Shimura's vector-valued modular forms, weight changing operators, and Laplacians (Q2316154)

This work is related to various operators acting on spaces of scalar-valued and vector-valued quasi-modular forms. More precisely, in the paper under review, the author investigates the various types of weight raising and weight lowering operators on quasi-modular forms, or equivalently on Shimura's vector-valued modular forms involving symmetric power representations. He also presents all the eigenfunctions of the two possible Laplacian operators. The paper under review is as a continuation of his previous work [Ramanujan J. 37, No. 1, 165--180 (2015; Zbl 1387.11031)].