Computations of spaces of Siegel modular cusp forms. (English) Zbl 1114.11045

Poor, Cris; Yuen, David S.

J. Math. Soc. Japan 59, No. 1, 185-222 (2007).

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 homomorphism. By using these linear relations and homomorphisms, the authors compute the Siegel cusp forms of degree \(n\) and weight \(k\) in some new cases: \((n,k)=(4,14),(4,16),(5,8),(5,10),(6,8)\). They put the open question of whether their technique always succeeds in a precise form. They also give many results, examples and tables in this paper, as well.

Reviewer: Yilmaz Simsek (Antalya)

MSC:

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

Keywords:

Siegel modular forms; Fourier coefficients