An elliptic curve over a scheme $S$ is the data of a proper smooth morphism of schemes $\pi: E\rightarrow S$ whose geometric fibres are connected curves of genus $1$ and a section $e: S \rightarrow E$.

A level $\Gamma(N)$–structure on an elliptic curve $E$ over a scheme $S$ is an isomorphism $E[N] \rightarrow (\mathbb{Z}/N\mathbb{Z})_S\times_S(\mathbb{Z}/N\mathbb{Z})_S$ of group schemes over $S$.

Let $R$ be an integral domain. The category $R-Ell$ is the category whose objects are elliptic curves $E\rightarrow S$ with $S$ an $R$-scheme and whose morphisms are cartesian square diagrams of $R$-morphisms.

$\Gamma(N)$ is a functor $R-Ell^{op}\rightarrow Set$ sending an elliptic curve to the set of level $\Gamma(N)$-structures on it.

For $N\geq 3$ and $R=\mathbb{Z}[1/N]$, results of Katz and Mazur imply that $\Gamma(N)$ is representable by an elliptic curve whose base is a smooth affine $\mathbb{Z}[1/n]$-curve.

What I am asking is for $N=1, 2$ is the moduli problem representable by something geometric (algebraic space, DM stack etc.)? Is there a reference establishing its good properties? I find navigating the literature difficult.