A judge at London's Westminster Magistrates' Court sentenced Alison Chabloz on Thursday to a 20-week suspended prison sentence, a year-long social media ban and community service.
Her songs, partly set to traditional Jewish folk music, included lyrics such as: "Did the Holocaust ever happen? Was it just a bunch of lies? Seems that some intend to pull the wool over our eyes."
Chabloz said the songs were satirical. But the 54-year-old Swiss-British singer was convicted last month of sending offensive, indecent or menacing messages.
Judge John Zani told Chabloz she had shown "no proper remorse" for her actions.
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