  We investigate non-semisimple modular categories with an eye towards a
structure theory, low-rank classification, and applications to low dimensional
topology and topological physics. We aim to extend the well-understood theory
of semisimple modular categories to the non-semisimple case by using
representations of factorizable ribbon Hopf algebras as a case study. We focus
on the Cohen-Westreich modular data, which is obtained from the
Lyubashenko-Majid modular representation restricted to the Higman ideal of a
factorizable ribbon Hopf algebra. The Cohen-Westreich $S$-matrix diagonalizes
the mixed fusion rules and reduces to the usual $S$-matrix for semisimple
modular categories. The paper includes detailed studies on small quantum groups
$U_qsl(2)$ and the Drinfeld doubles of Nichols Hopf algebras, especially the
$\mathrm{SL}(2, \mathbb{Z})$-representation on their centers, Cohen-Westreich
modular data, and the congruence kernel theorem's validity.
