You are not your mother's dependent and may file and claim your child.
However, a child can be the “qualifying child” dependent of any close relative in the household. If you live with your parents, it may be better if she claims your child. It may be worthwhile to prepare trial returns, both ways, to see which way the family comes out best. This tool may be useful: https://turbotax.intuit.com/tax-tools/calculators/taxcaster/?s=1.
But only one of you can claim the child. Your mother must have more income than you, to be eligible to claim your child.
