  The purpose of this article is to describe the integral cohomology of the
braid group B_3 and SL_2(Z) with local coefficients in a classical geometric
representation given by symmetric powers of the natural symplectic
representation.
  These groups have a description in terms of the so called "divided polynomial
algebra". The results show a strong relation between torsion part of the
computed cohomology and fibrations related to loop spaces of spheres.
