  Let $\Gamma$ be a Bianchi group associated to one of the five Euclidean
imaginary quadratic fields. We show that the space of weight $k$ period
polynomials for $\Gamma$ is ``dual'' to the space of weight $k$ modular symbols
for $\Gamma$, reflecting the duality between the first and second cohomology
groups of Bianchi groups. Using this result, we describe the action of Hecke
operators on the space of period polynomials for $\Gamma$ via the Heilbronn
matrices.
  In the second part of the paper, we numerically investigate congruences
between level 1 Bianchi eigenforms via computer programs which implement the
Hecke action on spaces of Bianchi period polynomials. Computations with the
Hecke action are used to indicate moduli of congruences between the underlying
Bianchi forms; we then prove the congruences using the period polynomials. From
this we find congruences between genuine Bianchi modular forms and both a
base-change Bianchi form and an Eisenstein series. We believe these congruences
are the first of their kind in the literature.
