is a modular form of weight n=2þ n on G0ðN Þ, where G 1⁄4 SL2ðZÞ and N is the level of Q, i.e., NQ 1 is integral and NQ 1 has even diagonal entries. This was proved by Schoeneberg  for even n and by Pfetzer  for odd n. Shimura  generalizes their results for arbitrary n and also computes the theta multiplier explicitly. Andrianov and Maloletkin [1, 2] generalize (1) and define theta series of higher degree. In , they construct Siegel modular forms by regarding theta series corresponding to positive-definite quadratic forms as specializations of symplectic theta functions. In addition, they apply a differential operator to the functional equation of the theta functions to show that theta series of higher degree with harmonic coefficients are also Siegel modular forms. In , they obtain analogous results for theta functions corresponding to indefinite quadratic forms. Stark  computes the theta multiplier for the symplectic theta function. As an application, he explicitly determines the theta multiplier of Andrianov’s and Maloletkin’s theta functions.