  It is one of the remarkable results of vertex operator algebras (VOAs) that
the graded traces (one-point correlation functions) of holomorphic VOAs are
modular functions. This paper explores the question of which modular functions
arise as the graded traces of holomorphic VOAs. For VOAs of small central
charge, i.e., $c\le 24$, and a non-zero weight-one subspace, we find that the
only conditions imposed on the modular fuctions are those that arise easily out
of our condition that the VOAs be of CFT type, that is that they have no
negative-weight subspaces and their zero-weight subspace is generated by the
vacuum vector.
