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Computing the Satake p-parameters of Siegel modular forms

Nathan C. Ryan
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Abstract

Hecke eigenvalues of classical modular forms often encode a wealth of arithmetic data. The Satake $p$-parameters of a Siegel modular form play a role analogous to the one played by Hecke eigenvalues in the characterization of classical modular forms. In this paper we present an algorithm by which we can compute the Satake $p$-parameters of a Siegel modular form $F$ if we are given the Hecke eigenvalues of $F$ with respect to the generators of the local Hecke algebra. We compute explicit examples and relate our computations to the Ramanujan-Petersson Conjecture.

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Nathan C. Ryan. 2004-11-17. Computing the Satake p-parameters of Siegel modular forms. https://arxiv.org/abs/math/0411393

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