vii, 41 p. A print copy of this thesis is available through the UO Libraries. Search the library catalog for the location and call number. / We generalize a theorem of Zhu relating the trace of certain vertex algebra representations and modular invariants to the arena of vertex super algebras. The theorem explains why the space of simple characters for the Neveu-Schwarz minimal models NS( p, q ) is modular invariant. It also expresses negative products in terms of positive products, which are easier to compute. As a consequence of the main theorem, the subleading coefficient of the singular vectors of NS( p, q ) is determined for p and q odd. An interesting family of q -series identities is established. These consequences established here generalize results of Milas in this field. / Adviser: Arkady Vaintrob