Let $\mathbb{k}$ be a field, $X$ an indeterminate and $R = \mathbb{k}[X]/(X^7 - 1)$. Determine the set
$$\left\{\dim_{\mathbb{k}} R/\mathfrak{m} \mid \mathfrak{m} \text{ is a maximal ideal in } R\right\}$$
in the following three cases: $\mathbb{k} = \mathbb{Q}$; $\mathbb{k} = \mathbb{C}$; $\mathbb{k}$ is a field of characteristic 7.