Dungeon Masters (or DMs) are allowed to run any level of quest without supervision. They also have all the authority of a Questrunner (see below). Additionally, Dungeon Masters may propose channel storylines that they would like to run to the Storytellers, and receive permission to run them.
To become a Dungeon Master, you must demonstrate consistent questrunning ability and trustworthiness, as well as a competent understanding of and respect for the rules of the game and of the channel. This usually means running at least ten quests, including at least one quest of levels 11+, though this is not a guarantee.