cuspidal group of $J_0(N)$
• Heegner points at Eisenstein primes and twists of elliptic curves