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PKS 1510-089 is a flat spectrum radio quasar strongly variable in the opticaland GeV range. We search for low-state VHE gamma-ray emission from PKS1510-089. We aim to characterize and model the source in a broad-band context,which would provide a baseline over which high states and flares could bebetter understood. We use daily binned Fermi-LAT flux measurements of PKS1510-089 to characterize the GeV emission and select the observation periods ofMAGIC during low state of activity. For the selected times we compute theaverage radio, IR, optical, UV, X-ray and gamma-ray emission to construct alow-state spectral energy distribution of the source. The broadband emission ismodelled within an External Compton scenario with a stationary emission regionthrough which plasma and magnetic field are flowing. We perform also theemission-model-independent calculations of the maximum absorption in the broadline region (BLR) using two different models. Results. The MAGIC telescopescollected 75 hrs of data during times when the Fermi-LAT flux measured above 1GeV was below 3x10-8cm-2s-1, which is the threshold adopted for the definitionof a low gamma-ray activity state. The data show a strongly significant(9.5{\sigma}) VHE gamma-ray emission at the level of(4.27+-0.61stat)x10-12cm-2s-1 above 150GeV, a factor 80 smaller than thehighest flare observed so far from this object. Despite the lower flux, thespectral shape is consistent with earlier detections in the VHE band. Thebroad-band emission is compatible with the EC scenario assuming a largeemission region located beyond the BLR. For the first time the gamma-ray dataallow us to place a limit on the location of the emission region during a lowgamma-ray state of a FSRQ. For the used model of the BLR, the 95% C.L. on thelocation of the emission region allows us to place it at the distance >74% ofthe outer radius of the BLR.

Detection of persistent VHE gamma-ray emission from PKS 1510-089 by the MAGIC telescopes during low states between 2012 and 2017