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Reduction modulo p of cuspidal representations and weights in Serre's conjecture

Let 𝒪 be the ring of integers of a p‐adic field and 𝔭 its maximal ideal. This paper computes the Jordan–Hölder decomposition of the reduction modulo p of the cuspidal representations of GL2(𝒪/𝔭e) for e ⩾ 1. An alternative formulation of Serre's conjecture for Hilbert modular forms is then provided.