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We determine the number of level 1, polarized, algebraic regular, cuspidalautomorphic representations of GL_n over Q of any given infinitesimalcharacter, for essentially all n <= 8. For this, we compute the dimensions ofspaces of level 1 automorphic forms for certain semisimple Z-forms of thecompact groups SO_7, SO_8, SO_9 (and G_2) and determine Arthur's endoscopicpartition of these spaces in all cases. We also give applications to the 121even lattices of rank 25 and determinant 2 found by Borcherds, to level oneself-dual automorphic representations of GL_n with trivial infinitesimalcharacter, and to vector valued Siegel modular forms of genus 3. A part of ourresults are conditional to certain expected results in the theory of twistedendoscopy.

Level one algebraic cusp forms of classical groups of small ranks