The fact of him being Hawkmoth makes this obvious that the has created some crimes however

One thing is Gabriel Agreste isn't just commiting crimes as Hawkmoth, but also has his civilian form.

That crime is child abuse towards Adrien.

He may not be doing anything physically, but he has been mentally  abusing him.

Points

• Neglect

•  Manipulative; Makes Adrien often feel as if he wrong for not matching his standards.

Examples: Anytime Adrien argues with him, Gabriel will threaten pull him out of school.

Told him to do extra pinao lessons if he messes up.

Adrien worse fear in sandboy was being in a cage because his father hardly gives him freedom to do things that the wants to such as something as simple as hanging out with friends.

• Isolation;  keeping away form others isn't good either because this often makes him have the feeling of loneliness.

•  Controlling and treats Adrien as an object. If Adrien doesn't do what he says or makes a mistake Gabriel will put Adrien down in the low as if he isn't human. Such as when Adrien lost his book because Lila throw it in the trash can and Marinette stole the book from the trash can. Be immediately says he will pull him out of school even though he had a copy of the book on his tablet. Also, forces Adrien to do a lot of activities. Modeling, fencing, pianos and other things such as that. He may enjoy them but that is a lot to do for a boy. Keep in mind that his father makes his schedule up for him, so..he doesn't have much say in his life.

To be honest if Chole told her dad about Adrien's father isolating him, he would be in jail by now.