  We perform a high statistics study of the $J^{P}=0^{+}$ and $1^{+}$
charmed-strange mesons, $D_{s0}^*(2317)$ and $D_{s1}(2460)$, respectively. The
effects of the nearby $DK$ and $D^{*}K$ thresholds are taken into account by
employing the corresponding four quark operators. Six ensembles with $N_f=2$
non-perturbatively ${\cal O}(a)$ improved clover Wilson sea quarks at $a=0.07$
fm are employed, covering different spatial volumes and pion masses: linear
lattice extents $L/a=24,32,40,64$, equivalent to 1.7 fm to 4.5 fm, are realised
for $m_{\pi}=290$ MeV and $L/a=48,64$ or 3.4 fm and 4.5 fm for an almost
physical pion mass of $150$ MeV. Through a phase shift analysis and the
effective range approximation we determine the scattering lengths, couplings to
the thresholds and the infinite volume masses. Differences relative to the
experimental values are observed for these masses, however, this is likely to
be due to discretisation effects as spin-averaged quantities and splittings are
reasonably compatible with experiment. We also compute the weak decay constants
of the scalar and axialvector and find $f_V^{0^+}=114(2)(0)(+5)(10)$ MeV and
$f_A^{1^+}=194(3)(4)(+5)(10)$ MeV, where the errors are due to statistics,
renormalisation, finite volume and lattice spacing effects.
