Trent, a $35-$year$-$old taxpayer, earned $$87,000$ in wages. He is married, but he and his wife are in the process of getting a divorce, and they will file separate returns for $2023.$ They only lived together for six months during the year. What is Trent's maximum allowable contribution to a Roth IRA for $2023?$

$$0($He is not eligible to contribute to a Roth IRA.$)$

$$6,500$

$$7,500$

$$22,500$