Possible wrong character value on newforms

[jenpaulhus]

From the bug report:

The value of chi on https://www.lmfdb.org/ModularForm/GL2/Q/holomorphic/7/5/b/a/ should be -1 when evaluated at 3. The same issue is also on newform 7.3.b.a.

[edgarcosta]

Where is the contradiction?

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On Sun, Dec 29, 2024, 17:20 Jen Paulhus, Ph.D. ***@***.***> wrote: From the bug report: The value of chi on https://www.lmfdb.org/ModularForm/GL2/Q/holomorphic/7/5/b/a/ should be -1 when evaluated at 3. The same issue is also on newform 7.3.b.a. — Reply to this email directly, view it on GitHub <#6309>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/AACO2BSJQPH4ZEWHXHAAAHT2IBYSRAVCNFSM6AAAAABULFZWDSVHI2DSMVQWIX3LMV43ASLTON2WKOZSG43DENBSGUYDEOI> . You are receiving this because you are subscribed to this thread.Message ID: ***@***.***>

[jenpaulhus]

I think they are referring to the table in the Character values section where it has a value of +1? I can get more info from the person who submitted the bug if needed. I don't know newforms very well so if this is something that is obviously correct as stated on LMFDB, just let me know and I can convey to the person who submitted the bug report.

[roed314]

The character is 7.b which has order 2, so it's a bug that the image of 3 is 1 (this would be the trivial character). Indeed, if you click through to the character page, you see that it has image -1 on 3.

[edgarcosta]

Ups, never noticed that section in my life

[saruulbao]

Hi! I am the one reporting the issue. I know that when I go to the homepage of the characters, I see the correct values there so it's not really a mistake. I spotted some other ones: Newform orbit 8.5.d.a. (same issue as in the 7.3.b.a one) and Newform orbit 12.3.c.a (this one is even more weird as it tells you the value of the Nebentypus character at 7 is 0). I suspect there might be some systematic mistake in the display on the pages of these newforms. I really hope this issue can be addressed. Thank you!

[edgarcosta]

The problem is here:
https://github.com/LMFDB/lmfdb/blob/main/lmfdb/classical_modular_forms/web_newform.py#L961

which calls:
https://github.com/LMFDB/lmfdb/blob/main/lmfdb/classical_modular_forms/web_newform.py#L961
perhaps under the wrong assumptions?

but just quickly looking at I don't see anything wrong, and the data is correct, as we have:

'hecke_ring_character_values': [[3, [-1]]]

I hope this helps whoever has more time to dig into this.

[wwylele]

I think I figured out what went wrong and posted a fix in #6318

[roed314]

Great! I probably won't have time to review it this week, but perhaps someone else will. Thank you!

[saruulbao]

I think I figured out what went wrong and posted a fix in #6318

So instead of the actual value of the character, the newform page displayed the power of the primitive n-th root of unity where n is the order of the character? Thank you!