  We investigate the low-lying eigenmodes of the Dirac matrix with the aim to
gain more insight into the temperature dependence of the anomalous $U_A(1)$
symmetry. We use the overlap operator to probe dynamical QCD configurations
generated with (2+1)-flavors of highly improved staggered quarks. We find no
evidence of a gap opening up in the infrared region of the eigenvalue spectrum
even at $1.5\,T_c$, $T_c$ being the chiral crossover temperature. Instead, we
observe an accumulation of near-zero eigenmodes. We argue that these near-zero
eigenmodes are primarily responsible for the anomalous breaking of the axial
symmetry still being effective. At $1.5\,T_c$, these near-zero eigenmodes
remain localized and their distribution is consistent with the dilute instanton
gas picture. At this temperature, the average size of the instantons is
$0.223(8)\,\text{fm}$ and their density is $0.147(7)\,\text{fm}^{-4}$.
