  We study the quasi-admissibility and raisablility of some nilpotent orbits of
a covering group. In particular, we determine the degree of the cover such that
a given split nilpotent orbit is quasi-admissible and non-raisable. The
speculated wavefront sets of theta representations are also computed
explicitly, and are shown to be quasi-admissible and non-raisable. Lastly, we
determine the leading coefficients in the Harish-Chandra character expansion of
theta representations of covers of the general linear groups.
