$X_{\pm1}(M,MN)$ (awaiting review)

$X_{\pm1}(M,MN)$ is the modular curve $X_H$ for $H\le \GL_2(\widehat\Z)$ the inverse image of $\pm\begin{pmatrix} 1 & M* \\ 0 & 1+M* \end{pmatrix} \subset \GL_2(\Z/MN\Z)$. The modular curve $X_1(M,MN)$ is one of its quadratic refinements.

The canonical field of definition of $X_{\pm 1}(M,MN)$ is $\Q(\zeta_M)$, which means that the database of modular curves $X_H/\Q$ only includes $X_{\pm 1}(M,MN)$ for $M\le 2$.