Hilbert and Siegel Modular Forms: Thursday Report
- (Nathan, Nils) Discussion concerning the design of the class Siegel modular form
- How many coeffs of the singular part of a SMF of given prec does one need ?
- How to handle mixed precision when adding/multiplying forms of different prec type ?
- How to store the coefficients of odd weight forms ?
(Craig, Nils) Implemented Cython multiplication of Siegel modular forms into the class SiegelModularForm (no testing though because of a Cython bug)
(Nils) Wrote a portable pickling mechanism for class SiegelModularForm objects.
(Nils) Converted old data into instances of class SiegelModularForm, pickled them and uploaded the files to http://sage.math.washington.edu/home/nils.
- (Nathan) Finished faster significantly faster Cython code for multiplying Siegel modular forms (down from 90s for 500 loops to 7.6s for 500 loops)
- (Lassina) Lots and lots and lots of FCs of HMFs ...
Status as of Thursday
Recall: goal is a complete basis of SMFs on Sp(2,Z) for weight <= 50, Spinor zeta functions of the 'interesting' cusp forms, lcalc readable files of these L-functions.
We currently have:
All Maass cusp forms of weight <= 50
all 'interesting' cusp forms of weight <= 32
Already nicely working class SiegelModularForm to compute and manipulate Siegel modular forms. Initialisation is amongst others
possible via the uploaded data (e.g. cool over the net): http://sage.math.washington.edu/home/nils/Siegel-Modular-Forms/code/siegel-modular-forms.sage
sage: time F = siegel_modular_form(e4,m6(0),101) Creating I(f,g) Done CPU times: user 1.57 s, sys: 0.63 s, total: 2.20 s Wall time: 6.19 s sage: time F = siegel_modular_form(e4,m6(0),500) Creating I(f,g) Done CPU times: user 12.96 s, sys: 3.10 s, total: 16.05 s Wall time: 68.13 s sage: time F = siegel_modular_form(e4,m6(0),1000) Creating I(f,g) Done CPU times: user 40.61 s, sys: 6.59 s, total: 47.20 s Wall time: 333.87 s