Koecher principle (awaiting review)

Let $ f(\tau)=\sum_{n\in L_{\Gamma}^{\vee}} a(n) e^{2 \pi i \text{tr}(n\tau)}$ be the q-expansion of $f\in M_{\rho}(\Gamma)$. The Koecher principle says that, for degree $g\geqslant 2$, if $a(n)\neq 0$ then $n$ is positive semidefinite.