Let
$G$
be a connected, reductive algebraic group over a number field
$F$
and let
$E$
be an algebraic representation of
${G}_{\infty } $
. In this paper we describe the Eisenstein cohomology
${ H}_{\mathrm{Eis} }^{q} (G, E)$
of
$G$
below a certain degree
${q}_{ \mathsf{res} } $
in terms of Franke’s filtration of the space of automorphic forms. This entails a description of the map
${H}^{q} ({\mathfrak{m}}_{G} , K, \Pi \otimes E)\rightarrow { H}_{\mathrm{Eis} }^{q} (G, E)$
,
$q\lt {q}_{ \mathsf{res} } $
, for all automorphic representations
$\Pi $
of
$G( \mathbb{A} )$
appearing in the residual spectrum. Moreover, we show that below an easily computable degree
${q}_{ \mathsf{max} } $
, the space of Eisenstein cohomology
${ H}_{\mathrm{Eis} }^{q} (G, E)$
is isomorphic to the cohomology of the space of square-integrable, residual automorphic forms. We discuss some more consequences of our result and apply it, in order to derive a result on the residual Eisenstein cohomology of inner forms of
${\mathrm{GL} }_{n} $
and the split classical groups of type
${B}_{n} $
,
${C}_{n} $
,
${D}_{n} $
.