= Meromorphic n-differential
{title2=$\omega\in\Gamma_{\mathrm{mer}}(K_X^{\otimes n})$}
On a <Riemann surface>, a meromorphic n-differential is a meromorphic section of the $n$th power of the <canonical bundle>. In a coordinate it is $F(z)(dz)^n$, with coefficients transforming by the $n$th power of the derivative. At a ramification coordinate $w=t^e$, its pullback has order $e\operatorname{ord}_w\omega+n(e-1)$. At a <modular cusp>, the exponential coordinate gives $dz=(h/(2\pi i))dq/q$, so a weight-$2n$ form of cusp order $v$ produces a differential of order $v-n$.
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