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.
Seal of Ohio The Great Seal of the State of Ohio is the official insignia of the U.S. state of Ohio. All governmental offices, agencies, and courts in Ohio use variations of the state seal. Its primary feature is a circular coat of arms that depicts a sunrise in Chillicothe, Ohio's first capital, along with symbols of the state's origins. The seal sometimes appears with the state motto, "With God, all things are possible".