cuspform
A cusp form is a type of modular form with additional vanishing conditions at the cusps. Specifically, a cusp form of weight k for a congruence subgroup Γ, sometimes with a multiplier system (character) χ, is a holomorphic function on the upper half-plane that transforms like a modular form under the action of Γ and vanishes at every cusp. Equivalently, when expanded in a Fourier series at each cusp, a cusp form has no constant term; its q-expansion begins with a positive power of q = e^{2πi z}.
Cusp forms arise as the subspace S_k(Γ) of the space of modular forms of weight k for
Hecke operators act on spaces of cusp forms, preserving them. The cusp forms that are eigenforms for
A classical example is the Delta function Δ(z) = q ∏_{n≥1} (1 − q^n)^{24}, a weight 12 cusp