  In this note we prove a certain multiplicity formula regarding the
restriction of an irreducible admissible genuine representation of a 2-fold
cover $\widetilde{{\rm GL}}_{2}(E)$ of ${\rm GL}_{2}(E)$ to the 2-fold cover
$\widetilde{{\rm SL}}_{2}(E)$ of ${\rm SL}_{2}(E)$, and find in particular that
this multiplicity may not be one, a result that seems to have been noticed
before. The proofs follow the standard path via Waldspurger's analysis of theta
correspondence between $\widetilde{{\rm SL}}_{2}(E)$ and ${\rm PGL}_{2}(E)$.
