Using a numerical computational method, quasiprobability distributions of new kinds of even and odd nonlinear coherent states (EONLCS) are investigated. The results show that the distributions of the new even nonlinear coherent states (NLCS) are distinct from those of the new odd NLCS and imply that the new EONLCS always exhibit some different nonclassical effects. Finally, with the aid of newly introduced intermediate coordinate-momentum representation in quantum optics, the tomograms of the new EONLCS are calculated. This is a new way of obtaining the tomogram function.