form

A cusp form is a modular form for which the coefficient c(0) = 0 in the Fourier series f(τ) = sum_(n = 0)^∞ c(n) e^(2π i n τ) (Apostol 1997, p. 114). The only entire cusp form of weight k<12 is the zero function. The set of all cusp forms in M_k (all modular forms of weight k) is a linear subspace of M_k which is denoted M_(k, 0). The dimension of M_(k, 0) is 1 for k = 12, 16, 18, 20, 22, and 26. For a cusp form f element M_(2k, 0), c(n) = O(n^k) (Apostol 1997, p.