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In this paper, we study the $ K $-finite matrix coefficients of integrablerepresentations of the metaplectic cover of $ \mathrm{SL}_2(\mathbb R) $ andgive a result on the non-vanishing of their Poincar\'{e} series. We do this byadapting the techniques developed for $ \mathrm{SL}_2(\mathbb R) $ by Mui\'{c}to the case of the metaplectic group.

On the Non-Vanishing of Poincar\'{e} Series on the Metaplectic Group