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EFFICIENTLY GENERATED SPACES OF CLASSICAL SIEGEL MODULAR FORMS AND THE BÖCHERER CONJECTURE

Part of: Computational number theory Discontinuous groups and automorphic forms

Published online by Cambridge University Press:  01 April 2011

MARTIN RAUM
MARTIN RAUM*
Affiliation:
MPI für Mathematik, Vivatsgasse 7, 53111 Bonn, Germany (email: MRaum@mpim-bonn.mpg.de)
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Abstract

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We state and verify up to weight 172 a conjecture on the existence of a certain generating set for spaces of classical Siegel modular forms. This conjecture is particularly useful for calculations involving Fourier expansions. Using this generating set, we verify the Böcherer conjecture for nonrational eigenforms and discriminants with class number greater than one. As a further application we verify another conjecture for weights up to 150 and investigate an analog of the Victor–Miller basis. Additionally, we describe some arithmetic properties of the basis we found.

Keywords

Siegel modular formsBöcherer conjectureHecke actioncomputation

MSC classification

Secondary: 11F46: Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms 11Y99: None of the above, but in this section
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 89 , Issue 3 , December 2010 , pp. 393 - 405
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2011

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