A bstract An angular analysis of the B 0 → K* 0 e + e − decay is performed using a data sample corresponding to an integrated luminosity of 9 fb − 1 of pp collisions collected with the LHCb experiment. The analysis is conducted in the very low dielectron mass squared ( q 2 ) interval between 0 . 0008 and 0 . 257 GeV 2 , where the rate is dominated by the B 0 → K * 0 γ transition with a virtual photon. The fraction of longitudinal polarisation of the K * 0 meson, F L , is measured to be F L = (4 . 4 ± 2 . 6 ± 1 . 4)%, where the first uncertainty is statistical and the second systematic. The $$ {A}_{\mathrm{T}}^{\mathrm{Re}} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>A</mml:mi> <mml:mi>T</mml:mi> <mml:mi>Re</mml:mi> </mml:msubsup> </mml:math> observable, which is related to the lepton forward-backward asymmetry, is measured to be $$ {A}_{\mathrm{T}}^{\mathrm{Re}} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>A</mml:mi> <mml:mi>T</mml:mi> <mml:mi>Re</mml:mi> </mml:msubsup> </mml:math> = − 0 . 06 ± 0 . 08 ± 0 . 02. The $$ {A}_{\mathrm{T}}^{(2)} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>A</mml:mi> <mml:mi>T</mml:mi> <mml:mfenced> <mml:mn>2</mml:mn> </mml:mfenced> </mml:msubsup> </mml:math> and $$ {A}_{\mathrm{T}}^{\mathrm{Im}} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>A</mml:mi> <mml:mi>T</mml:mi> <mml:mi>Im</mml:mi> </mml:msubsup> </mml:math> transverse asymmetries, which are sensitive to the virtual photon polarisation, are found to be $$ {A}_{\mathrm{T}}^{(2)} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>A</mml:mi> <mml:mi>T</mml:mi> <mml:mfenced> <mml:mn>2</mml:mn> </mml:mfenced> </mml:msubsup> </mml:math> = 0 . 11 ± 0 . 10 ± 0 . 02 and $$ {A}_{\mathrm{T}}^{\mathrm{Im}} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>A</mml:mi> <mml:mi>T</mml:mi> <mml:mi>Im</mml:mi> </mml:msubsup> </mml:math> = 0 . 02 ± 0 . 10 ± 0 . 01. The results are consistent with Standard Model predictions and provide the world’s best constraint on the b → sγ photon polarisation.