This table was originally created by Michael Juergens during his dissertation project as: Extremal lattices It is maintained and updated here by Gabriele Nebe.

**Keywords**: modular lattices, tables, minimal norm, quadratic forms

Part of the **Catalogue of Lattices**
which is a joint project of
**Gabriele Nebe**,
RWTH Aachen university
(nebe@math.rwth-aachen.de)
and
**Neil J. A. Sloane**,
**(njasloane@gmail.com)**.

A **strongly N-modular** lattice is an even lattice of even level N
which is similar to all its partial dual lattices.
Extremal strongly modular lattices are those lattices
of square free level N with divisor sum dividing 24 for which
the minimum is as high as the theory of modular forms allows it to be,
for a precise definition see
Quebbemann, H.-G. Atkin-Lehner eigenforms and strongly modular lattices.
Enseign. Math. (2) 43 (1997).

2 | 3 | 5 | 6a | 6b | 7 | 11 | 14 | 15 | 23 | |
---|---|---|---|---|---|---|---|---|---|---|

2 | - | 1 | - | - | - | 1 | 1 | - | - | 1 |

4 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |

6 | - | 1 | - | - | - | 1 | 1 | - | - | - |

8 | 1 | 2 | 1 | 1 | 1 | 1 | 1 | 2 | - | |

10 | - | 3 | - | - | - | 4 | 2 | - | - | - |

12 | 3 | 1 | 4 | 6 | 4 | 0 | 0 | 1 | 3 (5) | - |

14 | - | 1 | - | - | - | 1 | ? | - | - | - |

16 | 1 | 6 | 1 | 8 | ≥ 18 | - | ? | ≥ 1 | - | |

18 | - | 37 | - | - | - | 0 | ? | - | - | - |

20 | 3 | ≥ 100 | ≥ 72 | ? | ≥ 13 | ≥ 1 | - | ? | ? | - |

22 | - | ≥ 1000 | - | - | - | ? | ? | - | - | - |

24 | ≥ 8 | ≥ 1 | ≥ 1 | ≥ 2 | 0 | - | ? | ? | - | |

26 | - | ≥ 6 | - | - | - | ? | - | - | - | - |

28 | ≥ 24 | ≥ 9 | ≥ 1 | ? | ? | ? | - | ? | ? | - |

30 | - | ≥ 2 | - | - | - | - | - | - | - | - |

32 | ≥ 7 | ≥ 33 | ? | ? | ? | - | - | - | - | |

34 | - | ≥ 100 | - | - | - | ? | - | - | - | - |

36 | ≥ 3 | ? | ? | ? | ? | - | - | - | - | - |

38 | - | ? | - | - | - | ? | - | - | - | - |

40 | ≥ 6 | ≥ 1 | ? | ? | ? | - | - | - | - | |

42 | - | ? | - | - | - | - | - | - | - | - |

44 | ≥ 1 | ? | ? | ? | ? | - | - | - | - | - |

46 | - | ? | - | - | - | ? | - | - | - | - |

48 | ≥ 6 | ? | ? | ? | - | - | - | - | - |