Magneto-transport measurements on electrons confined to a 57 nm-wide, GaAs quantum well reveal that the correlated electron states at low Landau level fillings ($ u$) display a remarkable dependence on the symmetry of the electron charge distribution. At a density of $1.93 times 10^{11}$ cm$^{-2}$, a developing fractional quantum Hall state is observed at the even-denominator filling $ u = 1/4$ when the distribution is symmetric, but it quickly vanishes when the distribution is made asymmetric. At lower densities, as we make the charge distribution asymmetric, we observe a rapid strengthening of the insulating phases that surround the $ u = 1/5$ fractional quantum Hall state.
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