Résumé
Let F be a totally real field in which p is unramified. Let r be a modular representation of G_F on a two dimension mod p vector space satisfying the Taylor--Wiles hypotheses and tamely ramified and generic at a place v above p. Let m be the corresponding Hecke eigensystem.We describe the m-torsion in the mod p cohomology of Shimura curves with full congruence level at v as a GL_2(k_v)-representation.