Shaking at idle

I own a 2003 330xi. I am having problems with the check engine light coming on when the cars cold. I got the codes checked and BANK1 and Bank4 came up. It already had brand new spark plugs and I just changed the coils. The engine shaking only happens when I turn the car on and it's less than 40 degrees Fahrenheit. After letting it hear up and driving the shaking goes and the check engine light goes away sometimes. Please help. I'm don't want to throw money into the wrong places anymore