  Recent theories of charge density wave (CDW) order in high temperature
superconductors have predicted a primarily d CDW orbital symmetry. Here, we
report on the orbital symmetry of CDW order in the canonical cuprate
superconductors La1.875Ba0.125CuO4 (LBCO) and YBa2Cu3O6.67 (YBCO), using
resonant soft x-ray scattering and a model mapped to the CDW orbital symmetry.
From measurements sensitive to the O sublattice, we conclude that LBCO has
predominantly s' CDW orbital symmetry, in contrast to the d orbital symmetry
recently reported in other cuprates. Additionally, we show for YBCO that the
CDW orbital symmetry differs along the a and b crystal axes and that these both
differ from LBCO. This work highlights CDW orbital symmetry as an additional
key property that distinguishes the different cuprate families. We discuss how
the CDW symmetry may be related to the "1/8--anomaly" and to static spin
ordering.
