Fiber product (awaiting review)

If $H$ and $H'$ are open subgroups of $\GL_2(\widehat \Z)$, the fiber product $X_H\times X_H'$ of the modular curves $X_H$ and $X_H'$ is their fiber product as algebraic stacks over $X(1)$.

Concretely, in the case that $H$ and $H'$ have coprime levels $N$ and $N'$, this means that $X_H\times X_H' = X_{H\cap H'}$, a modular curve of level $NN'$.