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Efficiently generated spaces of classical Siegel modular forms and the Böcherer conjecture. (English) Zbl 1285.11078

Summary: 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.

MSC:

11F46 Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms
11F67 Special values of automorphic \(L\)-series, periods of automorphic forms, cohomology, modular symbols
11-04 Software, source code, etc. for problems pertaining to number theory

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References:

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