  We introduce a cumulant expansion to parameterize possible initial conditions
in relativistic heavy ion collisions. We show that the cumulant expansion
converges and that it can systematically reproduce the results of Glauber type
initial conditions. At third order in the gradient expansion, the cumulants
characterize the triangularity $<r^3 \cos3(\phi - \psi_{3,3})>$ and the dipole
asymmetry $<r^3 \cos(\phi- \psi_{1,3})>$ of the initial entropy distribution.
We show that for mid-peripheral collisions the orientation angle of the dipole
asymmetry $\psi_{1,3}$ has a $20%$ preference out of plane. This leads to a
small net $v_1$ out of plane. In peripheral and mid-central collisions the
orientation angles $\psi_{1,3}$ and $\psi_{3,3}$ are strongly correlated. We
study the ideal hydrodynamic response to these cumulants and determine the
associated $v_1/\epsilon_1$ and $v_3/\epsilon_3$ for a massless ideal gas
equation of state. $v_1$ and $v_3$ develop towards the edge of the nucleus, and
consequently the final spectra are more sensitive to the viscous dynamics of
freezeout. The hydrodynamic calculations for $v_3$ are compared to Alver and
Roland fit of two particle correlation functions. Finally, we propose to
measure the $v_1$ associated with the dipole asymmetry and the correlations
between $\psi_{1,3}$ and $\psi_{3,3}$ by measuring a two particle correlation
with respect to the participant plane, $<\cos(\phi_a - 3\phi_b + 2\Psi_{PP})>$.
The hydrodynamic prediction for this correlation function is several times
larger than a correlation currently measured by the STAR collaboration,
$<\cos(\phi_a + \phi_\b - 2\Psi_{PP})>$.
