A Center Controller reported the airspace chart at their sector had not been updated with a revised higher Minimum Enroute Altitude resulting in the reporter working an aircraft flying below the MEA.

Narrative

The previous sector controller coordinated non-radar Aircraft X coming over the fix ZZZZZ and then established on the airway VXXX at an altitude of 120 (twelve thousand feet MSL) which according to my overhead sector charts stated was the top altitude for the route. I approved this altitude and routing into my airspace. A few minutes later Aircraft X popped up on radar and I saw that they appeared to not be established on the airway but presently at a safe altitude for their current position. Aircraft X was then advised to turn left(can't remember specific heading I gave) to join the airway and continue to maintain 12;000ft as there was a 12;600 MIA (Minimum IFR Altitude) at their immediate 12 O'clock and about 10 miles. Aircraft X made the appropriate turn in a timely manner and reported established on the airway. The data tag began to MSAW alert. I investigated the MSAW alert and verified that Aircraft X was established on the airway. I then rechecked the overhead chart to verify that 12;000ft MSL was a safe altitude for the aircraft. My supervisor then came and inquired about the airway and the safety of the aircraft reference the MSAW alert. I advised my supervisor that the aircraft was safe at the airway altitude of 12;000ft MSL. After further inspection from my supervisor it was determined that the overhead chart above the position I was working was not current at the new MEA on the victor route VXXX is 13;000ft. By the time that information was confirmed the aircraft was north and clear of the 12;600 MIA polygon and no longer required an altitude of 13;000ft MSL. Suggestion: Current overhead charts; current information.