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Capparelli conjectured two modular identities for partitions whose partssatisfy certain gap conditions, where were motivated by the calculation ofcharacters for the standard modules of certain affine Lie algebras and byvertex operator theory. These identities were subsequently proved and refinedby Andrews, who related them to Jacobi theta functions, and also byAlladi-Andrews-Gordon, Capparelli, and Tamba-Xie. In this paper we prove twonew companions to Capparelli's identities, where the evaluations are expressedin terms of Jacobi theta functions and false theta functions.

False theta functions and companions to Capparelli's identities