Standard modular curves (awaiting review)

Let $M$ and $N$ denote positive integers and $\ell$ a prime. Each modular curve below "parametrizes" elliptic curves with a particular type of level structure. Standard modular curves include:

$X_0(N)$, $X_1(N)$, $X_{\pm 1}(N)$, $X_{\mathrm{arith},1}(M,MN)$, $X_{\mathrm{arith},\pm 1}(M,MN)$, $X(N)$, $X_{\mathrm{sp}}(N)$, $X_{\mathrm{sp}}^+(N)$, $X_{\mathrm{ns}}(N)$, $X_{\mathrm{ns}}^+(N)$, $X_{S_4}(\ell)$, $X_{\mathrm{arith}}(N)$

The curves above are all modular curves specified by an open subgroup $H \le \GL_2(\widehat{\Z})$ of level $N$, $MN$, or $\ell$.