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We characterize Siegel cusp forms in the space of Siegel modular forms of large weightk  &gt;   2  ⁢  n{k&gt;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.

Cuspidality and the growth of Fourier coefficients of modular forms