Given the congruence subgroup \(\Gamma_0 (N)\) of \(\text{SL}_2 (\mathbb Z)\) the first étale cohomology group \(H^1 (X_0 (N)_{\overline {\mathbb Q}}, \mathbb Q_\ell)\) of the associated modular curve \(X_0 (N)\) gives rise to a certain Galois representation (i.e. one of \(\text{Gal}(\overline{\mathbb Q}/ \mathbb Q))\) which corresponds to a cuspidal automorphic representation of \(\text{SL}_2\). In turn, this automorphic representation is related to a cuspidal cohomology class in \(H^1(\Gamma_0 (N) \backslash H; \mathbb C)\). The two corresponding \(L\)-series coincide. In this paper some (computational) evidence is given that a certain cuspidal cohomology class for the congruence subgroup \(\Gamma_0 (128)\) of \(\text{SL}_3 (\mathbb Z)\) is related to a (compatible system of \(\lambda\)-adic) three-dimensional Galois representation(s). The authors checked the coincidence of the local \(L\)-factors for all primes \(p\), \(3\leq p\leq 67\).