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Let  F  be a totally real field,  p  ≧ 3 a rational prime unramified in  F , and    a place of  F  over  p . Let    be a two-dimensional mod  p  Galois representation which is assumed to be modular of some weight and whose restriction to a decomposition subgroup at    is irreducible. We specify a set of weights, determined by the restriction of  ρ  to inertia at   , which contains all the modular weights for  ρ . This proves part of a conjecture of Diamond, Buzzard, and Jarvis, which provides an analogue of Serre's epsilon conjecture for Hilbert modular forms mod  p .

Weights of Galois representations associated to Hilbert modular forms