  It has been conjectured that the classical dynamics of M theory is equivalent
to a null geodesic motion in the infinite-dimensional coset space E10/K(E10)
where K(E10) is the maximal compact subgroup of the hyperbolic Kac-Moody group
E10. We here provide further evidence for this conjecture by showing that the
leading higher order corrections, quartic in the curvature and related
three-form dependent terms, correspond to negative imaginary roots of E10. The
conjecture entails certain predictions for which higher order corrections are
allowed: in particular corrections of type R^M (DF)^N are compatible with E10
only for M+N=3k+1. Furthermore, the leading parts of the R^4, R^7,... terms are
predicted to be associated with singlets under the SL(10) decomposition of E10.
Although singlets are extremely rare among the altogether 4,400,752,653
representations of SL(10) appearing in E10 up to level l \leq 28, there are
indeed singlets at levels l=10 and l =20 which do match with the R^4 and the
expected R^7 corrections. Our analysis indicates a far more complicated
behavior of the theory near the cosmological singularity than suggested by the
standard homogeneous ans\"atze.
