This paper introduces a fully symmetrized Hamiltonian formalism designed for description of vibrational motion in ammonia (and any XH3 molecule). A major feature of our approach is the introduction of complex basis vibrational wavefunctions in product form, satisfying the complex symmetry species (CSS) of the molecular symmetric top point group (D
3h). The described formalism for ammonia is an adaptation of the approach, previously developed and applied to benzene, based on the CSS of the point group D
6h. The molecular potential energy surface (PES) is presented in the form of a Taylor series expansion around the planar equilibrium state. Using the described formalism, calculations have been carried out on the vibrational overtone and combination levels in 14NH3 up to vibrational excitation energies corresponding to the fourth N-H stretch overtone. The results from the calculations are adjusted to experimentally measured data, in order to determine the values of the harmonic and some anharmonic force constants of the molecular PES.