A simple closed formula for Fourier coefficients of certain eta-quotients

Published 18 Aug 2024 in math.NT | (2408.09480v1)

Abstract: We give a list of $83$ holomorphic eta-quotients of integral weight. For each of them we give a simple closed formula for its Fourier coefficients $c(l)$ where $l\equiv1\bmod{m}$ with some fixed $m\mid24$. The proof involves Wohlfahrt's extension of Hecke operators and a dimension formula for spaces of modular forms of general multiplier system.

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Xiao-Jie Zhu

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