SHIMURA CORRESPONDENCE FOR LEVEL p AND THE CENTRAL VALUES OF L-SERIES

Given a weight 2 and level p modular form f , we construct two weight /2 modular forms (possibly zero) of level 4p 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 /2 modular forms of any level, provided one knows how to compute ideal classes representatives.