Siegel cusp form of degree 2 (awaiting review)

Let $f$ be a vector-valued Siegel modular form on an arithmetic subsgroup $\Gamma$ of $\GSp(4,\Q)$ then $f$ is called a cusp form if for any $\gamma\in \Sp(4,\Q)$, we have \[ \Phi(f\vert_{k,j}\gamma)=0 \] where $\Phi$ denotes the Siegel operator while $\vert_{k,j}$ denotes the slash operator.