= Solution
<Statistical isotropy> and <statistical reflection symmetry> allow the <spectral tensor> to contain only $\delta_{ij}$ and $k_i k_j$:
$$
\widehat C_{ij}(\mathbf k)=A(k)\delta_{ij}+D(k)k_i k_j.
$$
The <solenoidal magnetic-field constraint> is essential here. Taking its <Fourier transform> gives $k_i\widehat B_i=0$, hence $k_i\widehat C_{ij}=0$ and $A+Dk^2=0$. Thus the <spectral tensor> is a scalar multiple of the <transverse projector of a vector field>. Its <trace> is $2A$, so the prescribed normalization gives
$$
\boxed{\widehat C_{ij}(\mathbf k)=H(k)\left(\delta_{ij}-\frac{k_i k_j}{k^2}\right),\qquad k\ne0.}
$$
This is the <solenoidal isotropic spectral tensor>. Without the <solenoidal> condition, isotropy and reflection symmetry would leave two scalar functions. Without reflection symmetry, an antisymmetric term proportional to $i\epsilon_{ijm}k_m$ could additionally encode <magnetic helicity>.
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