A model-independent multipole analysis of $^{238}\mathrm{U}$(e,e'f) coincidence data, taken at four momentum transfers (0.2\ensuremath{\le}${q}_{\mathrm{eff}\mathrm{\ensuremath{\le}}0.7}$ ${\mathrm{fm}}^{\mathrm{\ensuremath{-}}1}$; \ensuremath{\omega}=4--22 MeV) yields both E1, E2/E0, and E3 form factors and strength distributions. The E2/E0 strength distribution in the fission channel shows two distinct bumps centered at \ensuremath{\omega}\ensuremath{\simeq}10 and 14 MeV, exhausting up to 12 MeV (19\ifmmode\pm\else\textpm\fi{}2)% of the isoscalar E2 sum rule. The extracted form factors can be described within a hydrodynamical model by use of parameters ${c}_{\mathrm{tr}/{c}_{0}=1.2}$ and 1.0 for E1 and E2, respectively.