Cuspidality and the growth of Fourier coefficients of modular forms

Abstract

Abstract We characterize Siegel cusp forms in the space of Siegel modular forms of large weight {k>2n} on any Siegel congruence subgroup Γ of any degree n and any level N, by a suitable growth of their Fourier coefficients (e.g., by the well-known Hecke bound) at any one of the cusps. For this, we use a ‘local’ approach as compared to our previous results on this topic. We also touch upon the question in the context of vector-valued modular forms.