To be ~ means to be well-known for something bad.
...an area ~ for drugs, crime and violence...
She told us the story of one of Britain’s most ~ country house murders.
= infamous
ADJ: oft ADJ for n/-ing
~ly
The train company is overstaffed and ~ly inefficient...
Doctors ~ly neglect their own health and fail to seek help when they should.
ADV: usu ADV group, also ADV before v