  Let $V$ be a rational, selfdual, $C_2$-cofinite vertex operator algebra of
CFT type, and $G$ a finite automorphism group of $V.$ It is proved that the
kernel of the representation of the modular group on twisted conformal blocks
associated to $V$ and $G$ is a congruence subgroup. In particular, the
$q$-character of each irreducible twisted module is a modular function on the
same congruence subgroup. In the case $V$ is the Frenkel-Lepowsky-Meurman's
moonshine vertex operator algebra and $G$ is the monster simple group, the
generalized McKay-Thompson series associated to any commuting pair in the
monster group is a modular function.
