Mock period functions in higher level cases

Generalizing the results of Bringmann, Diamantis and Raum [3] we investigate a generating series of non-critical values which can be interpreted as a mock period function and prove that non-critical values can be encoded into a sesquiharmonic Maass form in higher level cases. Moreover we prove Eichler-Shimura-type isomorphism for the space of period polynomials and for that of mock period functions in level p with p∈{2,3}.