Try adding paragraphs and more white space.
13 years old: Ok
IQ:134: I doubt this, IQ tests depend on when they are taken; I scored 154 when I was 11 and nowadays I doubt I would come above 140; also depending what your "specialism" is and if you are a good receiver to input or just have more mathematical approach to things this does not say much.
Mature/Troubled: If your Father died you have my condolences, but it might have been traumatic; I had a similar emotional shock and it did not manifest into a depression until I was 18, so good luck.
Well behaved: most people say this of themselves, but I am not the one to judge this; you at least seem to understand grades are important.
I think your mother is right, and hear me out

The fact that people your age play this games is not inheretaly bad but it is also a trend, even if it ends up with you not being allowed you should be happy to have a PS3. They gave it to you and if you are smart you would not spend that amount of money on a console at your age; games are expansive enough as it is so due to you probably not having a job yet it cuts into savings that are also meant for your future.
Due to this fact she has extra saying over it because she owns the console (or at least has the argument you did not work for it yourself, and that also skips the possibility that you can use the "I worked for it that is mature" argument)
I would not let myself(or my children) play games like MW2 until they are about 16; and this comes from somebody that played GTA3 was he was about 12.
I would try a reasonable discussion with clear "rules" and pointers to how she can see it if affects you, and it it would affect you allow her to take it away no questions asked.
Also the fact that you might be American and she is brainwashed by the media might not help.
There are plenty games outside of MW2 and trading it in will not be that hard, and if you fall out of a social circle due to this, I know this sounds silly, do no worry because you will loose people and friendship a lot before you are done with school.
I'm not trying to act high and mighty here, so if I come across like that I am sorry.