Search for Quadrupole Strength in the Electroexcitation of theΔ+(1232)

High-precision ${}^1\mathrm{H}\left({e,e}^{\prime }p\right){\pi }^0$ measurements at $Q^2=0.126\mathrm{}(\mathrm{GeV}/c{)}^2$ are reported, which allow the determination of quadrupole amplitudes in the ${\gamma }^{*}N\to \Delta$ transition; they simultaneously test the reliability of electroproduction models. The derived quadrupole-to-dipole ( $I=3/2\mathrm{}$) amplitude ratios, $R_{\mathrm{SM}}=(-6.5\mathrm{}\pm {0.2}_{\mathrm{stat}+\mathrm{sys}}\pm {2.5}_{\mathrm{mod}})\%$ and $R_{\mathrm{EM}}=(-2.1\mathrm{}\pm {0.2}_{\mathrm{stat}+\mathrm{sys}}\pm {2.0}_{\mathrm{mod}})\%$, are dominated by model error. Previous $R_{\mathrm{SM}}$ and $R_{\mathrm{EM}}$ results should be reconsidered after the model uncertainties associated with the method of their extraction are taken into account.