Narain moduli space ($O(d,d+16;\mathbb{Z})\backslash O(d,d+16)/(O(d)\times O(d+16))$)

For a toroidally compactified heterotic string, the torus metric, antisymmetric tensor and gauge Wilson lines determine a positive $d$-plane in a charge space of signature $(d,d+16)$, modulo lattice identifications. The continuous dimension is $d(d+16)$; the coupling is an additional modulus. The three-torus case has fifty-seven shape and Wilson-line parameters.