A modular form of weight k is a holomorphic function on the upper half plane Imz > 0, such that f((az + b)/(cz + d)) = (cz + d)^k f(z) and f(z) can be expressed as a Fourier series

where the Fourier coefficients c(n) are integers. Note that f(z + 1) = f(z) and so modular forms have period 1. The only function with odd weight is the zero function.