Turkey Vulture (Cathartes aura)
If you see a vulture (or a buzzard, if you prefer) in New Mexico, it's safe to assume that it's a turkey vulture. The adults' bare red heads make it easy to clinch the ID. When gliding, turkey vultures tend to hold their wings in a shallow V (dihedral) and to teeter a bit.
Juvenile turkey vultures have black heads, which might tempt you to misidentify them as black vultures (Coragyps atratus). However, that species almost never visits the state.