  In this article, we review some aspects of logarithmic conformal field
theories which can be inferred from the characters of irreducible submodules of
indecomposable modules. We will mainly consider the W(2,2p-1,2p-1,2p-1) series
of triplet algebras and a bit logarithmic extensions of the minimal Virasoro
models. Since in all known examples of logarithmic conformal field theories the
vacuum representation of the maximally extended chiral symmetry algebra is an
irreducible submodule of a larger, indecomposable module, its character
provides a lot of non-trivial information about the theory such as a set of
functions which spans the space of all torus amplitudes. Despite such
characters being modular forms of inhomogeneous weight, they fit in the
ADET-classification of fermionic sum representations. Thus, they show that
logarithmic conformal field theories naturally have to be taken into account
when attempting to classify rational conformal field theories.
