Translator Disclaimer
January, 2007 Computations of spaces of Siegel modular cusp forms
Cris POOR, David S. YUEN
J. Math. Soc. Japan 59(1): 185-222 (January, 2007). DOI: 10.2969/jmsj/1180135507

Abstract

Simple homomorphisms to elliptic modular forms are defined on the ring of Siegel modular forms and linear relations on the Fourier coefficients of Siegel modular forms are implied by the codomains of these homomorphisms. We use the linear relations provided by these homomorphisms to compute the Siegel cusp forms of degree n and weight k in some new cases: ( n , k ) = ( 4 , 14 ) , ( 4 , 16 ) , ( 5 , 8 ) , ( 5 , 10 ) , ( 6 , 8 ) . We also compute enough Fourier coefficients using this method to determine the Hecke eigenforms in the nontrivial cases. We also put the open question of whether our technique always succeeds in a precise form. As a partial converse we prove that the Fourier series of Siegel modular forms are characterized among all formal series by the codomain spaces of these homomorphisms and a certain boundedness condition.

Citation

Download Citation

Cris POOR. David S. YUEN. "Computations of spaces of Siegel modular cusp forms." J. Math. Soc. Japan 59 (1) 185 - 222, January, 2007. https://doi.org/10.2969/jmsj/1180135507

Information

Published: January, 2007
First available in Project Euclid: 25 May 2007

zbMATH: 1114.11045
MathSciNet: MR2302669
Digital Object Identifier: 10.2969/jmsj/1180135507

Subjects:
Primary: 11F46
Secondary: 11F27, 11F30

Rights: Copyright © 2007 Mathematical Society of Japan

JOURNAL ARTICLE
38 PAGES


SHARE
Vol.59 • No. 1 • January, 2007
Back to Top