Efficiently generated spaces of classical Siegel modular forms and the Boecherer conjecture

Details Efficiently generated spaces of classical Siegel modular forms and the Boecherer conjecture Efficiently generated spaces of classical Siegel modular forms and the Boecherer conjecture

2010-02-20

arxiv.org/abs/1002.3883v1

Mathematics

Number Theory

17 pages, 7 tables, 1 plot

Scientific paper

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 Boecherer conjec- ture for non-rational eigenforms. As one further application we verify another conjectures for weights up to 150 and investigate an analogue of the Victor-Miller basis. Additionally, we describe some arithmetic properties of the basis we found.

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