Re: inconsistency in mfcoefs

[Karim Belabas <Karim.Belabas@math.u-bordeaux.fr>]

* John Cremona [2018-08-30 14:43]:
> I will have more questions.  Just one or two for now:  in the setup as you
> describe it, when chi has order 2*m with m odd you use polcyclo(m,t) to
> define the bottom extension rather than polcyclo(2*m,t).

Yes.

> Of course that's only a sign change in t and mathematically trivial
> but it means that we cannot "see" that character order from the
> modulus.

Indeed, but you can still see it from the character itself. E.g.,

  [N, k, chi] = mfparams(Snew);
  znorder(chi)

> (Obviously I am happy when the order is 1 or 2 not to have
> any extension at all for the bottom layer).  I have to detect in my
> code when the order is 2 mod 4 when I define chipoly.
>
> Next, when the layer Q(chi)/Q is nontrivial but Q(f)=Q(chi) the polynomial
> you give for the trivial relative extension is just y rather than something
> with polmod coefficients (with a cyclotomic modulus).  That's the (only)
> reason I am having to construct the polcyclo myself.

You do not need to construct the chipoly: <modular form space>.mod gives
it to you. In your original example:

 N=11; k=3; G=znstar(N,1); chi=[1]; CHI = [G,chi];
 Snew = mfinit([N,k,CHI],0);

? Snew.mod
%3 = t^4 + t^3 + t^2 + t + 1

? charorder(G,chi)  \\ another way of getting the character order
%4 = 10

> I left the questions implicit: these are fairly trivial points which have
> certainly tripped up this pari user (and used up quite a lot of his time).

Have fun ! :-)

    K.B.
--
Karim Belabas, IMB (UMR 5251)  Tel: (+33) (0)5 40 00 26 17
Universite de Bordeaux         Fax: (+33) (0)5 40 00 21 23
351, cours de la Liberation    http://www.math.u-bordeaux.fr/~kbelabas/
F-33405 Talence (France)       http://pari.math.u-bordeaux.fr/  [PARI/GP]
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