The Bloch–Okounkov theorem for congruence subgroups and Taylor coefficients of quasi-Jacobi forms

Abstract There are many families of functions on partitions, such as the shifted symmetric functions, for which corresponding q -brackets quasimodular forms. We extend these so that a congruence subgroup. Moreover, we find subspaces -bracket is modular form. These results follow from properties Taylor coefficients strictly meromorphic quasi-Jacobi forms around rational lattice points.