Weights of Galois representations associated to Hilbert modular forms

Let F be a totally real field, p ≧ 3 a rational prime unramified in F, and p a place of F over p. Let p : Gal(F̄ / F) → GL ₂(double-struck F sign̄_p 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 p is irreducible. We specify a set of weights, determined by the restriction of p to inertia at p, which contains all the modular weights for p. 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.