Congruences between modular forms and lowering the level mod l^n

TL;DR

This paper investigates the behavior of inertia groups in modular Galois representations modulo l^n and generalizes Ribet's level-lowering theorem in certain cases.

Contribution

It extends Ribet's level-lowering results to a broader context involving inertia groups and modular Galois representations mod l^n.

Findings

Generalized Ribet's level-lowering theorem

Analyzed inertia group behavior in modular Galois representations

Provided new conditions for level lowering

Abstract

In this article we study the behavior of inertia groups for modular Galois mod l^n representations and in some cases we give a generalization of Ribet's lowering the level result