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We give a formula for divisors of modular units on $X_1(N)$ and use it to prove that the $\mathbb{Q}$-gonality of the modular curve $X_1(N)$ is bounded above by $\left[\frac{11N^2}{840}\right]$, where $[\bullet]$ denotes the nearest integer.

A Divisor Formula and a Bound on the $$\mathbb {Q}$$-Gonality of the Modular Curve $$X_1(N)$$