The axisymmetric electrostatic eigenmodes of spheroidal pure electron plasmas have been studied experimentally. It is confirmed that the observed spheroidal plasma attains a theoretically expected equilibrium density distribution, with the exception of a low-density distribution surrounding the plasma. When the eigenmode frequency observed for the plasma is compared with the frequency predicted by the dispersion relation derived under the assumption of ideal conditions wherein the temperature is zero and the boundary is located at an infinite distance from the plasma, it is observed that the absolute value of the observed frequency is systematically higher than the theoretical prediction. Experimental examinations and numerical calculations indicate that the finite temperature effect alone cannot account for the upward shift of the eigenmode frequency, which is significantly affected by image charges induced on the conducting boundary.