The label of a Bianchi newform has the form *field*-*level*-*suffix*.

Here *field* is the base number field $K$, and is denoted by its standard label; *level* is an integral ideal of $K$, denoted by its standard label; and *suffix* is a sequence of one or more letters representing the index of the form in a sorted list of newforms of the same level. Forms at the same level are sorted first by dimension, then by lexicographical order of the Fourier coefficients, which are themselves sorted according to the standard ordering of integral ideals.

For example, the Bianchi newform with label *2.0.4.1-61650.6-a* has base field $\mathbb{Q}(\sqrt{-1})$ (with label 2.0.4.1), level $(219-117i)$ (with norm 61650 and label 61650.6) and suffix $a$ (being the first of three newforms of dimension $1$ at that level).

**Authors:**

**Knowl status:**

- Review status: reviewed
- Last edited by John Cremona on 2017-06-27 16:04:16

**Referred to by:**

- lmfdb/bianchi_modular_forms/bianchi_modular_form.py (line 394)
- lmfdb/bianchi_modular_forms/templates/bmf-browse.html (line 39)
- lmfdb/bianchi_modular_forms/templates/bmf-newform.html (line 25)
- lmfdb/bianchi_modular_forms/templates/bmf-search_results.html (line 15)
- lmfdb/bianchi_modular_forms/templates/bmf-space.html (line 91)

**History:**(expand/hide all)

- 2017-06-27 16:04:16 by John Cremona (Reviewed)