Images de représentations galoisiennes associées à certaines formes modulaires de Siegel de genre 2

Abstract

We study the image of the [Formula: see text]-adic Galois representations associated to the four vector valued Siegel modular forms appearing in the work of Chenevier and Lannes [3]. These representations are symplectic of dimension 4. Following methods used by Dieulefait in [4], we determine the primes [Formula: see text] for which these representations are absolutely irreducible. In addition, we show that their image is “full” for all primes [Formula: see text] such that the associated residual representation is absolutely irreducible, except in two cases.