  Let $X$ be a complex smooth quasi-projective surface acted upon by a finite
group $G$ such that the quotient $X/G$ has singularities only of ADE type. We
obtain an explicit expression for the generating series of the Euler
characteristics of the zero-dimensional components in the moduli space of
zero-dimensional subschemes on $X$ invariant under the action of $G$. We show
that this generating series (up to a suitable rational power of the formal
variable) is a holomorphic modular form.
