Context : Environmental effects are known to have an important influence on cluster galaxies , but studies at very faint magnitudes ( R > 21 ) are almost exclusively based on imaging .
We present here a very deep spectroscopic survey of galaxies on the line of sight to the Coma cluster .

Aims : After a series of papers based on deep multi–band imaging of the Coma cluster , we explore spectroscopically part of the central regions of Coma , in order to confirm and generalize previous results , concerning in particular the galaxy luminosity function , red sequence , stellar populations and the most likely formation scenario for the Coma cluster .

Methods : We have obtained reliable VIMOS redshifts for 715 galaxies in the direction of the Coma cluster centre in the unprecedented magnitude range 21 \leq R \leq 23 , corresponding to the absolute magnitude range -14 \leq { M _ { R } } \leq - 12 .

Results : We confirm the substructures previously identified in Coma by Adami et al .
( 2005a ) , and identify three new substructures .
We detect a large number of groups behind Coma , in particular a large structure at z \sim 0.5 , the SDSS Great Wall , and a large and very young previously unknown structure at z \sim 0.054 , which we named the background massive group ( BMG ) .
These structures account for the mass maps derived from a recent weak lensing analysis by Gavazzi et al .
( 2009 ) .
The orbits of dwarf galaxies are probably anisotropic and radial , and could originate from field galaxies radially falling into the cluster along the numerous cosmological filaments surrounding Coma .
Spectral characteristics of Coma dwarf galaxies show that red or absorption line galaxies have larger stellar masses and are older than blue or emission line galaxies .
R \leq 22 galaxies show less prominent absorption lines than R \geq 22 galaxies .
This trend is less clear for field galaxies which are similar to R \geq 22 Coma galaxies .
This suggests that part of the faint Coma galaxies could have been recently injected from the field following the NGC 4911 group infall .
We present a list of five Ultra Compact Dwarf galaxy candidates which need to be confirmed with high spatial resolution imaging with the HST .
We also globally confirm spectroscopically our previous results concerning the galaxy luminosity functions based on imaging down to R=23 ( { M _ { R } } = -12 ) and find that dwarf galaxies follow a red sequence similar to that drawn by bright Coma galaxies .

Conclusions : Spectroscopy of faint galaxies in Coma confirms that dwarf galaxies are very abundant in this cluster , and that they are partly field galaxies that have fallen onto the cluster along cosmological filaments .