We study the spectrum, unitarity bound and holographic central charge of spin-2 operators in a warped AdS2 × S2 × T4 × Iψ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\mathcal{I}}_{\\psi } $$\\end{document} × Iρ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\mathcal{I}}_{\\rho } $$\\end{document} background in the Type IIB theory. We were able to identify a class of solutions that is completely independent of the functions that define the background solution. We comment on the relation of our results to the previous ones in the literature.