  The congruence subgroup property is established for the modular
representations associated to any modular tensor category. This result is used
to prove that the kernel of the representation of the modular group on the
conformal blocks of any rational, C_2-cofinite vertex operator algebra is a
congruence subgroup. In particular, the q-character of each irreducible module
is a modular function on the same congruence subgroup. The Galois symmetry of
the modular representations is obtained and the order of the anomaly for those
modular categories satisfying some integrality conditions is determined.
