Cusp Form

A cusp form is a Modular Form for which the coefficient $c(0)=0$ in the Fourier Series

$$f(\tau)=\sum_{n=0}^\infty c(n)e^{2\pi in\tau}$$

(Apostol 1997, p. 114). The only entire cusp form of weight $k<12$ is the zero function (Apostol 1997, p. 116). 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 $M_{k,0}$.

See also Modular Form

References

Apostol, T. M. Modular Functions and Dirichlet Series in Number Theory, 2nd ed. New York: Springer-Verlag, pp. 114 and 116, 1997.