Delta form

In mathematics, Delta is a modular form, arising from the discriminant of an elliptic curve. As a modular form it is a cusp form of weight 12 and level 1 for the full modular group. It is an eigenform for the Hecke algebra.

The q-expansion is


 * $$\Delta/(2\pi)^{12} = q \prod_{n=1}^\infty \left(1-q^n\right)^{24} = \sum_n \tau(n) q^n ,\,$$

where τ is Ramanujan's tau function. Since Δ is a Hecke eigenform, the tau function is multiplicative.

Dedekind's eta function is a 24-th root of Δ.