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Computations of Galois representations associated to modular forms of level one

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Tian P.

Acta Arithmetica

2014

tom 164

nr 4

399-411

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 uper bound on Lehmer's conjecture for Ramanujan's tau function.

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1 Acta Arithmetica

1 Tian P.

1 2014

Wyniki wyszukiwania

Computations of Galois representations associated to modular forms of level one