You don’t say what modem you bought – is it one of the ones on the TWC approved list? If not, that could be an issue. Is it DOCSIS 2 or 3?
Assuming it’s a compatible model, first thing I’d do is return it for a replacement.
If that doesn’t fix the problem, then the next thing I’d worry about is the cable lines themselves. Do you have TWC cable TV, too? And does that have problems? That would be a clue that it’s the cable lines.