Does the vibration go away at a higher speed, like 70 or 75? If it vibrates at 60 but goes away at 70, it's probably out of balance like Larry said. If it is still present at any speed, it's probably a bigger issue like bent rim or axle, etc... It could also be a manufacturing defect in the tire, or an improperly mounted tire.
Here is a good article about diagnosing tire and wheel vibrations, including matching the high spot on the tire with the wheel, balance, and out-of-round situations.
Particularly with low-profile tires, as I imagine you have on your M3, the wheels can take a real beating that a higher profile tire would absorb. It's just made worse by the stiff sidewalls on high performance tires. A few years ago a friend bought a used car with aftermarket wheels and 35 series tires. We went for a ride in it and I remarked on the vibration, and it ended up being bent wheels.