On the computation of Galois representations associated to level one modular forms

Details On the computation of Galois representations associated to level one modular forms On the computation of Galois representations associated to level one modular forms

2007-10-05

arxiv.org/abs/0710.1237v1

Mathematics

Number Theory

15 pages

Scientific paper

In this paper we explicitly compute mod-l Galois representations associated to modular forms. To be precise, we look at cases with l<=23 and the modular forms considered will be cusp forms of level 1 and weight up to 22. We present the result in terms of polynomials associated to the projectivised representations. As an application, we will improve a known result on Lehmer's non-vanishing conjecture for Ramanujan's tau function.

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