  We address the scaling behavior of the covariance of the magnetic field in
the three-dimensional kinematic dynamo problem when the boundary conditions
and/or the external forcing are not isotropic. The velocity field is gaussian
and $\delta$-correlated in time, and its structure function scales with a
positive exponent $\xi$. The covariance of the magnetic field is naturally
computed as a sum of contributions proportional to the irreducible
representations of the SO(3) symmetry group. The amplitudes are non-universal,
determined by boundary conditions. The scaling exponents are universal, forming
a discrete, strictly increasing spectrum indexed by the sectors of the symmetry
group. When the initial mean magnetic field is zero, no dynamo effect is found,
irrespective of the anisotropy of the forcing. The rate of isotropization with
decreasing scales is fully understood from these results.
