  Let $F \in \mathbf{Z}[\boldsymbol{x}]$ be a diagonal, non-singular quadratic
form in $4$ variables. Let $\lambda(n)$ be the normalised Fourier coefficients
of a holomorphic Hecke form of full level. We give an upper bound for the
problem of counting integer zeros of $F$ with $|\boldsymbol{x}| \leq X$,
weighted by $\lambda(x_1)$.
