Lift of the Trivial Representation: The Nonsplit Type $D$ Case

Let $\widetilde G$ be a nonlinear double cover of the real points of a connected, simply connected, semisimple complex group. In previous work, we introduced $\prod_{ρ/2}^s(\widetilde G)$, the set of genuine small representations with infinitesimal character $ρ/2$ in the simply laced setting, and sh