Holomorphic modular bootstrap revisited

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