  In this work we revisit the "holomorphic modular bootstrap", i.e. the
classification of rational conformal field theories via an analysis of the
modular differential equations satisfied by their characters. By making use of
the representation theory of ${\rm PSL}(2,\mathbb{Z}_n)$, we describe a method
to classify allowed central charges and weights $(c,h_i)$ for theories with any
number of characters $d$. This allows us to avoid various bottlenecks
encountered previously in the literature, and leads to a classification of
consistent characters up to $d=5$ whose modular differential equations are
uniquely fixed in terms of $(c,h_i)$. In the process, we identify the full set
of constraints on the allowed values of the Wronskian index for fixed $d\leq
5$.
