Where did you buy the battery? New battery should be pre-charge

Fully charged battery voltage is ~12.6v

Battery Approximate Average Cell
Voltage State-of-charge Specific Gravity

12.66 100% 1.265
12.45 75% 1.225
12.24 50% 1.190
12.06 25% 1.155
11.89 0% 1.120

from
http://www.type2.com/library/electrip/batfaq.htm

You might also want to measure battery voltage with another multimeter. 10.6v sounds really low. Given it still can start your car, its real voltage might be higher than measured.