  The Hofstadter energy spectrum provides a uniquely tunable system to study
emergent topological order in the regime of strong interactions. Previous
experiments, however, have been limited to the trivial case of low Bloch band
filling where only the Landau level index plays a significant role. Here we
report measurement of high mobility graphene superlattices where the complete
unit cell of the Hofstadter spectrum is accessible. We observe coexistence of
conventional fractional quantum Hall effect (QHE) states together with the
integer QHE states associated with the fractal Hofstadter spectrum. At large
magnetic field, a new series of states appear at fractional Bloch filling
index. These fractional Bloch band QHE states are not anticipated by existing
theoretical pictures and point towards a new type of many-body state.
