  Let V^L and V^R be simple vertex operator algebras satisfying certain natural
uniqueness-of-vacuum, complete reducibility and cofiniteness conditions and let
F be a conformal full field algebra over the tensor product of V^L and V^R. We
prove that the q_\tau-\bar{q_\tau}-traces (natural traces involving
q_\tau=e^{2\pi i\tau} and \bar{q_\tau}=\bar{e^{2\pi i\tau}}) of geometrically
modified genus-zero correlation functions for F are convergent in suitable
regions and can be extended to doubly periodic functions with periods 1 and
\tau. We obtain necessary and sufficient conditions for these functions to be
modular invariant. In the case that V^L=V^R and F is one of those constructed
by the authors in \cite{HK}, we prove that all these functions are modular
invariant.
