  In this paper we describe the general theory of constructing toroidal
compactifications of locally symmetric spaces and using these to compute
dimension formulas for spaces of modular forms. We focus explicitly on the case
of the orthogonal locally symmetric spaces arising from quadratic forms of
signature $(2,n)$, giving explicit details of the constructions, structures and
results in these cases. This article does not give explicit cone
decompositions, compute explicit intersection pairings, or count cusps and thus
does not give any complete formulas for the dimensions.
  This article is still `in preparation'.
