Hida theory for special orders

Abstract

This note is devoted to the study of families of quaternionic modular forms arising from orders defined by Pizer. In this situation, the Hecke-eigenspaces are 2-dimensional contrary to the classical case of Eichler orders. The main result is a Control Theorem in the spirit of Hida, interpolating these 2-dimensional Hecke-eigenspaces. We restrict our attention to a definite rational quaternion algebra ramified at a single odd prime $\ell$.

arXiv comment20 pages. Comments are welcome. Final version, accepted for publication in Int. J. Number Theory: fixed some typos, improved exposition, and incorporated the reviewer's comments