Exact formulas for traces of singular moduli of higher level modular functions Original Research Article

Zagier proved that the traces of singular values of the classical j-invariant are the Fourier coefficients of a weight 3/2 modular form and Duke provided a new proof of the result by establishing an exact formula for the traces using Nieburʹs work on a certain class of non-holomorphic modular forms. In this short note, by utilizing Nieburʹs work again, we generalize Dukeʹs result to exact formulas for traces of singular moduli of higher level modular functions.