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