Search

The trace of Hecke operators with respect to a unit group of an order in a quaternion algebra has been given in Eichler [1], [2] in the case when the order is of square-free level. The purpose of this note is to study the order of type (q1, q2, q3) (see text 1.1), in the case, of cube-free level, and to give a formula for the trace of Hecke operators in the case q3 = 2.

A relationship between local Hecke series ofSp(ν, ℚ p ) for ν=1, 2, and 3 is given.

Let G, H, K be groups such that G is normal in K and G ⊆ H ⊆ K. Let I(H, K) be the set of inner automorphisms of K restricted to H; thus α ∊ I(H, K) if and only if, for some κ∊ K, α(h) = k-1hk for all h ∊ H. Let φ be an isomorphism of H/G onto a subgroup Hφ/G of K/G. An isomorphism Φ of H onto H(φ) is called an extension of ø ifΦ(h)G = φ(hG) for all h∊H.