  We study an extreme value distribution for the unipotent flow on the modular
surface $\mathrm{SL}_2(\mathbb{R})/\mathrm{SL}_2(\mathbb{Z})$. Using tools from
homogenous dynamics and geometry of numbers we prove the existence of a
continuous distribution function $F(r)$ for the normalized deepest cusp
excursions of the unipotent flow. We find closed analytic formulas for $F(r)$
for $r \in [-\frac{1}{2} \log 2, \infty)$, and establish asymptotic behavior of
$F(r)$ as $r \to -\infty$.
