Dimension formula for the twisted Jacquet module of a cuspidal representation of $\text{GL}(2n,{\mathbb{F}}_q)$

Let $F$ be a finite field and $G=\text{GL}(2n,F)$. In this paper, we calculate the dimension of the twisted Jacquet module ${\pi }_{N,{\psi }_A}$ where $A\in \text{M}(n,F)$ is a rank $k$ matrix and $\pi$ is an irreducible cuspidal representation of $G$.