@Joe jaszczak: No, I didn't know that. Thanks for pointing that out. I tried that, and the print is on the right in the image below.
@ajk: I tried your STL with the wall, and the result is on the left in the image. I think it's about the same quality as what you got.

The store print is printed using their fine setting (100 um layers). But still the quality isn't that good. The part has been partly fixed before I took this picture. Most importantly, I cut off a couple of extra loops of filament on the outside of the arches. What's especially bad is the pillar portion under the dome, with lots of extra bits sticking out.
The ajf print came out as the best so far. The worst part is in the undersides of the arches, but that's true of all the parts printed without supports, and it's not worse on this part than others.