  In this paper, in the basis of $M^{}_{\rm R}$ being diagonal, we survey the
simplified textures of $M^{}_{\rm D}$ for realizing the trimaximal neutrino
mixing and their consequences for the low-energy neutrino observables and
leptogenesis. We first formulate the general texture of $M^{}_{\rm D}$ for
realizing the trimaximal mixing, and then, following the Occam's razor
principle, examine if its parameters can be further reduced, giving more
simplified textures of it. Our analysis is restricted to the simple but
instructive scenario that there is only one phase parameter $\phi$ responsible
for the CP violating effects at low energies and leptogenesis. Our attention is
paid to the simplified textures of $M^{}_{\rm D}$ where there are some
vanishing elements (a sign of Abelian flavor symmetries) or equalities among
non-vanishing elements (a sign of non-Abelian flavor symmetries). On the basis
of these simplified textures, we further examine if $\phi$ can also take a
particular value (a sign of CP symmetries). The consequences of the
phenomenologically-viable simplified textures for the low-energy neutrino
observables and leptogenesis are studied.
