Using the link between Galois representations and modular forms established by Serre’s Conjecture, we compute, for every prime , a lower bound for the number of isomorphism classes of Galois representation of on a two–dimensional vector space over which are irreducible, odd, and unramified outside .
We show that if is an extremal even unimodular lattice of rank with , then is generated by its vectors of norms and . Our result is an extension of Ozeki’s result for the case .
Let be a positive integer divisible by 4, a prime, an elliptic cuspidal eigenform (ordinary at ) of weight , level 4 and non-trivial character. In this paper we provide evidence for the Bloch-Kato conjecture for the motives and , where is the motif attached to . More precisely, we prove that under certain conditions the -adic valuation of the algebraic part of the symmetric square -function of evaluated at provides a lower bound for the -adic valuation of the order of the Pontryagin...
In this article we study the behavior of inertia groups for modular Galois mod representations and in some cases we give a generalization of Ribet’s lowering the level result (cf. [9]).
Vector-valued Siegel modular forms may be found in certain cohomology groups with coefficients lying in an irreducible representation of the symplectic group. Using functoriality in the coefficients, we show that the ordinary components of the cohomology are independent of the weight parameter. The meaning of ordinary depends on a choice of parabolic subgroup of , giving a particular direction in the change of weight. Our results complement those of Taylor and Tilouine-Urban for the two other possible...