LMFDB - Database - mf_hecke_nf ((description not yet updated on this server))

Formats: - HTML - YAML - JSON - 2026-03-02T04:34:36.865529

Query: /api/mf_hecke_nf/?_offset=0

Column	Type
an	jsonb
ap	jsonb
char_orbit_index	smallint
field_poly	numeric[]
hecke_orbit_code	bigint
hecke_ring_character_values	jsonb
hecke_ring_cyclotomic_generator	integer
hecke_ring_denominators	numeric[]
hecke_ring_inverse_denominators	numeric[]
hecke_ring_inverse_numerators	numeric[]
hecke_ring_numerators	numeric[]
hecke_ring_power_basis	boolean
hecke_ring_rank	integer
label	text
level	integer
maxp	integer
weight	smallint

{'an': [[1, 0, 0, 0], [0, 0, -1, 0], [0, 1, 0, 0], [1, 0, 0, 0], [0, 0, 0, 0], [-2, 0, 0, -1], [0, 2, -2, 0], [0, 0, 1, 0], [1, 0, 0, 1], [0, 0, 0, 0], [4, 0, 0, 1], [0, 1, 0, 0], [0, 1, -2, 0], [2, 0, 0, -2], [0, 0, 0, 0], [-5, 0, 0, 0], [0, -2, 0, 0], [0, -3, 1, 0], [4, 0, 0, 0], [0, 0, 0, 0], [4, 0, 0, 0], [0, -3, -2, 0], [0, 0, -2, 0], [2, 0, 0, 1], [0, 0, 0, 0], [4, 0, 0, -1], [0, -1, 2, 0], [0, 2, -2, 0], [-1, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 1], [0, 0, 3, 0], [0, 5, 2, 0], [4, 0, 0, 2], [0, 0, 0, 0], [1, 0, 0, 1], [0, 4, 0, 0], [0, 0, -4, 0], [0, 0, 0, -1], [0, 0, 0, 0], [2, 0, 0, 2], [0, 0, -4, 0], [0, -5, 4, 0], [4, 0, 0, 1], [0, 0, 0, 0], [6, 0, 0, 0], [0, -5, 4, 0], [0, -5, 0, 0], [5, 0, 0, -4], [0, 0, 0, 0], [-8, 0, 0, -2], [0, 1, -2, 0], [0, 1, -2, 0], [-4, 0, 0, 1], [0, 0, 0, 0], [-2, 0, 0, 2], [0, 4, 0, 0], [0, 0, 1, 0], [-4, 0, 0, 2], [0, 0, 0, 0], [6, 0, 0, 0], [0, -3, 2, 0], [0, -2, 6, 0], [1, 0, 0, 0], [0, 0, 0, 0], [-16, 0, 0, -5], [0, 2, 2, 0], [0, -2, 0, 0], [-4, 0, 0, -2], [0, 0, 0, 0], [0, 0, 0, -2], [0, 3, -1, 0], [0, 0, 4, 0], [-8, 0, 0, -4], [0, 0, 0, 0], [4, 0, 0, 0], [0, 4, 0, 0], [0, 3, -2, 0], [8, 0, 0, -1], [0, 0, 0, 0], [-3, 0, 0, -2], [0, -6, 2, 0], [0, -8, 2, 0], [4, 0, 0, 0], [0, 0, 0, 0], [-2, 0, 0, 5], [0, -1, 0, 0], [0, 3, 2, 0], [6, 0, 0, 2], [0, 0, 0, 0], [8, 0, 0, -4], [0, 0, -2, 0], [0, 1, 2, 0], [-2, 0, 0, 5], [0, 0, 0, 0], [6, 0, 0, 3], [0, 0, 4, 0], [0, 12, -13, 0], [12, 0, 0, 4], [0, 0, 0, 0]], 'ap': [[0, 0, -1, 0], [0, 1, 0, 0], [0, 0, 0, 0], [0, 2, -2, 0], [4, 0, 0, 1], [0, 1, -2, 0], [0, -2, 0, 0], [4, 0, 0, 0], [0, 0, -2, 0], [-1, 0, 0, 0], [0, 0, 0, 1], [0, 4, 0, 0], [2, 0, 0, 2], [0, -5, 4, 0], [0, -5, 4, 0], [0, 1, -2, 0], [-4, 0, 0, 2], [6, 0, 0, 0], [0, 2, 2, 0], [0, 0, 0, -2], [0, 0, 4, 0], [8, 0, 0, -1], [0, -8, 2, 0], [6, 0, 0, 2], [0, 0, 4, 0], [-10, 0, 0, -2], [0, 0, -2, 0], [0, -2, 2, 0], [-6, 0, 0, 3], [0, -2, 8, 0], [0, 0, -2, 0], [-4, 0, 0, 0], [0, 0, -4, 0], [4, 0, 0, 2], [-14, 0, 0, -3], [0, 0, 0, -4], [0, 0, -8, 