Modular Forms
Fundamental domain · |j(τ)| coloring · Lattice sums · SL(2,ℤ) symmetry
Upper Half-Plane — |Δ(τ)| coloring
Lattice & Hecke orbit T_n
Function
Δ(τ) discriminant
j-invariant
E₄ Eisenstein
E₆ Eisenstein
Im range
2.50
Hecke n
3
q-terms
20
Render
Modular:
f((aτ+b)/(cτ+d)) = (cτ+d)ᵏ f(τ), ad−bc=1
Δ(τ) = q ∏(1−qⁿ)²⁴
, q=e²πiτ
Hecke T_n:
sublattices of index n → eigenforms