Tim Campion already pointed out FAQ post the question: [What can I do to lift or reduce a suspension?](https://meta.stackexchange.com/q/316631) I will add also link to another answer on Meta Stack Exchange: [Where I can complain about an unfair account suspension?](https://meta.stackexchange.com/q/165359#165360)

Apart from replying to the moderator message, you can also use [the contact form](https://mathoverflow.net/contact) to contact Stack Exchange Team. On MathOverflow you have also an option to [contact the MO moderators](https://meta.mathoverflow.net/questions/833/who-are-the-mathoverflow-moderators/834#834) using email. (This is specific for MO, other sites in the Stack Exchange network do not have such option.) In an older discussion it was [mentioned by a MO moderator](https://meta.mathoverflow.net/questions/1066/protest-for-my-account-suspension/1068#1068) that this is a possibility how to object to a suspension.

If you use the first option, you're communicated with the Stack Exchange employees. The second option means contacting directly the MathOverflow moderators.