Journal of the Mathematical Society of Japan

Computations of spaces of Siegel modular cusp forms

Cris POOR and David S. YUEN

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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.

Article information

J. Math. Soc. Japan, Volume 59, Number 1 (2007), 185-222.

First available in Project Euclid: 25 May 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11F46: Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms
Secondary: 11F30: Fourier coefficients of automorphic forms 11F27: Theta series; Weil representation; theta correspondences

Siegel modular forms polarized lattices Fourier coefficients


POOR, Cris; YUEN, David S. Computations of spaces of Siegel modular cusp forms. J. Math. Soc. Japan 59 (2007), no. 1, 185--222. doi:10.2969/jmsj/1180135507.

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