  We examine the coexisting spin and charge density waves as a possible ground
state of the magic-angle twisted bilayer graphene. When interactions are not
included, the spectrum of the material has 4 (8 if spin is taken into account)
almost flat almost degenerate bands. Interactions break down the degeneracy
forming an order parameter which is usually assumed to be a spin density wave
with a preset spin structure. Here we take into account a possible charge
density wave contribution to the order parameter, that is, inhomogeneous
distribution of the charge density within a twisted graphene supercell. We also
calculate self-consistently the spin structure of the order parameter. We find
that the density wave order is stable in the whole doping range from $-4$ to
$+4$ extra electrons per supercell. The spin texture changes from collinear at
zero doping to almost coplanar at finite doping. The density wave order shows
nematic distortion when we dope the system. We demonstrate that the local spin
magnetization is much stronger than the charge density variation, unless the
doping exceeds $3$ extra electrons or holes per supercell.
