Theta function of a lattice

Let $𝐿$ be a positive definite lattice. The theta function $𝜗 𝐿$ of $𝐿$ is the formal series comp

𝜗 𝐿 (𝑞) = \sum 𝛼 \in 𝐿 𝑞 ⟨ 𝛼, 𝛼 ⟩ / 2 = \sum 𝑚 \in ℚ | 𝐿 𝑚 | 𝑞 𝑚 / 2