What is the expiation for a female student taking money from her mother for luxuries without her knowledge, and how can she seek God's forgiveness and avoid her mother's anger?

If you deceived your mother about your need for money for studying and then took it for other purposes, you have done wrong and committed something forbidden, because a Muslim's money is not permissible [to take] except with their willing consent. The expiation for this is sincere repentance. If you can inform your mother, then do so; otherwise, supplicate for her extensively and resolve to return the money you took without her consent, even if indirectly.