Computing the homology of SL_{3}(Z) with infinitedimensional coefficient modules
A. Ash, D. Pollack
Let p be a prime and Γ a congruence subgroup of SL_{3}(Z) which is Iwahori at p. Suppose f is a noncritical Hecke eigenclass in the homology of
Γ with trivial Q_{p}coefficients. In [4] we outlined a method
to compute to any desired degree of accuracy a lift of f to a homology class F with coefficients in a module of padic distributions with trivial highest weight.
Then we studied how to deform F to an analytic family of homology classes in distribution modules with varying highest padic weight.
In this paper we explain how to realize these deformations in an actual computer program, and we report on our initial computations of examples.
The calculation boils down to row reduction of an infinite matrix over a ring R of power series in three variables over Z_{p}.
To carry this out, we must approximate, using finite quotients of R.
Advanced Studies: EuroTbilisi Mathematical Journal, Special Issue (9  2021), pp. 4765
