  An angular analysis of the $B^0 \rightarrow K^{*0} e^+ e^-$ decay is
performed using a data sample, corresponding to an integrated luminosity of 3.0
${\mbox{fb}^{-1}}$, collected by the LHCb experiment in $pp$ collisions at
centre-of-mass energies of 7 and 8 TeV during 2011 and 2012. For the first time
several observables are measured in the dielectron mass squared ($q^2$)
interval between 0.002 and 1.120${\mathrm{\,Ge\kern -0.1em V^2\!/}c^4}$. The
angular observables $F_{\mathrm{L}}$ and $A_{\mathrm{T}}^{\mathrm{Re}}$ which
are related to the $K^{*0}$ polarisation and to the lepton forward-backward
asymmetry, are measured to be $F_{\mathrm{L}}= 0.16 \pm 0.06 \pm0.03$ and
$A_{\mathrm{T}}^{\mathrm{Re}} = 0.10 \pm 0.18 \pm 0.05$, where the first
uncertainty is statistical and the second systematic. The angular observables
$A_{\mathrm{T}}^{(2)}$ and $A_{\mathrm{T}}^{\mathrm{Im}}$ which are sensitive
to the photon polarisation in this $q^2$ range, are found to be
$A_{\mathrm{T}}^{(2)} = -0.23 \pm 0.23 \pm 0.05$ and
$A_{\mathrm{T}}^{\mathrm{Im}} =0.14 \pm 0.22 \pm 0.05$. The results are
consistent with Standard Model predictions.
