  Understanding the nature of the mysterious pseudogap phenomenon is one of the
most important issues associated with cuprate high-$T_c$ superconductors. Here,
we report $^{17}$O nuclear magnetic resonance (NMR) studies on two planar
oxygen sites in stoichiometric cuprate YBa$_2$Cu$_4$O$_8$ to investigate the
symmetry breaking inside the pseudogap phase. We observe that the Knight shifts
of the two oxygen sites are identical at high temperatures but different below
$T_{\rm nem} \sim$ 185 K, which is close to the pseudogap temperature
$T^{\ast}$. Our result provides a microscopic evidence for intra-unit-cell
electronic nematicity. The difference in quadrupole resonance frequency between
the two oxygen sites is unchanged below $T_{\rm nem}$, which suggests that the
observed nematicity does not directly stem from the local charge density
modulation. Furthermore, a short-range charge density wave (CDW) order is
observed below $T \simeq$ 150 K. The additional broadening in the $^{17}$O-NMR
spectra because of this CDW order is determined to be inequivalent for the two
oxygen sites, which is similar to that observed in case of nematicity. These
results suggest a possible connection between nematicity, CDW order, and
pseudogap.
