Regularity of quotients of Drinfeld modular schemes

Let $A$ be the coordinate ring of a projective smooth curve over a finite field minus a closed point. For a nontrivial ideal $I\subset A$, Drinfeld defined the notion of structure of level $I$ on a Drinfeld module. We extend this to that of level $N$, where $N$ is a finitely generated torsion $A$-module. The case where $N=(I^{-1}\mathrm{/}A{)}^d$, where $d$ is the rank of the Drinfeld module,coincides with the structure of level $I$. The moduli functor is representable by a regular affine scheme. The automorphism group ${\mathrm{A}\mathrm{u}\mathrm{t}}_A(N)$ acts on the moduli space. Our theorem gives a class of subgroups for which the quotient of the moduli scheme is regular. Examples include generalizations of ${\mathrm{\Gamma }}_0$ and of ${\mathrm{\Gamma }}_1$. We also show that parabolic subgroups appearing in the definition of Hecke correspondences are such subgroups.