Modular group: SL₂(ℤ) acts on ℍ by τ↦(aτ+b)/(cτ+d). Modular forms satisfy f(γτ)=(cτ+d)ᵏf(τ). The fundamental domain is {τ: |τ|≥1, |Re(τ)|≤½}.
Δ(τ) = q∏(1−qⁿ)²⁴, q=e²πiτ — weight 12, the unique cusp form of its weight up to scaling.
Δ(τ) = q∏(1−qⁿ)²⁴, q=e²πiτ — weight 12, the unique cusp form of its weight up to scaling.