A theorem of Mœglin-Waldspurger for covering groups

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Let E be a non-Archimedian local field of characteristic zero and residue characteristic p. Let G be a connected reductive group defined over E and π an irreducible admissible representation of G= G(E). A result of C. Mœglin and J.-L. Waldspurger (for p ≠ 2) and S. Varma (for p=2) states that the leading coefficient in the character expansion of π at the identity element of G(E) gives the dimension of a certain space of degenerate Whittaker forms. In this paper we generalize this result of Mœglin-Waldspurger to the setting of covering groups G of G.