  We consider spaces of modular forms attached to definite orthogonal groups of
low even rank and nontrivial level, equipped with Hecke operators defined by
Kneser neighbours. After reviewing algorithms to compute with these spaces, we
investigate endoscopy using theta series and a theorem of Rallis. Along the
way, we exhibit many examples and pose several conjectures. As a first
application, we express counts of Kneser neighbours in terms of coefficients of
classical or Siegel modular forms, complementing work of Chenevier-Lannes. As a
second application, we prove new instances of Eisenstein congruences of
Ramanujan and Kurokawa-Mizumoto type.
