  We examine the eigenfrequencies of gravitational waves from the protoneutron
stars (PNSs) provided via the core-collapse supernovae, focusing on how the
frequencies depend on the dimension of numerical simulations especially for the
early phase after core bounce. As expected, we find that the time evolution of
gravitational wave frequencies depends strongly on the dimension of numerical
simulation as well as the equation of state for high density matter. Even so,
we find that the fundamental frequency as a function of PNS average density and
the ratio of the specific eigenfrequencies to the fundamental frequency as a
function of PNS properties are independent of the dimension of the numerical
simulations, where the dependence of the equation of state is also very weak in
this early postbounce phase. Thus, one can safely discuss the gravitational
wave frequencies of the PNSs as a function of the PNS average density or
compactness even with the frequencies obtained from the one dimensional
simulations. We also provide phenomenological relation between the compactness
and average density as well as the relation among the $f$-, $p$-, and $g$- mode
frequencies.
