Delta form

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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

${\displaystyle \mathrm{\Delta }/(2\pi {)}^{12}=q{\displaystyle \prod _{n=1}^{\mathrm{\infty }}}{(1-q^n)}^{24}=\sum _n\tau (n)q^n,}$

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.