Open Access
June 2015 The Fourier expansion of Hecke operators for vector-valued modular forms
Oliver Stein
Funct. Approx. Comment. Math. 52(2): 229-252 (June 2015). DOI: 10.7169/facm/2015.52.2.4


We compute the Fourier expansion of Hecke operators on vector-valued modular forms for the Weil representation associated to a lattice $L$. The Hecke operators considered in this paper include operators $T(p^{2l})$ where $p$ is a prime dividing the level of the lattice $L$. Additionally, an explicit formula for a general type of Gauss sum associated to a lattice $L$ drops out as a by-product.


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Oliver Stein. "The Fourier expansion of Hecke operators for vector-valued modular forms." Funct. Approx. Comment. Math. 52 (2) 229 - 252, June 2015.


Published: June 2015
First available in Project Euclid: 18 June 2015

zbMATH: 06862260
MathSciNet: MR3358318
Digital Object Identifier: 10.7169/facm/2015.52.2.4

Primary: 11F25 , 11F27
Secondary: 11E08 , 11L05

Keywords: Fourier expansion , Gauss sums , Hecke operators , vector-valued modular forms , Weil representation

Rights: Copyright © 2015 Adam Mickiewicz University

Vol.52 • No. 2 • June 2015
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