On Wed, Apr 15, 2009 at 6:20 AM, Steve Finch <[email protected]> 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) > > How do I compute the dimension of the space of modular forms of weight > 3/2, level 28 and trivial character? For starters, read Cohen-Oesterle's paper "Dimensions des espaces de formes modulaires", H Cohen, J Oesterle - Lecture Notes in Mathematics, 1977, on dimension formulas and implement their algorithm, then post a patch. For your convenience I've posted a scan to http://sage.math.washington.edu/home/wstein/patches/Cohen-Oesterle-Dimensions_des_espaces_de_formes_modulaires.pdf The above algorithm is implemented in the case of integral weight in sage-3.*/devel/sage/sage/modular/dims.py > Same question for the space of cusp forms. > Same question for the space of primitive cusp forms. -- William --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to [email protected] 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 -~----------~----~----~----~------~----~------~--~---
