Let \(d \ge 2\) and let \(\mathbb{S}^d_R\) denote a \(d\)-sphere with radius \(R>0\). We define for \(l\in \mathbb{N}_0\) the eigenspace \(H_l = \span \langle Y_{l,1}, \ldots, Y_{l, n_l}\rangle\), where \(Y_{l,m}\) denote spherical harmonics on \(\mathbb{S}^d_R\). Then for \(N\in \mathbb{N}\)
\begin{equation*} \Pi_N = \bigoplus_{l=0}^{N} H_l \end{equation*}is the space of spherical polynomials of order at most \(N\).