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Restriction of Siegel modular forms to modular curves. (English) Zbl 1021.11012
In this paper the authors get linear relations among the Fourier coefficients of Siegel modular forms, considering homomorphisms from the ring of Siegel modular forms of a given degree to suitable rings of elliptic modular forms. This is a consequence of a construction similar to Eichler’s embedding trick. Using this construction they prove that the space of cusp forms of degree 4 and weight 10 is one dimensional.

MSC:
11F46 Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms
11F27 Theta series; Weil representation; theta correspondences
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