Here are the details I remember from the book:
There are five hypothetical levels of magic. The current highest level of magic that has been used is three by a two-three people. This magic isn't widely known among most humans of this world.
The protagonist in the story is a young male who is originally put into some camp where this magic can be made with some sort of technology as a support.
The camp director has a gun-looking thing that s/he believes may allow this magic to work outside of the technology. The protagonist tries it, and I believe ice in jagged shards are launched outwards, so the director considers it to be dangerous.
The camp gets raided, and the protagonist finds out that the magic does work outside of the machines. He gets inducted into this training facility where he can learn how to use his power. He needs to use some kind of stone for his power to work, though. It's not required; it just helps him overcome the mental roadblock.
In the past, his mother was approached by this man who wanted to date her or something. She rejected him and lives with only her son, the protagonist. I think I remember something about spaghetti?
Anyways, the protagonist arrives home to find that his mother's memory has been wiped about him, and she is dating the guy who she had rejected when she remembered the protagonist.
One of the level three people who is part of the training organization says that he will restore the protagonist's mother's memory if the protagonist helps them find the gun-like thing mentioned earlier. (I'm not 100% sure about whether it looked like a gun btw.)
So, they find it, and the level three guy tells the protagonist that they cannot bring back the mother's memories and that the gun-like thing was like the stone thing the protagonist had. It was just for overcoming the mental roadblock. The protagonist drops the helping stone, and in anger, he summons a tornado that catches people from the place he was inducted into and their opponents.
This is level three magic, so the level three guy was impressed. The protagonist chooses to leave the organization, though.
I also remember that the protagonist had a friend in the camp who was also inducted into the organization but chose to stay there at the end unlike the protagonist.