### Computing the level of a modular rigid Calabi-Yau threefold.

Dieulefait, Luis V. (2004)

Experimental Mathematics

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Dieulefait, Luis V. (2004)

Experimental Mathematics

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Gerhard Frey (2009)

Annales de la faculté des sciences de Toulouse Mathématiques

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P. Bayer, J. C. Lario (1992)

Compositio Mathematica

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Wiese, Gabor (2004)

Documenta Mathematica

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Bas Edixhoven (1999-2000)

Séminaire Bourbaki

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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.

Darmon, Henri (1999)

Annals of Mathematics. Second Series

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Wintenberger, J.-P. (2007)

Documenta Mathematica

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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...

Hulek, K., Spandaw, J., van Geemen, B., van Straten, D. (2001)

Advances in Geometry

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