In a 2005 paper, Yang constructed families of Hilbert Eisenstein series, which when restricted to the diagonal are conjecturedto span the underlying space of elliptic modular forms. Oneapproach to these conjectures is to show the non-vanishing of an innerproduct of elliptic eigenforms with the restrictions of Eisensteinseries. In this paper, we compute this inner product locally by usingexplicit values of new vectors in the Waldspurger model.