The present invention relates to a four-way conversion catalyst for the treatment of an exhaust gas stream of a gasoline engine, the catalyst comprising a porous wall-flow filter substrate comprising an inlet end, an outlet end, a substrate axial length extending between the inlet end and the outlet end, and a plurality of passages defined by porous internal walls of the porous wallflow filter substrate, wherein the plurality of passages comprise inlet passages having an open inlet end and a closed outlet end, and outlet passages having a closed inlet end and an open outlet end, wherein the interface between the passages and the porous internal walls is defined by the surface of the internal walls; wherein the porous internal walls comprise pores which comprise an oxidic component comprising a first refractory metal oxide, said first refractory metal oxide comprising aluminum, said oxidic component having a platinum group metal content in the range of from 0 to 0.001 weight-% based on the total weight of the oxidic component; wherein the catalyst further comprises a first three-way conversion catalytic coating, at least weight-% thereof being comprised in the pores of the internal walls, said first three-way conversion catalytic coating comprising an oxygen storage compound and a platinum group metal supported on a second refractory metal oxide.