We present a new measurement of the CKM matrix element $|V_{cb}|$ from $B^{0} to D^{*-} ell^+ u_ell$ decays, reconstructed with the full Belle data set of $711 , rm fb^{-1}$ integrated luminosity. Two form factor parameterizations, originally conceived by the Caprini-Lellouch-Neubert (CLN) and the Boyd, Grinstein and Lebed (BGL) groups, are used to extract the product $mathcal{F}(1)eta_{rm EW}|V_{cb}|$ and the decay form factors, where $mathcal{F}(1)$ is the normalization factor and $eta_{rm EW}$ is a small electroweak correction. In the CLN parameterization we find $mathcal{F}(1)eta_{rm EW}|V_{cb}| = (35.06 pm 0.15 pm 0.56) times 10^{-3}$, $rho^{2}=1.106 pm 0.031 pm 0.007$, $R_{1}(1)=1.229 pm 0.028 pm 0.009$, $R_{2}(1)=0.852 pm 0.021 pm 0.006$. For the BGL parameterization we obtain $mathcal{F}(1)eta_{rm EW}|V_{cb}|= (34.93 pm 0.23 pm 0.59)times 10^{-3}$, which is consistent with the World Average when correcting for $mathcal{F}(1)eta_{rm EW}$. The branching fraction of $B^{0} to D^{*-} ell^+ u_ell$ is measured to be $mathcal{B}(B^{0}rightarrow D^{*-}ell^{+} u_{ell}) = (4.90 pm 0.02 pm 0.16)%$. We also present a new test of lepton flavor universality violation in semileptonic $B$ decays, $frac{{cal B }(B^0 to D^{*-} e^+ u)}{{cal B }(B^0 to D^{*-} mu^+ u)} = 1.01 pm 0.01 pm 0.03~$. The errors correspond to the statistical and systematic uncertainties respectively. This is the most precise measurement of $mathcal{F}(1)eta_{rm EW}|V_{cb}|$ and form factors to date and the first experimental study of the BGL form factor parameterization in an experimental measurement.
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