Fourier expansion smf (awaiting review)

Let $f$ be a Siegel modular form of weight $\rho$ on a discrete subgroup $\Gamma$ of $\Sp(2g,\Q)$ that is commensurable with $\Sp(2g,\Z)$. Let $V_g(\Q)$ be the vector space of rational symmetric $g\times g$ matrices and \[ L_{\Gamma}= \left\{ s \in V_g(\Q)\, : \, \left( \begin{array}{ll} 1_g & s \\ 0 & 1_g \end{array}\right)\in \Gamma \right\} \] be the translation lattice, which is commensurable with $V_g(\Z)$. Its dual lattice is \[ L_{\Gamma}^{\vee}= \left\{ n\in V_{g}(\Q)\, : \, \text{ for any } s \in L_{\Gamma}, \text{tr}(sn) \in \Z \right\}. \] For $\tau \in \mathcal{H}_g$, there is a Fourier expansion \[ f(\tau)=\sum_{n\in L_{\Gamma}^{\vee}} a(n) e^{2 \pi i \text{tr}(n\tau)}. \]