  In this paper we establish a close connection between three notions at-
tached to a modular subgroup. Namely the set of weight two meromorphic modular
forms, the set of equivariant functions on the upper half-plane commuting with
the action of the modular subgroup and the set of elliptic zeta functions
generalizing the Weierstrass zeta functions. In particular, we show that the
equivariant functions can be parameterized by modular objects as well as by
elliptic objects.
