  Let $F$ be a non-Archimedian local field of characteristic zero and $E/F$ a
quadratic extension. The aim of the present article is to study the
multiplicity of an irreducible admissible representation of ${\rm GL}_2(F)$
occurring in an irreducible admissible genuine representation of non-trivial
two fold covering $\widetilde{{\rm GL}}_2(E)$ of ${\rm GL}_2(E)$.
