There is excessive and disturbing noise. Your enjoyment of your property is diminished. To prove your case, you can use police reports, witnesses, recordings, your own testimony and the testimony of neighbors or other witnesses. The amount you'll want to ask for will depend on how much the noise bothered you. Decide on a reasonable dollar amount per day, and multiply that figure by the number of days you've been seriously bothered.
Noisy neighbors are always bad news.
But when you share walls with the insensitive neighbor, the problem is especially vexing. Chances are your neighbor signed one too. A neighbor who is blasting the stereo in an unreasonable manner is probably violating the lease or rental agreement and can be evicted for doing so. If you warn your neighbor about the noise in writing and are sure that your lease entitles you to a reasonable amount of quiet, send a copy of the lease along with your letter. In your letter, tell the neighbor that the next complaint will be to the landlord or neighborhood association if the noise continues.