|Date||Dec 13, 2019|
Ramanujan's conjecture on the tau function, the Fourier coefficients of the discriminant function, led to the development of Hecke Theory. Many divisibility property of Fourier coefficients of modular functions were proved using the theory. Like the canonical basis of the space of modular functions form a Hecke system, we show that the Niebur-Poincare basis of the space of Harmonic Maass forms also form a Hecke system. As consequences, several arithmetic properties of Fourier coefficients of modular functions on the higher genus modular curves and mock modular functions are established.