The authors study theta representations \(\Theta^{(r)}_{2n}\) for coverings \(\mathrm{Sp}^{(r)}_{2n}(\mathbb{A})\) of symplectic groups \(\mathrm{Sp}_{2n}(\mathbb{A})\) of different degrees \(r\). When \(r\) is odd, under a conjecture on unipotent orbits, they construct a representation \(\sigma^{(2r)}_{2n-r+1}\) from \(\Theta^{(r)}_{2n}\) by a descent integral, and show that the representation is nonzero by computing its constant term. They hence conjecture that \(\sigma^{(2r)}_{2n-r+1}\) is indeed \(\Theta^{(2r)}_{2n-r+1}\). They also study some properties of \(\sigma^{(2r)}_{2n-r+1}\), namely, they show that the representation is globally generic. When \(r=n\), they prove that its Whittaker coefficient is factorizable, and analyze its unramified local factors. Finally, they show that the conjecture on unipotent orbits, and hence all the above results, holds for \(r=n=3\). This is a very pleasant paper as an example on the theory of automorphic representations of covering groups.