  Motivated by the recent scanning tunneling microscopy (STM) and neutron
scattering experiments, we investigate various charge density wave orders
coexisting with superconductivity in the cuprate superconductors. The explicit
expressions of the local density of states and its Fourier component at the
ordering wavevector for the weak charge modulations are derived. It is shown
that the STM experiments in $Bi_2Sr_2CaCu_2O_{8+\delta}$ cannot be explained by
a site- or bond-centered charge modulation alone, but agree well with the
presence of the dimerization hopping and transverse pairing modulations. We
also calculate the spectral function for the charged stripes, which is measured
by the ARPES experiments.
