Editing Cusp form (section)

==Dimension==
The dimensions of spaces of cusp forms are, in principle, computable via the [[Riemann–Roch theorem]].  For example, the [[Ramanujan tau function]] ''τ''(''n'') arises as the sequence of Fourier coefficients of the cusp form of weight 12 for the modular group, with ''a''<sub>1</sub>&nbsp;=&nbsp;1. The space of such forms has dimension&nbsp;1, which means this definition is possible; and that accounts for the action of [[Hecke operator]]s on the space being by [[scalar multiplication]] (Mordell's proof of Ramanujan's identities). Explicitly it is the '''modular discriminant'''

:<math>\Delta(z,q),</math>

which represents (up to a [[normalizing constant]]) the [[discriminant]] of the cubic on the right side of the [[Weierstrass equation]] of an [[elliptic curve]]; and the 24-th power of the [[Dedekind eta function]]. The Fourier coefficients here are written
<math display="block">\tau(n)</math>
and called '[[Ramanujan tau function|Ramanujan's tau function]]', with the normalization ''τ''(1) = 1.