Shifted convolution L-series values for elliptic curves

Using explicit constructions of the Weierstrass mock modular form and Eisenstein series coefficients, we obtain closed formulas for the generating functions of values of shifted convolution L -functions associated to certain elliptic curves. These identities provide a surprising relation between weight 2 newforms and shifted convolution L -values when the underlying elliptic curve has modular degree 1 with conductor N such that genus ( X 0 ( N ) ) = 1 .