This problem can be caused by either a leaking water inlet valve, or a condition known as "siphoning". Since you just recently moved, I would make sure you don't have a siphoning problem, first. The following link explains how:
Although siphoning normally refers to a constant drain problem where a washer has problems maintaining the proper water level, it can also lead to problems where the drain line will back up into the washer.
Now, if you follow the advice in the link and determine this is NOT caused by siphoning, I would suspect that you have a water inlet valve that is leaking. A tell-tale sign will be water trickling down the fill tube in the rubber door bellow. The water inlet valves have a diaphragm that is controlled by an electric solenoid. Sometimes the valve becomes clogged with sediment or deposits, causing the diaphragm not to close properly. If you live in an area that has hard water, or use well water, you may have hard water deposits or rust build up in the valve. You may be able to correct the problem by removing the valve and cleaning it with some distilled vinegar. You can remove the valve by following these steps:
1. Unplug the washer and turn off water supply at the taps.
2. Disconnect the water inlet hoses.
3. Remove washer top panel by removing the three screws that hold the panel in place in the rear of the washer. With the screws removed, the panel slides back, then off.
4. The inlet valve (this is what your water inlet hoses connect to) will be located in the left rear of the washer (facing from the front). Remove the dispenser hose(s) from the valve and the electric connections. Remember how the electrical connections are removed. They should be color coded. One is for HOT, one is for COLD.
5. Remove the mounting screws that hold the assembly in place.
Once you have the inlet valve removed, you can place it in some distilled vinegar and let it soak. Just don't submerge the electrical connections. If this does not correct your problem, replace the valve. Searspartsdirect.com and repairclinic.com are two notable web sites that I have frequently used. Just type in your complete model number to begin the parts search.
I hope you find this information helpful. Let me know if you require additional assistance.