  The Lorentzian Kac-Moody algebra E11, obtained by doubly overextending the
compact E8, is decomposed into representations of its canonical hyperbolic E10
subalgebra. Whereas the appearing representations at levels 0 and 1 are known
on general grounds, higher level representations can currently only be obtained
by recursive methods. We present the results of such an analysis up to height
120 in E11 which comprises representations on the first five levels. The
algorithms used are a combination of Weyl orbit methods and standard methods
based on the Peterson and Freudenthal formulae. In the appendices we give all
multiplicities of E10 occuring up to height 340 and for E11 up to height 240.
