Computing the Satake p-parameters of Siegel modular forms

2004/11/17 by Nathan C. Ryan, Ryan, Nathan C.
Mathematics · #11F46 #11F60 #65D20 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT) #math.AG #math.NT #msc:11F46 #msc:11F60 #msc:65D20

paper · pdf · doi:10.48550/arxiv.math/0411393

25 pages

arxiv created 2004/11/17 · arxiv updated 2009/12/01

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.

Related

• Hecke eigenvalues of Siegel modular forms (mod p) and of algebraic modular forms
• On the distribution of Satake parameters for Siegel modular forms
• Siegel modular forms (mod p) and algebraic modular forms
• Distinguishing Siegel modular forms
• Hecke eigenvalues of Siegel modular forms of "different weights"