Explicit structure of the graded ring of modular forms

TL;DR

This paper explicitly describes the structure of the graded ring of modular forms for various congruence subgroups, including some with half-integer weights, advancing understanding of modular form algebraic structures.

Contribution

It provides explicit descriptions of the graded rings of modular forms for multiple congruence groups, including those with half-integer weights, which was previously less understood.

Findings

Explicit structures for graded rings of modular forms for N=1,2,...,12,16,18.

Descriptions of modular forms of half-integer weight for certain groups.

Extension of known structures to additional congruence groups.

Abstract

We give explicit structure of the graded ring of modular forms with respect to Gamma(N) (N=1,2,3,4,5,6,7,8,9,10,12,16,18) and for some other congruence groups. We also study the modular forms of half-integer weight for certain groups.