Your rim may be just at or under the recommended minimum width for a 315/35-17 tire. The tire manufacturers and most retailers should have the recommended min./max rim width for the tires they offer. You could check this site to see if they have the tire you're looking for with rim width recommendations.
https://tiresize.com/tires/Nitto/NT05-315-35R17.htm I have no previous experience with tiresize.com, just attached their site for easy information access.