Thin tubes?

I finally got around to get an extra rear wheel for my CT.

The wheel I got is a 700C, but when I tried to tube/tire it, the tire expanded over the stem and does not sit properly. I have used the Continental Road Bike 700C Indoor Trainer Tire for several years, which of course, is not as forgiven as road tires.

I am thinking a narrower tube will do the trick, so it sits better in the rim.

Where can I get (and what is) the narrowest 700C tube?

Thank you

Typical tubes are 18-23C and should be fine. Just push up on the stem to make sure the tire beads get to seat below the tube (it’s very typical to have to do this). Also make sure the tube has some air in it (no real pressure) just to keep it round.