Label of an Hilbert Modular Form (awaiting review)

The label of a Galois orbit of Hilbert cuspforms is given by

(number field label) - (level label) - (orbit label)

separated by dashes.

The level ideal for Hilbert modular forms differs from the ideal label used in other parts of the LMFDB, since this data precedes the invention of these labels. Right now, the ideal is just labelled N.i where $N$ is the norm and i is a positive integer distinguishing ideals of the same norm. The ideal $\mathfrak{N}$ is described on the pages by $[N, n, \beta]$ where $N=\mathrm{Nm}(\mathfrak{N})$ is the absolute norm, $n$ generates the ideal $\mathfrak{N} \cap \Z$, and $\beta$ is some element such that $\mathfrak{N} = (N, n, \beta)$.

The orbit label is a letter again used to distinguish forms with the same number field and level.