Data inconsistency between LMFDB and Magma

[Cakti, B.G.]

Dear LMFDB Developers,

I am writing to share a possible data inconsistency between the LMFDB and Magma.

According to the LMFDB, there is only one Bianchi modular form at level norm 43 over $\mathbb{Q}(\sqrt{-43})$, namely the form with label 2.0.43.1-43.1-a. However, when I compute the newforms at the same level and over the same number field using Magma, I find that there are three newforms at this level.

Below, I have included the Magma code and its output for reference.

Could you please let me know whether the data at this level is complete, or if there might be an error?

Thank you very much for your time and help.

Best regards,
Begum

[John Cremona]

The newspace at that level has dimension 5 (see
https://www.lmfdb.org/ModularForm/GL2/ImaginaryQuadratic/2.0.43.1/43.1).
See also Magma's Dimension() functions on the space. The space splits
over Q as 1+2+2 as you can see from the output you attached -- two of
the 3 newform spaces there have dimension 2.

In the LMFDB at present we only display individual newforms when they
have dimension 1, i.e. when the Hecke eigenvalues are rational. The
other newforms have quadratic eigenvalues. in Q(sqrt(2)) and
Q(sqrt(5)) respectively. At some point we may also display details
for newforms of dimension greater than 1.

John Cremona

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