Paramodular newform (reviewed)

A paramodular form on $K(N)$ that is a Hecke eigenform is a newform if it is not a Gritsenko Lift and it is not the result of applying a level raising Hecke operator to a paramodular form of a lower level. There are three level raising operators (see Local newforms for GSp(4) by Brooks Roberts and Ralf Schmidt [10.1007/978-3-540-73324-9]):

$$\begin{aligned} V_m^+:& S_k(K(N)) \to S_k(K(mN))\\ V_m^-:& S_k(K(N)) \to S_k(K(mN))\\ U_m:& S_k(K(N)) \to S_k(K(m^2 N)). \end{aligned}$$