  We study the asymptotic growth of the degeneracy of the BPS local operators
with scaling dimension $n/2$ in the three-dimensional superconformal field
theories describing $N$ M2-branes. From the large $N$ supersymmetric indices we
obtain the asymptotic formulas for degeneracies of the M2-brane SCFTs according
to the Meinardus theorem. We observe an intriguing universal $n^{2/3}$ growth
of the degeneracies in various theories of M2-brane SCFTs. We also determine
the coefficients of $n^{2/3}$ growth as well as further corrections in these
theories explicitly.
