## Taiwanese Journal of Mathematics

### Hecke Bound of Vector-valued Modular Forms and its Relationship with Cuspidality

#### 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 $Q$.

#### Article information

Source
Taiwanese J. Math., Volume 22, Number 2 (2018), 301-311.

Dates
Revised: 7 July 2017
Accepted: 28 August 2017
First available in Project Euclid: 4 October 2017

https://projecteuclid.org/euclid.twjm/1507082429

Digital Object Identifier
doi:10.11650/tjm/170811

Mathematical Reviews number (MathSciNet)
MR3780718

Zentralblatt MATH identifier
06965371

#### Citation

Jin, Seokho; Lim, Jongryul; Lim, Subong. Hecke Bound of Vector-valued Modular Forms and its Relationship with Cuspidality. Taiwanese J. Math. 22 (2018), no. 2, 301--311. doi:10.11650/tjm/170811. https://projecteuclid.org/euclid.twjm/1507082429

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