Abstract
Abstract Let p 5 be a prime number. In 1994 Barthel and Livné gave a classification for irreducible representations of GL2 (F) over Fp , for F a p-adic field, discovering some objects, referred to as "supersingular", which appear as subquotients of a universal representations π(r, 0, 1). In this paper we give a detailed description the Iwahori structure of such universal representations for F an unramified extension of Qp . We determine a fractal structure which shows how and why the thechniques used for Qp fail and which let us determine"natural" subrepresentations of the universal object π(r, 0, 1). As a corollary, we get the Iwahori structure of tamely ramified principal series.