0], [0, -3, 8, 0], [0, 8, -6, 0], [0, 4, -12, 0], [12, 0, 0, 2], [-2, 0, 0, -5], [-16, 0, 0, 0], [0, 0, -4, 0], [0, -8, -4, 0], [0, 0, 0, -4], [-4, 0, 0, -3], [0, 0, 6, 0], [0, -4, -2, 0], [-6, 0, 0, 2], [0, 5, 2, 0], [8, 0, 0, -6], [10, 0, 0, 1], [4, 0, 0, -1], [0, 9, -6, 0], [0, -5, -8, 0], [10, 0, 0, -4], [8, 0, 0, 5], [0, 0, 4, 0], [2, 0, 0, 1], [0, -8, -6, 0], [0, 6, 4, 0], [0, 9, -4, 0], [0, 0, 0, -8], [0, -5, 6, 0], [0, -2, 12, 0], [12, 0, 0, -5], [0, -10, 0, 0], [0, -12, 6, 0], [10, 0, 0, -5], [0, 4, 8, 0], [-24, 0, 0, -3], [0, 0, 6, 0], [0, 9, -10, 0], [-12, 0, 0, -4], [0, 6, 2, 0], [2, 0, 0, -2], [0, -7, 6, 0], [-6, 0, 0, -3], [-2, 0, 0, -12], [20, 0, 0, 2], [-2, 0, 0, -8], [-16, 0, 0, 2], [0, -8, 20, 0], [16, 0, 0, 6], [0, 4, -10, 0], [6, 0, 0, 12], [0, 12, -16, 0], [14, 0, 0, -4], [0, 4, 6, 0], [0, 13, 4, 0], [-8, 0, 0, -1], [0, -6, 14, 0], [-20, 0, 0, 1], [12, 0, 0, 2], [0, 13, 4, 0], [-6, 0, 0, 5], [-14, 0, 0, -5], [0, -6, 6, 0], [30, 0, 0, 2], [0, 6, -6, 0], [0, -4, -12, 0], [0, 5, -8, 0], [-18, 0, 0, 0], [28, 0, 0, 0], [0, -2, 8, 0], [0, 16, -2, 0], [0, -7, 2, 0], [0, 0, 0, -9], [-14, 0, 0, -2], [0, -13, 4, 0], [0, 17, -2, 0], [0, -4, 20, 0], [28, 0, 0, -1], [-8, 0, 0, 6], [-6, 0, 0, 4], [0, -6, 6, 0], [0, 4, 10, 0], [0, -4, 16, 0], [-20, 0, 0, -9], [-26, 0, 0, 4], [0, -11, 18, 0], [0, -14, 20, 0], [0, 14, -2, 0], [28, 0, 0, 0], [-10, 0, 0, -3], [2, 0, 0, 11], [8, 0, 0, -2], [0, -4, 6, 0], [0, 0, -16, 0], [12, 0, 0, -1], [0, 0, 10, 0], [8, 0, 0, -12], [0, -2, 20, 0], [10, 0, 0, 12], [-2, 0, 0, 0], [0, -4, -24, 0], [0, -4, -2, 0], [0, -10, 12, 0], [6, 0, 0, -2], [-20, 0, 0, 0], [14, 0, 0, -1], [0, -20, 10, 0], [0, 5, 12, 0], [26, 0, 0, 0], [-16, 0, 0, 1], [0, 6, -12, 0], [0, -5, -10, 0], [28, 0, 0, -7], [0, 4, -2, 0], [0, -15, -2, 0], [10, 0, 0, -8], [0, -6, -2, 0], [0, -21, 12, 0], [0, -20, 10, 0], [-16, 0, 0, 3], [32, 0, 0, -6], [-34, 0, 0, 4], [0, -8, 24, 0], [22, 0, 0, -1], [0, -19, 4, 0], [0, 9, 10, 0], [0, 9, -16, 0], [20, 0, 0, 8], [0, 13, -14, 0], [0, 25, -4, 0], [24, 0, 0, 2], [0, 12, -16, 0]], 'char_orbit_index': 1, 'field_poly': [4, 0, -7, 0, 1], 'hecke_orbit_code': 27021597797778133, 'hecke_ring_cyclotomic_generator': 0, 'hecke_ring_denominators': [1, 1, 2, 1], 'hecke_ring_inverse_denominators': [1, 1, 1, 1], 'hecke_ring_inverse_numerators': [[1, 0, 0, 0], [0, 1, 0, 0], [4, 0, 0, 1], [0, 5, 2, 0]], 'hecke_ring_numerators': [[1, 0, 0, 0], [0, 1, 0, 0], [0, -5, 0, 1], [-4, 0, 1, 0]], 'hecke_ring_power_basis': False, 'hecke_ring_rank': 4, 'id': 50085, 'label': '725.2.a.g', 'level': 725, 'maxp': 997, 'weight': 2}

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.