Mod p representations of SL2(Qp)

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 SL2(Q(p)). We also define conductors and newforms for these representations and compute the conductors and the dimensions of spaces of newforms. (C) 2012 Elsevier Inc. All rights reserved.