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