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

Published online by Cambridge University Press:  01 April 2011

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.

Type
Research Article
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2011

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