A universal Galois representation attached to modular forms modulo 2

Let A be the algebra of Hecke operators acting on mod 2 cusp forms of level 1 and any weight. Nicolas and Serre have determined the structure of A: one has A similar or equal to F-2[[x, y]]. Let G(Q,2) be the Galois group of the maximal extension of Q unramified outside 2 and infinity, and let G be its maximal pro-2-quotient. One constructs a continuous Galois representation r: G -> SL2(A) such that tr r(Frob(p)) = T-p for all odd prime p. One also proves its uniqueness and one studies its irreducibility properties. (C) 2012 Publie par Elsevier Masson SAS pour l'Academie des sciences.