Bounds for the Petersson norms of the pullbacks of Saito-Kurokawa lifts

Abstract

Using the amplification technique, we prove that `mass' of the pullback of the Saito-Kurokawa lift of a Hecke eigen form $g\in S_{2k}$ is bounded by $k^{1-\frac{1}{210}+\epsilon}$. This improves the previously known bound $k$ for this quantity.