We present a global map of the amplitude of Mars' crustal magnetic field at 170-km altitude based on electron reflectometry, using data from the Magnetometer/Electron Reflectometer (MAG/ER) experiment on board Mars Global Surveyor. This new map contains features that are about seven times weaker than those in previously published maps obtained with the MAG alone from the 400-km-altitude mapping orbit. The increased sensitivity and nearly complete sampling reveal numerous weak magnetic sources in the northern lowlands. A group of these sources forms a nearly complete ring surrounding the Utopia basin, coinciding with a ridge of thickened crust. A larger 5800-km-diameter ring is defined by a ~120¿ arc of magnetic sources that extend to the north pole, supporting the hypothesis that part of the dichotomy boundary was established or modified by the Utopia impact. We also map the magnetic signatures of the Hellas, Argyre, and Isidis impact basins with increased dynamic range, confirming the large contrast in magnetic field strength between the basin interior and surroundings. Magnetic sources surround most of the Tharsis rise, except in the north, suggesting that the construction of Tharsis thermally demagnetized a large region of the northern lowlands. Thermal demagnetization is also suggested in the Elysium region, which intersects the inner Utopia magnetic ring, and south of the Hellas basin in the vicinity of Peneus Patera and Amphitrites Patera.