  The mini-superspace quantization of D=11 supergravity is equivalent to the
quantization of a E10/K(E10) coset space sigma model, when the latter is
restricted to the E10 Cartan subalgebra. As a consequence, the wavefunctions
solving the relevant mini-superspace Wheeler-DeWitt equation involve
automorphic (Maass wave) forms under the modular group W^+(E10)=PSL(2,O). Using
Dirichlet boundary conditions on the billiard domain a general inequality for
the Laplace eigenvalues of these automorphic forms is derived, entailing a wave
function of the universe that is generically complex and always tends to zero
when approaching the initial singularity. The significance of these properties
for the nature of singularities in quantum cosmology in comparison with other
approaches is discussed. The present approach also offers interesting new
perspectives on some long standing issues in canonical quantum gravity.
