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We investigate a Bose-Einstein condensate strongly coupled to an opticalcavity via a repulsive optical lattice. We detect a stable self-ordered phasein this regime, and show that the atoms order through an antisymmetric couplingto the P-band of the lattice, limiting the extent of the phase and changing thegeometry of the emergent density modulation. Furthermore, we find anon-equilibrium phase with repeated intense bursts of the intra-cavity photonnumber, indicating non-trivial driven-dissipative dynamics.

P-band induced self-organization and dynamics with repulsively driven ultracold atoms in an optical cavity