## Optimal levels for modular mod 2 representations over totally real fields

### Summary

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 ${F}=\Bbb Q$, 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.

### Mathematics Subject Classification

11F33, 11F80, 11F41, 11G18, 14G35

### Keywords/Phrases

Hilbert modular forms, totally real fields, Galois representations