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

Δ/(2π)12=q∏n=1∞(1−qn)24=∑nτ(n)qn,

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.