  We measure the mass dependence of the forward-backward charge asymmetry in
157,553 $p\bar{p} \rightarrow Z/\gamma^{*} \rightarrow e^+e^-$ interactions,
corresponding to 5.0 fb$^{-1}$ of integrated luminosity collected by the D0
experiment at the Fermilab Tevatron Collider at $\sqrt{s}=1.96$ TeV. The
effective weak mixing angle ($\sin^2\theta_{eff}^{lept}$) from this process
involving predominantly the first generation of quarks is extracted as
$\sin^2\theta_{eff}^{lept} = 0.2309 \pm 0.0008 ({stat.}) \pm 0.0006 ({syst.})$.
We also present the most precise direct measurement of the vector and
axial-vector couplings of $u$ and $d$ quarks to the $Z$ boson.
