  We discuss the canonical quantization of $N=1$ supergravity in the functional
Schrodinger representation. Although the form of the supersymmetry constraints
suggests that there are solutions of definite order $n$ in the fermion fields,
we show that there are no such states for any finite $n$. For $n=0$, a simple
scaling argument definitively excludes the purely bosonic states discussed by
D'Eath. For $n>0$, the argument is based on a mode expansion of the gravitino
field on the quantization 3-surface. It is thus suggested that physical states
in supergravity have infinite Grassmann number. This is confirmed for the free
spin-3/2 field, for which we find that states satisfying the gauge constraints
contain an infinite product of fermion mode operators.
