Abstract:

To a given vector-valued modular form of dimension 2, we may naturally associate a second-order linear ordinary differential equation with modular forms as coefficients (called a modular differential equation). In this talk, we discuss the converse problem and (partially) classify vector-valued modular forms formed by solutions of modular differential equations in the case the group is a triangle group commensurable with SL(2,Z). This is a joint work with Professor Chang-Shou Lin.