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Muto, Narita and Pitale construct counterexamples to the GeneralizedRamanujan Conjecture for GL(2,B) over the division quaternion algebra B withdiscriminant two via a lift from SL(2). In this paper, we try to exactlycharacterize the image of this lift. The previous methods of Maass, Kohnen orKojima do not apply here, hence we approach this problem via a combination ofclassical and representation theory techniques to identify the image.Crucially, we use the Jacquet Langlands correspondence described by Badulescuand Renard to characterize the representations.

Maass space for lifting to GL(2) over a division quaternion algebra