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December 2017 Theta products and eta quotients of level $24$ and weight $2$
Ayşe Alaca, Şaban Alaca, Zafer Selcuk Aygin
Funct. Approx. Comment. Math. 57(2): 205-234 (December 2017). DOI: 10.7169/facm/1628

Abstract

We find bases for the spaces $M_2\Big(\Gamma_0(24),(\frac{d}{\cdot})\Big)$ ($d=1,8,12, 24$) of modular forms. We determine the Fourier coefficients of all $35$ theta products $\varphi[a_1,a_2,a_3,a_4](z)$ in these spaces. We then deduce formulas for the number of representations of a positive integer $n$ by diagonal quaternary quadratic forms with coefficients $1$, $2$, $3$ or $6$ in a uniform manner, of which $14$ are Ramanujan's universal quaternary quadratic forms. We also find all the eta quotients in the Eisenstein spaces $E_2\Big(\Gamma_0(24),(\frac{d}{\cdot})\Big)$ ($d=1,8,12, 24$) and give their Fourier coefficients.

Citation

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Ayşe Alaca. Şaban Alaca. Zafer Selcuk Aygin. "Theta products and eta quotients of level $24$ and weight $2$." Funct. Approx. Comment. Math. 57 (2) 205 - 234, December 2017. https://doi.org/10.7169/facm/1628

Information

Published: December 2017
First available in Project Euclid: 28 March 2017

zbMATH: 06864172
MathSciNet: MR3732896
Digital Object Identifier: 10.7169/facm/1628

Subjects:
Primary: 11F11
Secondary: 11E20, 11F20, 11F27, 11F30

Rights: Copyright © 2017 Adam Mickiewicz University

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Vol.57 • No. 2 • December 2017
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