There is nothing for you to do until the dealer comes back with a diagnosis based on their reading of the codes.

It could be a fuel pump issue, but any potential cause would just be guessing, just let them do the diagnosis first.

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2007 X3 3.0si, 6 MT, Premium, White

Retired:
2008 535i, 6 MT, M Sport, Premium, Space Grey
2003 X5 3.0 Steptronic, Premium, Titanium Silver
2002 325xi 5 MT, Steel Grey
2004 Z4 3.0 Premium, Sport, SMG, Maldives Blue