Well, as part of a constant term of an Eisenstein series, it would appear in the constant term of an Eisenstein series attached to the 2,1 parabolic (or 1,2...) in GL3. My relatively recent book(s) with Cambridge U Press... also available on-line... treat some aspects of this, in both classical and adelic terms.

But also you should look at Langlands' SLN 544, and Goldfeld/Goldfeld-Hundley's books on GLn...

Well, as part of a constant term of an Eisenstein series, it would appear in the constant term of an Eisenstein series attached to the 2,1 parabolic (or 1,2...) in GL3, with the cuspform on the GL2 factor of the Levi component. My relatively recent book(s) with Cambridge U Press... also available on-line... treat some aspects of this, in both classical and adelic terms.

But also you should look at Langlands' SLN 544, and Goldfeld/Goldfeld-Hundley's books on GLn...