Algorithmic Construction of Vector-Valued Modular Forms and Application to an A4×ℤ4-invariant Model of Leptons
Abstract
We present an algorithmic procedure that constructs the Vector-Valued Modular Forms (VVMFs) of finite modular groups, as well as its implementation in a companion code. The usual method consists in building the first few VVMFs, whose tensor products then generate the others. We address the difficulty of systematically finding the minimal set of VVMFs that suffices to produce all higher-weight ones, and we propose a method to identify it that makes use of the Burnside-Brauer theorem. For any given group, whose basic group-theoretic and representation-theoretic description is provided by the user, the code determines the minimal set of VVMFs, explicitly builds it using general results of the theory of such functions, then performs the tensor products that generate any other VVMF. Importantly, it automatically takes into account all caveats that might arise during the study of new groups. Our approach reproduces the known results for the finite modular groups explored in the recent phenomenological literature on modular flavor symmetries, and works for additional groups which we tested. We illustrate our algorithm and the working of our code by studying a model of leptons based on the unexplored finite modular group A4×ℤ4.
Related
- Algorithmic Construction of Gapped Boundaries for Topological Stabilizer Codes: A Route to Low-Overhead Planar qLDPC Codes
- Spherical harmonic transform accelerated spectral construction of the U-matrix in the invariant imbedding T-matrix method
- Modular commutator as a robust topological invariant and approximate Markovianity
- Radiative Neutrino Mass in a Nonholomorphic T' Modular Invariant Model
- Efficient MPO Construction for Long-Range Hamiltonians with Periodic Boundary Conditions: Application to Many-Body Dynamics
BibTeX
@misc{bonnefoy2026algorithmic,
title = {{Algorithmic Construction of Vector-Valued Modular Forms and Application to an $A_4\times\mathbbZ_4$-invariant Model of Leptons}},
author = {Q. Bonnefoy and M. Rausch de Traubenberg and V. Saulquin},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.08387},
eprint = {2611.08387},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.08387},
}
RIS
TY - UNPB
TI - Algorithmic Construction of Vector-Valued Modular Forms and Application to an A_4×ℤ_4-invariant Model of Leptons
AU - Q. Bonnefoy
AU - M. Rausch de Traubenberg
AU - V. Saulquin
PY - 2026
DA - 2026/11/05
PB - arXiv
DO - 10.48550/arxiv.2611.08387
UR - https://arxiv.org/abs/2611.08387
AB - We present an algorithmic procedure that constructs the Vector-Valued Modular Forms (VVMFs) of finite modular groups, as well as its implementation in a companion code. The usual method consists in building the first few VVMFs, whose tensor products then generate the others. We address the difficulty of systematically finding the minimal set of VVMFs that suffices to produce all higher-weight ones, and we propose a method to identify it that makes use of the Burnside-Brauer theorem. For any given group, whose basic group-theoretic and representation-theoretic description is provided by the user, the code determines the minimal set of VVMFs, explicitly builds it using general results of the theory of such functions, then performs the tensor products that generate any other VVMF. Importantly, it automatically takes into account all caveats that might arise during the study of new groups. Our approach reproduces the known results for the finite modular groups explored in the recent phenomenological literature on modular flavor symmetries, and works for additional groups which we tested. We illustrate our algorithm and the working of our code by studying a model of leptons based on the unexplored finite modular group A_4×ℤ_4.
ER -