Measurement of branching fractions of color-suppressed decays of the $B^0$ meson to $D^{\left(*\right)0\mathrm{}}{\pi }^0,$ $D^{\left(*\right)0\mathrm{}}\eta ,$ $D^{\left(*\right)0\mathrm{}}\omega ,$ and $D^0{\eta }^{\prime }$

Using a sample of $88.8\times {10}^6$ $B\overline{B}$ events collected with the BABAR detector at the PEP-II storage rings at the Stanford Linear Accelerator Center, we measure the branching fractions of seven color-suppressed B-meson decays: $\mathcal{B}(B^0\to D^0{\pi }^0)=[2.9\pm 0.2(\mathrm{stat})\pm 0.3(\mathrm{syst}\left)\right]\times {10}^{-4},$ $\mathcal{B}(B^0\to D^{*0}{\pi }^0)=[2.9\pm 0.4(\mathrm{stat})\pm 0.5(\mathrm{syst}\left)\right]\times {10}^{-4},$ $\mathcal{B}(B^0\to D^0\eta )=[2.5\pm 0.2(\mathrm{stat})\pm 0.3(\mathrm{syst}\left)\right]\times {10}^{-4},$ $\mathcal{B}(B^0\to D^{*0}\eta )=[2.6\pm 0.4(\mathrm{stat})\pm 0.4(\mathrm{syst}\left)\right]\times {10}^{-4},$ $\mathcal{B}(B^0\to D^0\omega )=[3.0\pm 0.3(\mathrm{stat})\pm 0.4(\mathrm{syst}\left)\right]\times {10}^{-4},$ $\mathcal{B}(B^0\to D^{*0}\omega )=[4.2\pm 0.7(\mathrm{stat})\pm 0.9(\mathrm{syst}\left)\right]\times {10}^{-4},$ and $\mathcal{B}(B^0\to D^0{\eta }^{\prime })=[1.7\pm 0.4(\mathrm{stat})\pm 0.2(\mathrm{syst}\left)\right]\times {10}^{-4}.$ We set the 90% confidence-level upper limit: $\mathcal{B}(B^0\to D^{*0}{\eta }^{\prime })<\mathrm{}2.6\mathrm{}\times {10}^{-4}.$ The channels $B^0\to D^{*0}\eta ,$ $D^{*0}\omega ,$ and $D^0{\eta }^{\prime }$ are seen with more than five-sigma statistical significance. All of these branching fractions are significantly larger than theoretical expectations based on the “naive” factorization model.