Communications of the
Korean Mathematical Society CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024
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Commun. Korean Math. Soc. 2013; 28(3): 481-486

Printed July 1, 2013

https://doi.org/10.4134/CKMS.2013.28.3.481

Copyright © The Korean Mathematical Society.

On polynomial-structure of rings of modular forms for $\Gamma_0(N)$

Daeyeoul Kim and Yan Li

National Institute for Mathematical Sciences, China Agriculture University

Abstract

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In this note, we show that ${\mathcal M}(\Gamma_0(N))$ is a weighted polynomial ring if and only if $N=1, 2, 4$, where ${\mathcal M}(\Gamma_0(N))$ is the graded ring of integral-weighted modular forms for the congruence subgroup $\Gamma_0(N)$.

Keywords: modular forms, congruence subgroup, weighted polynomial ring

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