  We study bosonic symmetry protected topological (SPT) phases with $C_{2}$
rotational symmetry in four spatial dimensions which is not captured by the
group cohomology classification. By using the topological crystal approach, we
show that the topological crystalline state of this SPT phase is given by
placing an $E_{8}$ state on the two dimensional rotational invariant plane,
which provides a simple physical picture of this phase. Based on this
understanding, we show that a variant of QED4 with charge-1 and charge-3 Dirac
fermions is a field theoretical description of the three dimensional boundary.
We also discuss the connection to symmetric gapped boundary with topological
order and its anomaly signature.
