Pullbacks of Saito-Kurokawa lifts of square-free levels, their non-vanishing and the $L^2$-mass

Pramath Anamby, Soumya Das

We obtain the full spectral decomposition of the pullback of a Saito-Kurokawa (SK) newform $F$ of odd, square-free level; and show that the projections onto the elements $\mathbf g…