On polynomial-structure of rings of modular forms for $\Gamma_0(N)$
Commun. Korean Math. Soc. 2013 Vol. 28, No. 3, 481-486
Printed July 1, 2013
Daeyeoul Kim and Yan Li
National Institute for Mathematical Sciences, China Agriculture University
Abstract : 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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