DOCUMENTA MATHEMATICA, Vol. Extra Volume: John H. Coates' Sixtieth Birthday (2006), 533-550

Frazer Jarvis

Optimal Levels for Modular Mod 2 Representations over Totally Real Fields

In this paper, we study the level lowering problem for mod 2 representations of the absolute Galois group of a totally real field $\rF$. In the case $\rF=\Q$, 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.

2000 Mathematics Subject Classification: 11F33, 11F41, 11G18, 14G35

Keywords and Phrases: Hilbert modular forms, totally real fields, Galois representations

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