  The connection between initial-state geometry and anisotropic flow can be
quantified through a well-established mapping between $p_T$-integrated flow
harmonics and cumulants of the initial transverse energy distribution. In this
paper we successfully extend this mapping to also include $p_T$-differential
flow. In doing so, we find that subleading principal components of anisotropic
flow can reveal previously unobserved details of the hydrodynamic response, in
both the linear and the nonlinear regimes. Most importantly, we show that they
provide novel information on the small-scale structures present in the initial
stage of relativistic heavy-ion collisions.
