REPRESENTATIONS OF QUATERNION ALGEBRAS OVER LOCAL-FIELDS AND TRACE FORMULAS OF HECKE OPERATORS

The article gives an explicit expression to the restriction to each Cartan subgroup of an irreducible admissible representation of the quaternion algebra over a local field as a direct sum of characters of the Cartan subgroup. A formula for the character of the representation can be deduced easily from this result. Applying this result to the trace formula of Hecke operators, the authors computed several examples of characteristic polynomials of Hecke operators, for example, on S02(75). © 1993 Academic Press, Inc.