# Fourier series analogue for Modular Group?

is there a fourier series analogue to the modular group ?=?

$$zmapstofrac{az+b}{cz+d},$$

for example we could expand any function that satisfies the modular equation

$$f(frac{az+b}{cz+d}) =f(z)$$

in terms of simpler function which are modular , just in the same case as we expand any periodic function

$$f(x+T)=f(x)$$

in terms of exponential funtions (Fourier series) $$exp(inx)$$