On Thu, Feb 21, 2008 at 5:07 PM, David Joyner <[EMAIL PROTECTED]> wrote: > > 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.
SAGE currently has no functionality for computing with weight 1 modular forms, though certainly such functionality is planned (since we do have code for computing higher weight forms). Kevin Buzzard has written code for computing weight 1 forms in Magma, and made some largish tables. You should write to him. Also, I think Magma now has some new code for weight 1 forms, though I could be wrong. William --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---