Linear relations among half-integral weight Poincaré series

We construct an infinite family of half-integral weight Poincaré series coming from vector valued harmonic weak Maass forms, and investigate linear relations among the Poincaré series by applying a pairing between weakly holomorphic modular forms and harmonic weak Maass forms together with properties of Maass Poincaré series. We also show that the Poincaré series are characterized by the Fourier coefficients of half-integral weight cusp forms.