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


Authors: Oliver D. King, Cris Poor, Jerry Shurman and David S. Yuen
Journal: Math. Comp. 87 (2018), 879-892
MSC (2010): Primary 11F46; Secondary 11F30
DOI: https://doi.org/10.1090/mcom/3218
Published electronically: May 1, 2017
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Abstract | References | Similar Articles | Additional Information

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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Additional Information

Oliver D. King
Affiliation: Department of Mathematics, University of California, Berkeley, California 94720
Address at time of publication: Department of Neurology, University of Massachusetts Medical School, Worcester, Massachusetts 01655
Email: Oliver.King@umassmed.edu

Cris Poor
Affiliation: Department of Mathematics, Fordham University, Bronx, New York 10458
Email: poor@fordham.edu

Jerry Shurman
Affiliation: Department of Mathematics, Reed College, Portland, Oregon 97202
Email: jerry@reed.edu

David S. Yuen
Affiliation: Department of Mathematics and Computer Science, Lake Forest College, 555 N. Sheridan Road, Lake Forest, Illinois 60045
Address at time of publication: Department of Mathematics, University of Hawaii, 2565 McCarthy Mall, Honolulu, Hawaii 96822
Email: yuen@lakeforest.edu

DOI: https://doi.org/10.1090/mcom/3218
Keywords: Eisenstein series, $F_p$ polynomial, Siegel eigenform
Received by editor(s): March 18, 2016
Received by editor(s) in revised form: August 31, 2016, and September 16, 2016
Published electronically: May 1, 2017
Article copyright: © Copyright 2017 American Mathematical Society

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