The full group C*-algebra of the modular group is primitive. Bédos, E. & Omland, T. Proceedings of the American Mathematical Society, 140(4):1403–1411, 2012.
bibtex   
@article{bedos_full_2012,
	title = {The full group {C}*-algebra of the modular group is primitive},
	volume = {140},
	number = {4},
	journal = {Proceedings of the American Mathematical Society},
	author = {Bédos, Erik and Omland, Tron},
	year = {2012},
	pages = {1403--1411},
}

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