A forwarded email question about SAGE. Can anyone help?
> I have been led to believe that what I need to do is the following class
> field calculations. For
> Crespo's (1997) tetrahedral example f(x) = x^4-2x^3+2x^2-2x+3 the associated
> modular form of
> weight one is F=q-iq^3-q^5-iq^11 +iq^15-q^17 –iq^19 –iq^23+…. \in
> S_1(2^57^4,\chi_{\bf Q}(i)}).
> So there should be a cyclic cubic extension at the bottom and a biquadratic
> extension at the top.
> Thus, I should have a cyclic cubic ray class group and a ray class character
> of order 3 and a
> biquadratic ray class group and a pair of quadratic characters. So I need the
> values of the
> quadratic ray class characters for the primes over p in the cubic extension
> split in the associated
> quadratic extensions. I guess this involves computing the possible
> decomposition and inertia
> subgroups and then deciding (how?) which case one is in for a given prime p.
>
>
>
> The second example is from Tate (1976) where f(x) = x^4+3x^2-7x+4. Then
> modular form of
> weight one of level N=133. The cubic in this case is x^3+x^2-6x-7 (in
> Chinburg's Ad. Math. 48
> (1983) 82 paper). Chinburg lists the first few Hecke eigenvalues in this case
> as F =
> q+\omega^2q^2 –i\omega^2q^3 +i\omega^2q^5 +…Again I need to know the value of
> the ray
> class character of the quartic on the primes over p.
>
>
>
> Can you provide me any hints as to how I would approach this in SAGE or can
> you direct me to
> some SAGE expert how could help me implement the basic class field
> calculations in SAGE.
>
>
>
> Sincerely,
>
>
>
> Norm Hurt
>
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