Deposit
- Archive
- 10.5281/zenodo.14329286
- Paper
- Kim, C. H., and Lee, K. S. Basis of weakly holomorphic modular form spaces for squarefree level cases. Experimental Mathematics (2026), 1–49. DOI
- Software
- SAGE
How to read the files
Write \(\mathrm{Ex}(N)\) for the group of exact divisors of \(N\) under the operation \(e*e'=ee'/\gcd(e,e')^2\). A sign pattern \(\varepsilon\) for \(N\) is a group homomorphism \(\varepsilon\colon \mathrm{Ex}(N)\to\{\pm1\}\) with \(\varepsilon(1)=1\). For such an \(\varepsilon\), let \(M_k^{\varepsilon}(N)\) be the subspace of forms whose Atkin–Lehner eigenvalue is \(\varepsilon(p)\) for every prime \(p\mid N\), and define \(M_k^{!,\varepsilon}(N)\) in the same way inside the weakly holomorphic space.
Set \(m_{N,k}^{\varepsilon}=\max\{\mathrm{ord}_{\infty}f : f\in M_{N,k}^{\varepsilon}\}\). The form \(f\) with \(\mathrm{ord}_{\infty}f=m_{N,k}^{\varepsilon}\) is unique, and we write it as \(\Delta_{N,k}^{\varepsilon}\). The files give the recipe for constructing \(\Delta_{N,k}^{\varepsilon}\) together with its \(q\)-expansion.
The files are sorted by the level of the space. Each level has its own folder. Inside a folder there is one text file for every sign pattern at that level and every weight needed for the basis construction.
File names follow the convention D{level}{sign pattern}{weight}, where p stands for a plus sign and m stands for a minus sign. The file named D102pmm2 in the folder for \(N=102\) therefore deals with \(\Delta_{102,2}^{(+,-,-)}\), the form of level \(102\) and weight \(2\) with sign pattern \((+,-,-)\).
Last updated August 2026.