  Let $V$ be a strongly regular vertex operator algebra. For a state $h \in
V_1$ satisfying appropriate integrality conditions, we prove that the space
spanned by the trace functions Tr$_Mq^{L(0)-c/24}\zeta^{h(0)} ($M$ a
$V$-module) is a vector-valued weak Jacobi form of weight 0 and a certain index
$<h, h >/2$. We discuss refinements and applications of this result when $V$ is
holomorphic, in particular we prove that if $g = e^{h(0)}$ is a finite order
automorphism then Tr$_V q^{L(0)-c/24}g$ is a modular function of weight 0 on a
congruence subgroup of $SL_2(Z)$.
