Trigonal Modular Curves $X_0^{+d}(N)$

Abstract

For a positive integer $N$, let $X_0^*(N)$ denote the quotient curve of $X_0(N)$ by the Atkin-Lehmer involutions. In this paper, we determine the trigonality of $X_0^*(N)$ for all $N$. It turns out that there are seven values of $N$ for which $X_0^*(N)$ is a non-trivial trigonal curve.