Congruences modulo 2 for dimensions of spaces of cusp forms

In this paper, we give some congruences modulo 2 for dimensions of spaces of Siegel cusp forms of degree one or two. First, we review some known results for congruences between dimensions of spaces of cusp forms and class numbers of imaginary quadratic fields. Next, we give our main result which is a congruence relation for the degree two case. It is related to Arthur's conjecture for PGSp(2).