In this paper, we construct new Sidon spaces by using roots of irreducible polynomials and primitive elements in finite fields, and obtain new larger cyclic subspace codes. More specifically, given a prime power \(q\) and three positive integers \(k, m\) , and \(n\) , we use Sidon spaces of the form \( U_{i,J,R} = \left\{ a + u\sum _{l \in \Lambda _1}\gamma _{i,j_l} + \right. \left. u^{q^{s_{z}}} \sum _{t \in \Lambda _2} \xi _{i,r_t} \mid a \in \mathbb {F}_q, u \in \mathbb {F}_{q^k} \right\} \) , and obtain new cyclic subspace codes of size \( C_{\rho }^{\left| \Lambda _{1} \right| } C_{\theta }^{\left| \Lambda _{2} \right| } \frac{ q^{k} \left( q^{n}-1 \right) }{q-1} \) , where \(\rho = \lceil \frac{m}{2k} \rceil - 1\) , \(\theta = \lceil \frac{n}{2m} \rceil - 1\) .
