$k$-point semidefinite programming bounds for equiangular lines

We give a hierarchy of $k$-point bounds extending the Delsarte-Goethals-Seidel linear programming $2$-point bound and the Bachoc-Vallentin semidefinite programming $3$-point bound for spherical codes. An optimized implementation of this hierarchy allows us to compute~$4$, $5$, and $6$-point bounds for the maximum number of equiangular lines in Euclidean space with a fixed common angle.