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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 reference "Local newforms for GSp(4)" by Brooks Roberts and Ralf Schmidt).

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

Knowl status:
  • Review status: beta
  • Last edited by David Roe on 2018-12-13 14:20:12
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