  Interplay of nonlinear and quantum effects in the ground state of the
E$\otimes (b_1+b_2)$ Jahn-Teller model was investigated by the {\it variational
approach and exact numerical simulations}. They result in the recognition of
(i) importance of the admixture of {\it the first excited state of the
displaced harmonic oscillator} of the symmetric phonon mode in the ground state
of the system in the selftrapping-dominated regime; (ii) existence of {\it the
region of localized $b_1$-undisplaced oscillator states} in the
tunneling-dominated regime. The effect (i) occurs owing to significant decrease
of the ground state energy on account of the overlapping contribution of the
symmetric phonon mode between the states of the same parity. This contribution
considerably improves variational results especially in the
selftrapping-dominated regime. Close to the E$\otimes$e limit, the nonlinear
effects of {\it two-mode correlations} turn to be effective due to the
rotational symmetry of this case. In the tunneling-dominated regime the phonon
wave functions behave like the strongly localized harmonic oscillator ground
state and the effect (i) looses its significance.
