Siegel modular forms of half integral weight and a lifting conjecture

A conjecture on lifting to Siegel cusp forms of half-integral weight k - 1/2 of degree two front each pair of cusp forms of SL2 (Z) Of Weight 2k - 2 and 2k - 4 is given with a conjectural relation of the L functions and numerical evidences. We also describe the space of Siegel modular forms of half-integral weight, its "plus subspace," and Jacobi forms of degree two by explicitly given theta functions.