Using Katsurada’s determination of the Eisenstein series to compute Siegel eigenforms

King, Oliver; Poor, Cris; Shurman, Jerry; Yuen, David

doi:10.1090/mcom/3218

Using Katsurada’s determination of the Eisenstein series to compute Siegel eigenforms
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by Oliver D. King, Cris Poor, Jerry Shurman and David S. Yuen PDF

Math. Comp. 87 (2018), 879-892 Request permission

Abstract:

We compute Hecke eigenform bases of spaces of level one, degree three Siegel modular forms and $2$-Euler factors of the eigenforms through weight $22$. Our method uses the Fourier coefficients of Siegel Eisenstein series, which are fully known and computationally tractable by the work of H. Katsurada; we also use P. Garrett’s decomposition of the pullback of the Eisenstein series through the Witt map. Our results support I. Miyawaki’s conjectural lift, and they give examples of eigenforms that are congruence neighbors.

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