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} .