The first negative eigenvalue of Yoshida lifts

We prove that for any given $ϵ>0$, the first negative eigenvalue of the Yoshida lift $F$ of a pair of elliptic cusp forms $f,g$ having square-free levels (where $g$ has weight $2$ and satisfies $(\log Q_g{)}^2\ll \log Q_f$), occurs before $c_{ϵ}\cdot Q_F^{1\mathrm{/}2-2\theta +ϵ}$; where $Q_F,Q_f,Q_g$ are the analytic conductors of $F,f,g$ respectively, $\theta < 1/4$,and$c_{\epsilon}$isaconstantdependingonlyon$\epsilon$.