In this paper we study a negatively charged exciton (NCE),which is trapped by a two-dimensional (2D)parabolic potential.By using matrix diagonalization techniques,the correlation energies of the low-lying states withL = 0,1,and 2 are calculated as a function of confinement strength.We find that the size effects of different states aredifferent.This phenomenon can be explained as a hidden symmetry,which is originated purely from symmetry.Basedon symmetry,the features of the low-lying states are discussed in the influence of the 2D parabolic potential well.Itis found that the confinement may cause accidental degeneracies between levels with different low-excited states.It isshown that the effect of quantum confinement on the binding energy of the heavy hole is stronger than that of a lighthole. In this paper we study a negatively charged exciton (NCE), which is trapped by a two-dimensional (2D) parabolic potential. By using matrix diagonalization techniques, the correlation energies of the low-lying states with L = 0, 1 and 2 are calculated as a function of confinement strength. We find that the size effects of different states are different. This phenomenon can be explained as a hidden symmetry, which is originated purely from symmetry. The features of the low-lying states are discussed. in the influence of the 2D parabolic potential well. It has found that the confinement may cause accidental degeneracies between levels with different low-excited states. It isshown that the effect of quantum confinement on the binding energy of the heavy hole is stronger than that of a of lighthole