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Displaying similar documents to “Optimal levels for modular mod 2 representations over totally real fields.”

Congruences between modular forms and lowering the level mod ℓ n

Luis Dieulefait, Xavier Taixés i Ventosa (2009)

Journal de Théorie des Nombres de Bordeaux

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In this article we study the behavior of inertia groups for modular Galois mod ℓ n representations and in some cases we give a generalization of Ribet’s lowering the level result (cf. []).

Modularity of Galois representations

Chris Skinner (2003)

Journal de théorie des nombres de Bordeaux

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This paper is essentially the text of the author’s lecture at the 2001 Journées Arithmétiques. It addresses the problem of identifying in Galois-theoretic terms those two-dimensional, p -adic Galois representations associated to holomorphic Hilbert modular newforms.

Computations of Galois representations associated to modular forms of level one

Peng Tian (2014)

Acta Arithmetica

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We propose an improved algorithm for computing mod ℓ Galois representations associated to a cusp form f of level one. The proposed method allows us to explicitly compute the case with ℓ = 29 and f of weight k = 16, and the cases with ℓ = 31 and f of weight k = 12,20,22. All the results are rigorously proved to be correct. As an example, we will compute the values modulo 31 of Ramanujan's tau function at some huge primes up to a sign. Also we will give an improved...