On Apr 15, 4:52 pm, William Stein <wst...@gmail.com> wrote: > On Wed, Apr 15, 2009 at 6:20 AM, Steve Finch <sfin...@hotmail.com> wrote: > > > I suspect that these are simple questions, but need help getting > > started. Thank you! > > > How do I exhibit coefficients of the unique cusp form of weight 9/2, > > level 4 and trivial character? > > (The coefficients should be 1, -6, 12, -8, 0, 12, -48, 48, -15, ...) > > That appears to be the last form here, e.g., B[4]: > > sage: B = half_integral_weight_modform_basis(DirichletGroup(16)(1), 9, 40) > sage: for f in B: print f > q - 2*q^2 + 4*q^3 - 8*q^4 + 4*q^6 - 16*q^7 + 48*q^8 - 15*q^9 + 20*q^10 > - 4*q^11 - 96*q^12 - 40*q^14 + 80*q^15 + 64*q^16 + 96*q^17 - 78*q^18 - > 52*q^19 + 148*q^22 - 80*q^23 - 96*q^24 - 335*q^25 + 140*q^26 + 48*q^27 > + 384*q^28 - 200*q^30 - 160*q^31 - 384*q^32 + 672*q^33 - 88*q^34 + > 280*q^35 + 120*q^36 - 116*q^38 + 304*q^39 + O(q^40) > q^2 - 2*q^3 + 4*q^4 - 2*q^6 + 8*q^7 - 24*q^8 - 10*q^10 + 2*q^11 + > 48*q^12 + 20*q^14 - 40*q^15 - 32*q^16 + 39*q^18 + 26*q^19 - 74*q^22 + > 40*q^23 + 48*q^24 - 70*q^26 - 24*q^27 - 192*q^28 + 100*q^30 + 80*q^31 > + 192*q^32 + 44*q^34 - 140*q^35 - 60*q^36 + 58*q^38 - 152*q^39 + > O(q^40) > q^3 - 2*q^4 - 4*q^7 + 12*q^8 - q^11 - 24*q^12 + 20*q^15 + 16*q^16 - > 13*q^19 - 20*q^23 - 24*q^24 + 12*q^27 + 96*q^28 - 40*q^31 - 96*q^32 + > 70*q^35 + 30*q^36 + 76*q^39 + O(q^40) > q^4 - 6*q^8 + 12*q^12 - 8*q^16 + 12*q^24 - 48*q^28 + 48*q^32 - 15*q^36 + > O(q^40)
Well, B[3] is f(q^4) where f is the form that Steve Finch is after. His form is some linear combination of B[0], B[1] and B[3]. But we don't have any nice way of identifying the level 4 things as a subspace of the level 16 things; it's more or less just luck that the fourth echelon basis vector happens to be f(q^4). The fact that you wrote "DirichletGroup(16)(1)" rather than "trivial_character(16)" there suggests you spotted the same bug that I did: there is a bug with the __call__ method of Dirichlet characters, which I have opened a ticket for at http://trac.sagemath.org/sage_trac/ticket/5792. David --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
