Data set contents
Title: Data for “Dual linear programming bounds for sphere packing via modular forms” Authors: Henry Cohn and Nicholas Triantafillou
List of files, types, and sizes:
File name Type Size data.txt plain text 963 KB Notes:
This data set contains numerical data for the paper Dual linear programming bounds for sphere packing via modular forms by Cohn and Triantafillou (available on the arXiv with arXiv ID 1909.04772, at the URL https://arXiv.org/abs/1909.04772).
Specifically, the file data.txt contains the q-expansions of the modular forms used to establish the bounds listed in Table 6.1. Each modular form is introduced by a line such as “Weight k = 6, level N = 96, gap T = 9” in terms of the notation from the paper. The following lines list the coefficients ai of the modular form g and bi for g with 0 ≤ i < 500;e these coefficients are more than enough information to specify the modular forms uniquely. In the paper we normalize to set a0= 1, but in this data set we instead save space by rescaling
to eliminate denominators from the included coefficients. After these coefficients are listed, the file also includes the corresponding dual lower bound for center density in R2k, both as an exact rational number and truncated to six decimal places.
