Abstract
In Barthel and Livne (1994) [3] , the authors give a rough classification of mod p representations of GL 2 ( F ) where F is a finite extension of Q p . In Breuil (2003) [4] , the author gives a complete classification of mod p representations of GL 2 ( Q p ) . In this paper, using the classification in those two papers, we classify mod p representations of SL 2 ( Q p ) . We also define conductors and newforms for these representations and compute the conductors and the dimensions of spaces of newforms.
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