This tag is for questions relating to Modular Function or, Elliptic Modular Function.
A function is said to be Modular or, elliptic modular if it satisfies the following conditions:
$1.~~ f$ is meromorphic in the upper half-plane $H$,
$2.~~ f(\bf A\tau)=f(\tau)$ for every matrix $\bf A$ in the modular group Gamma,
$3.~~$ The Laurent series of $f$ has the form
$$ f(\tau)=\sum_{n=-m}^{\infty}a(n)e^{2\pi i n\tau} $$
A modular function is a function that, like a modular form, is invariant with respect to the modular group, but without the condition that $f (z)$ be holomorphic in the upper half-plane. Instead, modular functions are meromorphic.
References:
https://en.wikipedia.org/wiki/Modular_form#Modular_functions
