We identify the chiral and angular momentum content of the
leading quark-antiquark Fock component for the $\rho(770)$ and
$\rho(1450)$ mesons using a two-flavor lattice simulation with dynamical
Overlap Dirac fermions. We extract this information from the overlap factors
of two interpolating fields with different chiral structure. We find that
in the
angular momentum basis the $\rho(770)$ is a $^3S_1$
state, in accordance with the quark model. The $\rho(1450)$ is a $^3D_1$ state,
showing that the quark model wrongly assumes the $\rho(1450)$ to be a
radial excitation of the $\rho(770)$.
Further, we apply a low-mode truncation scheme of the Dirac operator and study
its effects on the chiral structure of the mesons.