Was your mother married? If so, and if her husband passed away at any time during their ownership, she would inherit her husband's ownership share in the property at a minimum. The cost basis would be the FMV of his share on the date of his passing.
If in a community property state, she gets a step-up in basis on the entire value of the house. Otherwise, she gets a step-up in basis of his 50% ownership in the property on the date of his passing.
Then, you would add the cost of any property improvements done "after" his passing, if you have the paperwork to prove the cost of those improvements.
