Assuming that your parent doesn’t treat the home as a rental there is no reason for you to report any income. At the most it could be argued that you are receiving a gift of the fair market value of the rent.
You do not report as income, that which you never received. Additionally, if you are not charging rent, then it's incorrect to report the property as a rental. Where a family member is living in a home owned by another family member rent free, that makes the home a 2nd home to the property owner; not a rental property.