On Fourier coefficients of Siegel modular forms of degree two with respect to congruence subgroups
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We prove a formula of Petersson’s type for Fourier coefficients of Siegel cusp forms of degree 2 with respect to congruence subgroups, and as a corollary, show upper bound estimates of individual Fourier coefficients. The method in this paper is essentially a generalization of Kitaoka’s previous work which studied the full modular case, but some modification is necessary to obtain estimates which are sharp with respect to the level aspect.
KeywordsSiegel modular form Fourier coefficients Petersson formula
Mathematics Subject Classification11F30 11F46
- 4.Iwaniec, H.: Topics in classical automorphic forms, graduate studies in mathematics 17. American Mathematical Society, Providence (1997)Google Scholar