  The cuprate high temperature superconductors develop spontaneous charge
density wave (CDW) order below a temperature $T_{CDW}$ and over a wide range of
hole doping (p). An outstanding challenge in the field is to understand whether
this modulated phase is related to the more exhaustively studied pseudogap and
superconducting phases. To address this issue it is important to extract the
energy scale $\Delta_{CDW}$ associated with the charge modulations, and to
compare it with the pseudogap (PG) $\Delta_{PG}$ and the superconducting gap
$\Delta_{SC}$. However, while $T_{CDW}$ is well-characterized from earlier
works little has been known about $\Delta_{CDW}$ until now. Here, we report the
extraction of $\Delta_{CDW}$ for several cuprates using electronic Raman
spectroscopy. Crucially, we find that, upon approaching the parent Mott state
by lowering $p$, $\Delta_{CDW}$ increases in a manner similar to the doping
dependence of $\Delta_{PG}$ and $\Delta_{SC}$. This shows that CDW is an
unconventional order, and that the above three phases are controlled by the
same electronic correlations. In addition, we find that $\Delta_{CDW} \approx
\Delta_{SC}$ over a substantial doping range, which is suggestive of an
approximate emergent symmetry connecting the charge modulated phase with
superconductivity.
