We prove an analogue of the strong multiplicity one theorem in the context of τ_n-spherical representations of the group G = SO(2,1)^° appearing in L²(Γ_i\G) for uniform torsion-free lattices Γ_i, i = 1, 2 in G. This is a generalisation of a previous result by the first author and C. S. Rajan in [BR11] for the case of G = SO(2,1)^°.

We thank the anonymous referee for their valuable comments. Gunja Sachdeva is supported by DST-SERB POWER Grant No. SPG/2022/001738.