We explore the properties of the H_beta emission line profile in a large, homogeneous and bright sample of N~470 low redshift quasars extracted from Sloan Digital Sky Survey (DR5). We approach the investigation from two complementary directions: composite/median spectra and a set of line diagnostic measures (asymmetry index, centroid shift and kurtosis) in individual quasars. The project is developed and presented in the framework of the so-called 4D Eigenvector 1 (4DE1) Parameter Space, with a focus on its optical dimensions, FWHM(H_beta) and the relative strength of optical FeII (R_FeII=W(FeII4434-4684)/W(H_beta)). We reenforce the conclusion that not all quasars are alike and spectroscopically they do not distribute randomly about an average typical optical spectrum. Our results give further support to the concept of two populations A and B (narrower and broader than 4000 km/s FWHM(H_beta), respectively) that emerged in the context of 4DE1 space. The broad H_beta profiles in composite spectra of Population A sources are best described by a Lorentzian and in Population B by a double Gaussian model. Moreover, high and low accretion sources (an alternative view of the Population A/B concept) not only show significant differences in terms of Black Hole (BH) mass and Eddington ratio L_bol/L_Edd, but they also show distinct properties in terms of line asymmetry, shift and shapes. We finally suggest that a potential refinement of the 4DE1 space can be provided by separating two populations of quasars at R_FeII~0.50 rather than at FWHM(H_beta)=4000 km/s. Concomitantly, the asymmetry and centroid shift profile measures at 1/4 fractional intensity can be reasonable surrogates for the FWHM(H_beta) dimension of the current 4DE1.
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