We provide algorithms and documention to compute the cohomology of congruence subgroups of the special linear group over the integers when n=3 using the well-rounded retract and the Voronoi decomposition. We define the Sharbly complex and how one acts on a k-sharbly by the Hecke operators. Since the norm of a sharbly is not preserved by the Hecke operators we also examine the reduction techniques described by Gunnells and present our implementation of said techniques for n=3.
College and Department
Physical and Mathematical Sciences; Mathematics
BYU ScholarsArchive Citation
Cocke, William Leonard, "Hecke Eigenvalues and Arithmetic Cohomology" (2014). All Theses and Dissertations. 4130.
Hecke Action, Arithmetic Cohomology, Sharblies, Modular Symbols