  Several early Universe scenarios predict a direction-dependent spectrum of
primordial curvature perturbations. This translates into the violation of the
statistical isotropy of cosmic microwave background radiation. Previous
searches for statistical anisotropy mainly focussed on a quadrupolar
direction-dependence characterised by a single multipole vector and an overall
amplitude $g_*$. Generically, however, the quadrupole has a more complicated
geometry described by two multipole vectors and $g_*$. This is the subject of
the present work. In particular, we limit the amplitude $g_*$ for different
shapes of the quadrupole by making use of Planck 2015 maps. We also constrain
certain inflationary scenarios which predict this kind of more general
quadrupolar statistical anisotropy.
