Doe form 1116 reduce the amount of foreign tax I can claim as a credit? I paid $604 inforeign tax, but am only getting credit for $540

It depends on your situation. You don't always get to take the full Foreign Tax Credit, there are several limitations and these are figured on Form 1116. 

Click here for more information about the limitations.

If you are not allowed the full amount of the Foreign Tax Credit that was paid, the excess carries forward until you are able to use it.