Large Hecke eigenvalues and an Omega result for non Saito--Kurokawa lifts

We prove a result on the distribution of Hecke eigenvalues, ${\mu }_F(p^r)$ (for $r=1,2$ or $3$) of a non Saito–Kurokawa lift $F$ of degree $2$. As a consequence, we obtain an Omega result for the Hecke eigenvalues for such an $F$, which is the best possible in terms of orders of magnitude.