The effects of plasma shaping, in particular of the triangularity delta, on plasma turbulence, in terms of relative density fluctuations, have been studied in the TCV tokamak. It has been found that for inner wall limited L-mode plasmas, negative triangularity leads to a substantial reduction of turbulence amplitude, as well as of the spectral index and correlation length, consistent with the beneficial effect on energy confinement. Crucially, this reduction extends deep in the core, where the local triangularity becomes vanishingly small. A stabilizing effect of effective collisionality on trapped electron mode turbulence was also observed. These observations are consistent with previous experimental results on the effects of triangularity and collisionality on electron heat transport, as well as with global gyrokinetic GENE simulation results.