A theorem of Mæglin and Waldspurger for covering groups

Let E be a nonarchimedean local field of characteristic zero and residual characteristic p. Let G be a connected reductive group defined over E and π an irreducible admissible representation of G(E). A result of C. Moeglin 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 Moeglin and Waldspurger to the setting of covering groups of G(E).