First Rankin-Cohen bracket ($[f,g{]}_1=\ell gDf-kfDg$)

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 $kfDg-\ell gDf$; its negative is equally modular. Differentiation kills each constant Fourier coefficient, proving cusp vanishing.