  We show that a conspicuous wave packet of ultracold noninteracting Bosonic
atoms emerges in a 1-dimensional parabolic optical lattice as in the setup of
the Aarhus experiment [P. L. Pedersen ${\it et}$ ${\it al.}$, Phys. Rev. A
${\bf 88}$, 023620 (2013)], given the lattice height is harmonically modulated
with a particular amplitude at a resonant frequency. We show that this wave
packet, coined "${\it 4bandPWP}$" here, executes stable time-wise periodic
motion for infinitely long time. We apply the Floquet theory to analyze the
parameter dependence of ${\it 4bandPWP}$ in detail. Our analysis shows that it
consists mainly of two principal Floquet eigenstates of the periodically driven
Hamiltonian. The informative Husimi representation yields temporal slices of
the phase space of ${\it 4bandPWP}$, visually identifying moments where the
inter-band transitions take place. The provided data should aid the experiment
in locating ${\it 4bandPWP}$.
