  We examine the perennial quantum spin-liquid candidate $S=1/2$ Heisenberg
antiferromagnet on the kagome lattice. Our study is based on achieving Lanczos
diagonalization of the Hamiltonian on a $48$ site cluster in sectors with
dimensions as a large as $5 \times 10^{11}$. The results reveal novel intricate
structures in the low-lying energy spectrum. These structures by no means
unambiguously support an emerging consensus of a $\mathbb{Z}_2$ spin liquid
ground state, but instead appear compatible with several scenarios, including
four-fold topological degeneracy, inversion symmetry breaking and a combination
thereof. We discuss finite-size effects, such as the apparent absence of ETH,
and note that while considerably reduced, some are still present for the
largest cluster. Finally, we observe that an XXZ model in the Ising limit
reproduces remarkably well the most striking features of finite-size spectra.
