= Coset norm of a modular form
{title2=$\operatorname{Nm}(f)=\prod_{\alpha\in\Gamma\backslash\Gamma'}f|_k\alpha$}
For a finite-index inclusion of modular groups and a form with trivial multiplier, multiply its <slash operator for modular forms> translates over left coset representatives. Right multiplication permutes the factors, producing a form of weight $k[\Gamma':\Gamma]$ for the larger group. <modular cusp> <cusp widths> determine the orders contributed by the factors; the product is nonzero if the original form is nonzero.
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