  We present $I=1/2$ $D^\ast\pi$ scattering amplitudes from lattice QCD and
determine two low-lying $J^P=1^+$ axial-vector $D_1$ states and a $J^P=2^+$
tensor $D_2^\ast$. Computing finite-volume spectra at a light-quark mass
corresponding to $m_\pi=391$ MeV, for the first time, we are able to constrain
coupled $J^P=1^+$ $D^\ast\pi$ amplitudes with $^{2S+1}\ell_J\,=\,^3S_1$ and
$^3\!D_1$ as well as coupled $J^P=2^+$ $D\pi\{^1\!D_2\}$ and $D^\ast\pi
\{^3\!D_2\}$ amplitudes via L\"uscher's quantization condition. Analyzing the
scattering amplitudes for poles we find a near-threshold bound state, producing
a broad feature in $D^\ast\pi\{^3\!S_1\}$. A narrow bump occurs in
$D^\ast\pi\{^3\!D_1\}$ due to a $D_1$ resonance. A single resonance is found in
$J^P=2^+$ coupled to $D\pi$ and $D^\ast\pi$. A relatively low mass and large
coupling is found for the lightest $D_1$, suggestive of a state that will
evolve into a broad resonance as the light quark mass is reduced. An earlier
calculation of the scalar $D_0^\ast$ using the same light-quark mass enables
comparisons to the heavy-quark limit.
