Extending the unconditional support in an Iwaniec–Luo–Sarnak family

We study the harmonically weighted one-level density of low-lying zeros of $L\text{ -}$functions in the family of holomorphic newforms of fixed even weight $k$ and prime level $N$ tending to infinity. For this family, Iwaniec, Luo and Sarnak proved that the Katz–Sarnak prediction for the one-level density holds unconditionally when the support of the Fourier transform of the implied test function is contained in $(-3∕2,3∕2)$. This result was improved by Ricotta–Royer, who increased the admissible support for $k\ge 4$ in a way that is asymptotically as good as the best known GRH result. We extend the admissible support for all $k\ge 2$ to $(-{\Theta }_k,{\Theta }_k)$, where ${\Theta }_2=1.866\dots <!--FUNCTION\; APPLICATION-->$ and ${\Theta }_k$ tends monotonically to $2$ asymptotically five times faster than what was previously known. The main novelty in our analysis is the use of zero-density estimates for Dirichlet $L$-functions.