Shimura correspondence for level p2 and the central values of L-series

Given a weight 2 and level p2 modular form f, we construct two weight 3/2 modular forms (possibly zero) of level 4p2 and non-trivial character mapping to f via the Shimura correspondence. Then we relate the coefficients of the constructed forms to the central value of the L-series of certain imaginary quadratic twists of f. Furthermore, we give a general framework for our construction that applies to any order in definite quaternion algebras, with which one can, in principle, construct weight 3/2 modular forms of any level, provided one knows how to compute ideal classes representatives.