The modality of a Borel subgroup in a simple algebraic group of type $E_8$

Let $G$ be a simple algebraic group over an algebraically closed field $k$, where $\mathrm{c}\mathrm{h}\mathrm{a}\mathrm{r}k$ is either 0 or a good prime for $G$. We consider the modality $\mathrm{m}\mathrm{o}\mathrm{d}(B:\mathfrak{u})$ of the action of a Borel subgroup $B$ of $G$ on the Lie algebra $\mathfrak{u}$ of the unipotent radical of $B$, and report on computer calculations used to show that $$\mathrm{m}\mathrm{o}\mathrm{d}$(B:\mathfrak u) = 20$,when$G$isoftype$\mathrm E_8$. This completes the determination of the values for $\mathrm{m}\mathrm{o}\mathrm{d}(B:\mathfrak{u})$ for $G$ of exceptional type.