In this talk I will review our ongoing activity on twisted bilayer graphene at the first magic angle. I will first discuss the constraints on a low energy description put forth by the spatial symmetries of the Bloch wavefunction obtained through a realistic tight-binding calculation performed on a relaxed structure.

Next I will propose a minimal tight-binding model that reproduces the elementary band representation of the emergent P622 low-energy space group.

Finally, I will show how the emergent symmetry shows up in the phonon spectrum, which suggests the intriguing possibility of an Exe Jahn-Teller effect as a possible mechanism to split the so-called valley degeneracy.