  Full-sky maps of the cosmic microwave background temperature reveal a 7%
asymmetry of fluctuation power between two halves of the sky. A common
phenomenological model for this asymmetry is an overall dipole modulation of
statistically isotropic fluctuations, which produces particular off-diagonal
correlations between multipole coefficients. We compute these correlations and
construct corresponding estimators for the amplitude and direction of the
dipole modulation. Applying these estimators to various cut-sky temperature
maps from Planck and WMAP data shows consistency with a dipole modulation,
differing from a null signal at 2.5$\sigma$, with an amplitude and direction
consistent with previous fits based on the temperature fluctuation power. The
signal is scale dependent, with a statistically significant amplitude at
angular scales larger than 2 degrees. Future measurements of microwave
background polarization and gravitational lensing can increase the significance
of the signal. If the signal is not a statistical fluke in an isotropic
Universe, it requires new physics beyond the standard model of cosmology.
