  In this paper, by inputting the Bessel identities over the complex field in
previous work of the authors, the Waldspurger formula of Baruch and Mao is
extended from totally real fields to arbitrary number fields. This is applied
to give a non-trivial bound towards the Ramanujan conjecture for automorphic
forms of the metaplectic group $\widetilde{\mathrm{SL}}_2$ for the first time
in the generality of arbitrary number fields.
