Ring of quasimodular forms over a cocompact group.

We describe the additive structure of the graded ring (M) over tilde* (Gamma) of quasimodular forms over any discrete and cocompact group Gamma subset of PSL(2, R). We show that this ring is not finitely generated. We calculate the exact number of new generators of weight k (even). This number is constant for k sufficiently large and equals dim(C) I/(I boolean AND I-2), where I and (I) over tilde are the ideals of modular forms and quasimodular forms, respectively, over Gamma of strictly positive weight.