2003 Other BMW Models p/s noise

Please help! I just replaced the power steering and hoses in my 2003 540I BMW. I have noticed a humming noise in my steering system ONLY when I turn to the left in an arc between around 45-75 degrees. Meaning when I turn to the left slightly, no sound. But if I turn sharper to the left, a humming noise is present. Also, it will not make that noise on a cold engine or steering system. Meaning I have to drive about 10 minutes before the noise starts to surface. I can't find this reason for this noise. I brought my car to the BMW dealership and they ran it through multiple diagnostic tests ($115 worth) only to tell me they don't know what is going on. Aaahhh! So, what do you think? I am pretty sure it is not my pump, that would make sense for the noise but that would be if I turned to both sides and it made a noise. But it doesn't. Only to the left. PLEASE help.

Thanks.

Chris