Ring of modular forms
In mathematics, the ring of modular forms associated to a subgroup Γ of the special linear group SL(2, Z) is the graded ring generated by the modular forms of Γ. The study of rings of modular forms describes the algebraic structure of the space of modular forms. == Definition == Let Γ be a subgroup of SL(2, Z) that is of finite index and let Mk(Γ) be the vector space of modular forms of weight k.