Abstract
Let p be an odd rational prime and F a p-adic field. We give a realization of the universal p- modular representationsof GL2(F) in terms of an explicit Iwasawa module. We specialize our constructions to the case F = Qp , giving a detailed description of the invariants under principal congruence subgroups of irreducible admissible p-modular representations of GL2(Qp), generalizing previous works of Breuil and Paskunas. We apply these results to the local/global compatibility of Emerton, giving a generalization of the classical multiplicity one results for the Jacobians of modularcurves with arbitrary level at p.