Before today, every source on the subject talks about algebraic models of the modular curve $X(N)$ over $\mathbb{Q}(\zeta_N)$, but in Ogg's paper "Rational Points on Certain Elliptic Modular Curves", he says that there is a canonical $\mathbb{Q}$-rational model of $X(N)$, where the cusps are rational over $\mathbb{Q}(\zeta_N)$, and identifying the cusps with pairs $(x,y)\in(\mathbb{Z}/N\mathbb{Z})^2/(\pm 1)$ for which $\gcd(x,y,N) = 1$, there is an action of the Galois group $(\mathbb{Z}/N\mathbb{Z})^*$ on the cusps acting via multiplication on the first coordinate (ie, $x$).

Ogg calls it a "model of Shimura, as communicated to me by Casselman", and cites a preprint: "W. Casselman, *The Arithmetic of the cusps of the classical modular curves* (to appear)", which I can't seem to find anywhere.

Can someone point out a good reference for this model?

thanks,

- will