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Abstract: - Let p be a prime number and K a finite unramified extension of Qp. When p is large enough with respect to [K : Qp], and under mild genericity assumptions, we proved in our previous work that the admissible smooth representations it of GL2(K) which occur in Hecke eigenspaces of the mod p cohomology of Shimura curves are of finite length. In this paper, we obtain various refined results about the structure of subquotients of it, such as their Iwahori-socle filtrations and K1-invariants, where K1 is the principal congruence subgroup of GL2(OK). We also determine the Hilbert series of it as a Iwahori-representation under these conditions.

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