A **cusp form** is a holomorphic elliptic modular form $f$ over the group $\Gamma$ such that $f$ vanishes at all cusps of $\Gamma$. In particular, the constant terms in the Fourier expansion of $f$ vanish.

Cusp forms of the same weight and multiplier system that are defined over the same group form a $\mathbb{C}$-vector space.

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