Ternary quadratic forms and half-integral weight modular forms

Let k be a positive integer such that k equivalent to 3 mod 4, and let N be a positive square-free integer. In this paper, we compute a basis for the two-dimensional subspace S-k/2(Gamma(0)(4N),F) of half-integral weight modular forms associated, via the Shimura correspondence, to a newform F is an element of Sk-1(Gamma(0)(N)), which satisfies L(F, 1/2) not equal 0. This is accomplished by using a result of Waldspurger, which allows one to produce a basis for the forms that correspond to a given F via local considerations, once a form in the Kohnen space has been determined.