  We study spatially periodic orbits for a coupled map lattice of sine circle
maps with nearest neighbour coupling and periodic boundary conditions. The
stability analysis for an arbitrary spatial period k is carried out in terms of
the independent variables of the problem and the stability matrix is reduced to
a neat block diagonal form. For a lattice of size kN, we show that the largest
eigenvalue for the stability matrix of size $kN \times kN$ is the same as that
for the basic spatial period k matrix of size $k \times k$. Thus the analysis
for a kN lattice case can be reduced to that for a k lattice case. We
illustrate this explicitly for a spatial period two case. Our formalism is
general and can be extended to any coupled map lattice. We also obtain the
stability regions of solutions which have the same spatial and temporal period
numerically. Our analysis shows that such regions form a set of Arnold tongues
in the $\Omega-\epsilon-K$ space. The tongues corresponding to higher spatial
periods are contained within the tongues seen in the temporally periodic
spatial period one or synchronised case. We find an interesting new bifurcation
wherein the the spatially synchronised and temporal period one solution
undergoes a bifurcation to a spatio-temporal period two travelling wave
solution. The edges of the stability interval of this solution are analytically
obtained.
