Character-sheaf basis conjecture for class functions

Let $G_0$ be any connected unipotent group over ${\mathbb F}_q$, let $G=G_0\otimes_{{\mathbb F}_q}{\mathbb F}$ with Frobenius $\operatorname{Fr}$, and let $CS(G)^{\operatorname{Fr}}$ consist of character sheaves $M$ with $\operatorname{Fr}^*M\cong M$. For each such $M$, choose an isomorphism $\psi_M:\operatorname{Fr}^*M\xrightarrow{\sim}M$ and let $t_M$ be the corresponding trace function. The character-sheaf basis conjecture. The functions

$$\\{t_M\\}_{M\in CS(G)^{\operatorname{Fr}}}$$

form a basis for the space of class functions on $G_0({\mathbb F}_q)$.