  Magic-angle twisted bilayer graphene (MATBG) exhibits a rich variety of
electronic states, including correlated insulators, superconductors, and
topological phases. Understanding the microscopic mechanisms responsible for
these phases requires determining the interplay between electron-electron
interactions and quantum degeneracy due to spin and valley degrees of freedom.
Signatures of strong electron-electron correlations have been observed at
partial fillings of the flat electronic bands in recent spectroscopic
measurements. Transport experiments have shown changes in the Landau level
degeneracy at fillings corresponding to an integer number of electrons per
moir\'e unit cell. However, the interplay between interaction effects and the
degeneracy of the system is currently unclear. Using high-resolution scanning
tunneling microscopy (STM), we observed a cascade of transitions in the
spectroscopic properties of MATBG as a function of electron filling. We find
distinct changes in the chemical potential and a rearrangement of the
low-energy excitations at each integer filling of the moir\'e flat bands. These
spectroscopic features are a direct consequence of Coulomb interactions, which
split the degenerate flat bands into Hubbard sub-bands. We find these
interactions, the strength of which we can extract experimentally, to be
surprisingly sensitive to the presence of a perpendicular magnetic field, which
strongly modifies the spectroscopic transitions. The cascade of transitions we
report here characterizes the correlated high-temperature parent phase from
which various insulating and superconducting ground-state phases emerge at low
temperatures in MATBG.
