Unimodular lattices in dimensions 14 and 15 over the Eisenstein integers

TL;DR

This paper classifies all indecomposable unimodular hermitian lattices in dimensions 14 and 15 over Eisenstein integers, identifying those with minimal norm 3 and providing a complete enumeration.

Contribution

It provides a complete classification of indecomposable unimodular hermitian lattices in these dimensions over Eisenstein integers, including their minimal norms.

Findings

One lattice in dimension 14 has minimal norm 3.

Two lattices in dimension 15 have minimal norm 3.

Complete enumeration of such lattices in these dimensions.

Abstract

All indecomposable unimodular hermitian lattices in dimensions 14 and 15 over the ring of integers in $\mathbb{Q}(\sqrt{-3})$ are determined. Precisely one lattice in dimension 14 and two lattices in dimension 15 have minimal norm 3.