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Fix Dirichlet character for newform orbit whose dimension is 1 #6318

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@wwylele wwylele commented Jan 8, 2025

This is my attempt of fixing #6309 . The hecke_ring_character_values field in this file seems to have double meaning: the generator value can be either the actual dirichlet character value (the complex e^{...}), or the log of it. Which way to interpret it depends on the existence of non-0 hecke_ring_cyclotomic_generator. Meanwhile, ConreyCharacter.values_gens always return the log value. This creates a discrepancy in this specific dim==1 code block, where hecke_ring_cyclotomic_generator is set to 0 (meaning hecke_ring_character_values should be interpreted as the final values), but hecke_ring_character_values stores the log values. A small transformation is needed here

A similar transformation is done here:

vals = [[v[0],[1] if v[1] == 0 else [-1]] for v in vals]

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Just to add some more info, according to the schema we have:
columns.mf_hecke_nf.hecke_ring_character_values

list of pairs [[m1,[a11,...,a1n]],...[mr,[a1r,...,arn]]] where mi are generators of (Z/NZ)* and [ai1,...,ain] is the value of chi(mi) expressed in terms of the Hecke ring basis or in cyclotomic representation [[c,e]] encoding c x zeta_m^e where m is hecke_ring_cyclotomic_generator`

while
columns.mf_newforms.char_values

quadruple where N is the level, n is the order of the character, u is a list of generators for the unit group of Z/NZ, and v is a corresponding list of integers for which chi(u[i]) = zeta_n^v[i]

@wwylele Would you mind adding some tests showing that the bug is fixed?

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wwylele commented Jan 9, 2025

Sure, let me add some

@wwylele wwylele force-pushed the main branch 2 times, most recently from 5f37980 to abfac98 Compare January 9, 2025 02:35
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wwylele commented Jan 9, 2025

I added some test. I am not quite happy that I did text matching over a whole html table. Is there a html parser in the testing framework that I am not aware of?

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