Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 137 / 4 / a / i

Let $\mathcal{L}$ be the set of lattices in $\mathbb{C}$. The lattice model of a modular form isFor the normalization used here, the $n$th Hecke operator on lattice functions isThere are finitely many such superlattices, and scaling gives a bijection between those above $\Lambda$ and those above $\lambda \Lambda$, so $T_{n}F$ again has weight $k$.