The last few months have seen the discovery of a second Martian Trojan (1998 VF31), as well as two further possible candidates (1998 QH56 and 1998 SD4). Together with the previously discovered Martian satellite 5261 Eureka, these are the only known possible solar system Trojan asteroids not associated with Jupiter. Here, maps of the locations of the stable Trojan trajectories of Mars are presented. These are constructed by integrating an ensemble of in-plane and inclined orbits in the vicinity of the Martian Lagrange points for between 25 million and 60 million years. The survivors occupy a band of inclinations between 15 degrees and 40 degrees and longitudes between 240 degrees and 330 degrees at the L5 Lagrange point. Around the L4 point, stable Trojans inhabit two bands of inclinations (15 degrees < i < 30 degrees and 32 degrees < i < 40 degrees) with longitudes restricted between 25 degrees and 120 degrees. Both 5261 Eureka and 1998 VF31 lie deep within one of the stable zones, which suggests they may be of primordial origin. Around Mars, the number of such undiscovered primordial objects with sizes greater than 1 km may be as high as 50. The two candidates 1998 QH56 and 1998 SD4 are not presently on Trojan orbits and will enter the sphere of influence of Mars within half a million years.

14 pages, 3 figures, in press at the Astrophysical Journal (Letters)