Bull. Korean Math. Soc. 2023; 60(1): 237-255
Online first article January 26, 2023 Printed January 31, 2023
https://doi.org/10.4134/BKMS.b220078
Copyright © The Korean Mathematical Society.
Rhode Island
In this article, we find bases for the spaces of modular forms $M_{2}(\Gamma _{0}(88),\big( \frac{d}{\cdot }\big) )$ for $d=1,8,44\text{ and }88$. We then derive formulas for the number of representations of a positive integer by the diagonal quaternary quadratic forms with coefficients $1,2,11$ and $ 22 $.
Keywords: Eta quotients, Dedekind eta function, theta products, Eisenstein series, modular forms, cusp forms, quadratic forms, representation numbers
MSC numbers: 11E25, 11E20, 11F11, 11F20, 11F27
Supported by: This material is based upon a work supported by the Simons Foundation Institute Grant Award ID 507536 while the author was in residence at the Institute for Computational and Experimental Research in Mathematics in Providence, RI.
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