Research proof index

Serre derivative of E₆: serre_D 6 E₆ = - 2⁻¹ * E₄². Uses the dimension argument: 1. serre_D 6 E₆ is weight-8 slash-invariant (by serre_D_slash_invariant) 2. Weight-8 modular forms are 1-dimensional, spanned by E₄² 3. Constant term is -1/2 (from D E₆ → 0, E₂ → 1, E₆ → 1)