  The purpose of this paper is to provide answers to some questions raised in a
paper by Kaneko and Koike about the modularity of the solutions of a
differential equations of hypergeometric type. In particular, we provide a
number-theoretic explanation of why the modularity of the solutions occurs in
some cases and does not occur in other cases. This also proves their conjecture
on the completeness of the list of modular solutions after adding some missing
cases.
