Optimal levels for modular mod 2 representations over totally real fields

Abstract

In this paper, we study the level lowering problem for mod 2 representations of the absolute Galois group of a totally real field $F$. In the case $F=\mathbb{Q}$, this was done by Buzzard; here, we generalise some of Buzzard's results to higher weight and arbitrary totally real fields, using Rajaei's generalisation of Ribet's theorem and previous work of Fujiwara and the author.