ON POLYNOMIAL-STRUCTURE OF RINGS OF MODULAR FORMS FOR Γ₀(N)

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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References

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