An explicit structure of the graded ring of modular forms of small level

Suda Tomohiko; Saito Hayato

An explicit structure of the graded ring of modular forms of small level

Number Theory 2011-08-31 v3

Authors: Suda Tomohiko , Saito Hayato

Abstract

In this paper, we study the explicit structure of the graded ring of elliptic modular forms for the congruence subgroup $\Gamma_0(N)$ with N=1,2,3,4,5,6,7,8,9,10,12,16,18,25. More precisely, making use of some relations between Fourier expansions, we determine the ring by a quotient of the polynomial ring in several variables.

Keywords

graded ring of modular forms elliptic modular forms congruence subgroup Fourier expansions polynomial ring quotient ring

Cite

@article{arxiv.1108.3933,
  title  = {An explicit structure of the graded ring of modular forms of small level},
  author = {Suda Tomohiko and Saito Hayato},
  journal= {arXiv preprint arXiv:1108.3933},
  year   = {2011}
}

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