Hi
The Coordinator role has "admin rights", ie all rights,
to a space and all sub-spaces that inherit permissions from it. This includes assigning permissions to others. Orginally we did have administrator; it is still there in the config, but hidden. We did this to avoid confusion with the administrator for the repository. By the way, you have the right to disable permission inheritance, which should be used with caution as you can "cut yourself off" unless you have owner rights.
The configuration is in permissionModel.xml. You can add your own administrator role here if required. You would just have to change expose false to expose true on the permission group that already exists. You may need some internationalisation hook for the UI.
I would recommend you stick with coordinator or create a new role. Leave the term administrator to apply to the repository as a whole.
Regards
Andy