  An analogue over imaginary quadratic fields of a result in algebraic number
theory known as Ihara's lemma is established. More precisely, we show that for
a prime ideal P of the ring of integers of an imaginary quadratic field F, the
kernel of the sum of the two standard P-degeneracy maps between the cuspidal
sheaf cohomology H^1_!(X_0, M_0)^2 --> H^1_!(X_1, M_1) is Eisenstein. Here X_0
and X_1 are analogues over F of the modular curves X_0(N) and X_0(Np),
respectively. To prove our theorem we use the method of modular symbols and the
congruence subgroup property for the group SL(2) which is due to Serre.
