Either a leak under the toilet, or it is not properly vented.

to expound on "warmfridge's" answer when the toilet was installed the wax ring which seals the toilet to the flange some times slips and doesnt make a good seal or isnt large enough to make the seal which then requires a larger wax ring or two doubled up. Venting can be a major problem because if the toilet was moved from a previous location they may not have the vent properly connected or even vented at all. Either way you need to call the plumber that installed it all back to have him fix it.
The other question I would have is what did they do with the old toilet location? how was it sealed? or removed? If it wasnt properly sealed it could be leaking sewer gas because toilet drains depend on the trap in the toilet itself to stop gas seepage. Remove the toilet and you have an open pipe to the sewer.

Thanks so much for your quick information! Now the smell is beginning to be faintly detected downstairs below this bathroom. Is there any danger from these gases until the plumber arrives?

build ups of methane gas can be explosive but rare in cases such as yours. But get the plumber there to get it fixed.

I just heard a story on the radio that Chinese drywall sold and installed the past two years is now smelling of sulphur and causing corrosion and some health problems. I've read a couple posts on this forum about a bad smell coming from walls. It's had to believe this was actually made and sold.

Here is a link that might be useful: Chinese drywall problems story

That chinese drywall is causing HUGE problems. It corrodes all copper wires and copper plumbing, copper in the air conditioner and HVAC, so any house with it is essentially a gut job to repair.

There is a "tent the house and fumigation" type of remediation available that neutralizes the nasties in the drywall. But if the wiring and plumbing is trashed...it's still a gut job.

Remediation is going to be huge.

Thanks, all, and for the input on chinese drywall - that is a truly an enormous nightmare.

I don't think this is related since this is new drywall just installed, well after all the reports of the chinese product problems were established. I don't think they are still importing it any longer, but I could be wrong.

The other reason is that this is specifically a sewer smell. We just remodeled 3 rooms all at once, but neither of the other two rooms has this odor, so it is less likely to be coming from drywall which is common to all 3 rooms.

I have a message in to our contractor and his plumber, so hopefully I will hear back tomorrow.