SIEGEL MODULAR-FORMS AND THETA-SERIES ATTACHED TO QUATERNION ALGEBRAS.2.

We continue our study of Yoshida's lifting, which associates to a pair of automorphic forms on the adelic multiplicative group of a quaterni on algebra a Siegel modular form of degree 2. We consider here the cas e that the automorphic forms on the quaternion algebra correspond to m odular forms of arbitrary even weights and square free levels; in part icular we obtain a construction of Siegel modular forms of weight 3 at tached to a pair of elliptic modular forms of weights 2 and 4.