Context : Low luminosity radio galaxies ( LLRGs ) typically reside in dense megaparsec-scale environments and are often associated with brightest cluster galaxies ( BCGs ) .
They are an excellent tool to study the evolution of molecular gas reservoirs in giant ellipticals , even close to the active galactic nucleus .

Aims : We investigate the role of dense megaparsec-scale environment in processing molecular gas in LLRGs in the cores of galaxy ( proto- ) clusters .
To this aim we selected within the COSMOS and DES surveys a sample of five LLRGs at z = 0.4 - 2.6 that show evidence of ongoing star formation on the basis of their far-infrared ( FIR ) emission .

Methods : We assembled and modeled the FIR-to-UV spectral energy distributions ( SEDs ) of the five radio sources to characterize their host galaxies in terms of stellar mass and star formation rate .
We observed the LLRGs with the IRAM-30m telescope to search for CO emission .
We then searched for dense megaparsec-scale overdensities associated with the LLRGs using photometric redshifts of galaxies and the Poisson Probability Method , which we have upgraded using an approach based on the wavelet-transform ( \mathit { w } PPM ) , to ultimately characterize the overdensity in the projected space and estimate the radio galaxy miscentering .
Color-color and color-magnitude plots were then derived for the fiducial cluster members , selected using photometric redshifts .

Results : Our IRAM-30m observations yielded upper limits to the CO emission of the LLRGs , at z = 0.39 , 0.61 , 0.91 , 0.97 , and 2.6 .
For the most distant radio source , COSMOS-FRI 70 at z = 2.6 , a hint of CO ( 7 \rightarrow 6 ) emission is found at 2.2 \sigma .
The upper limits found for the molecular gas content M ( { H } _ { 2 } ) / M _ { \star } < 0.11 , 0.09 , 1.8 , 1.5 , and 0.29 , respectively , and depletion time \tau _ { dep } \lesssim ( 0.2 - 7 ) Gyr of the five LLRGs are overall consistent with the corresponding values of main sequence field galaxies .
Our SED modeling implies large stellar-mass estimates in the range \log ( M _ { \star } / M _ { \odot } ) = 10.9 - 11.5 , typical for giant ellipticals .
Both our \mathit { w } PPM analysis and the cross-matching of the LLRGs with existing cluster/group catalogs suggest that the megaparsec-scale overdensities around our LLRGs are rich ( \lesssim 10 ^ { 14 } ~ { } M _ { \odot } ) groups and show a complex morphology .
The color-color and color-magnitude plots suggest that the LLRGs are consistent with being star forming and on the high-luminosity tail of the red sequence .
The present study thus increases the still limited statistics of distant cluster core galaxies with CO observations .

Conclusions : The radio galaxies of this work are excellent targets for ALMA as well as next-generation telescopes such as the James Webb Space Telescope .