What is the name of the primary symbol, which is now outlawed outside of the context of art or science, and was widely used even on the state flag?
Strafgesetzbuch section 86a The German "Strafgesetzbuch" (Criminal Code) in § 86a outlaws "use of symbols of unconstitutional organizations" outside of the contexts of "art or science, research or teaching". This concerns Nazi symbolism in particular and is part of the denazification efforts following the fall of the Third Reich.
Flag of Springfield, Illinois The municipal flag of Springfield, Illinois, is the lawful flag of the capital of the U.S. state of Illinois, Springfield. Its background is "Old Glory blue". The flag is emblazoned with a circle of 20 small, white stars, all pointed upward; the circle is offset, slightly, to the left of the flag. Those stars encircle a large, white-bordered "Old Glory red" star, also pointed upward. The center star is described as two stars, one atop the other, in the Springfield, Illinois Code of Ordinances. Today, the flag has the words "Springfield Illinois," across its bottom; earlier photographs show no lettering on the flag.