  We carried out deep H$\alpha$ narrowband imaging with 10 hours net
integrations towards the young protocluster, USS1558$-$003 at $z=2.53$ with the
Subaru Telescope. This system is composed of four dense groups with massive
local overdensities, traced by 107 H$\alpha$ emitters (HAEs) with stellar
masses and dust-corrected star formation rates down to $1\times10^8$ M$_\odot$
and 3 M$_\odot$yr$^{-1}$, respectively. We have investigated the environmental
dependence of various physical properties within the protocluster by comparing
distributions of HAEs in higher and lower densities with a standard
Kolmogorov--Smirnov test. At 97\% confidence level, we find enhanced star
formation across the star-forming main sequence of HAEs living in the most
extreme `supergroup', corresponding to the top quartile of overdensities.
Furthermore, we derive distribution functions of H$\alpha$ luminosity and
stellar mass in group and intergroup regions, approximately corresponding to 30
times and 8 times higher densities than the general field. As a consequence, we
identify by 0.7 and 0.9 dex higher cutoffs in H$\alpha$ luminosity and stellar
mass functions in the dense groups, respectively. On the other hand, HAEs in
the intergroup environment of the protocluster show similar distribution
functions to those of field galaxies despite residing in significant
overdensities. In the early phase of cluster formation, as inferred from our
results, the densest parts in the protocluster have had an accelerated
formation of massive galaxies. We expect that these eventually grow and
transform into early-type galaxies at the bright end of the red sequence as
seen in present-day rich clusters of galaxies.
