= First Rankin-Cohen bracket
{title2=$[f,g]_1=\ell gDf-kfDg$}
For <modular forms> $f,g$ of weights $k,\ell$, respectively, the displayed combination cancels the anomaly in <derivative transformation of a weak modular form> and is a weight-$k+\ell+2$ <cusp form>. Equivalently, for weights $k,\ell$ in the order $f,g$, a conventional first bracket is $k fDg-\ell gDf$; its negative is equally modular. Differentiation kills each constant <Fourier coefficient>, proving cusp vanishing.
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