  We address here the question of whether the characters of an RCFT are modular
functions for some level N, i.e. whether the representation of the modular
group SL_2(Z) coming from any RCFT is trivial on some congruence subgroup. We
prove that if the matrix T, associated to $(\matrix{1&1\cr 0&1})\in{\rm
SL}_2(\Z)$, has ODD order, then this must be so. When the order of T is even,
we present a simple test which if satisfied -- and we conjecture it always will
be -- implies that the characters for that RCFT will also be level N. We use
this to explain three curious observations in RCFT made by various authors.
