  We carry out some computations of vector valued Siegel modular forms of
degree two, weight (k,2) and level one. Our approach is based on Satoh's
description of the module of vector-valued Siegel modular forms of weight (k,
2) and an explicit description of the Hecke action on Fourier expansions. We
highlight three experimental results: (1) we identify a rational eigenform in a
three dimensional space of cusp forms, (2) we observe that non-cuspidal
eigenforms of level one are not always rational and (3) we verify a number of
cases of conjectures about congruences between classical modular forms and
Siegel modular forms.
