Abstract
In this paper, we prove that if the Fourier coefficients of a vector-valued modular form satisfy the Hecke bound, then it is cuspidal. Furthermore, we obtain an analogous result with regard to Jacobi forms by applying an isomorphism between vector-valued modular forms and Jacobi forms. As an application, we prove a result on the growth of the number of representations of $m$ by a positive definite quadratic form $Q$.
Citation
Seokho Jin. Jongryul Lim. Subong Lim. "Hecke Bound of Vector-valued Modular Forms and its Relationship with Cuspidality." Taiwanese J. Math. 22 (2) 301 - 311, April, 2018. https://doi.org/10.11650/tjm/170811
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