Database - mf_hecke_nf (Traces of Hecke operators acting on Galois orbits of newforms)

Formats: - HTML - YAML - JSON - 2026-05-01T19:46:10.006730

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, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0, 1, 0, 0, 0], [-2, 0, 0, 0, 0, 0, 2, 0, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, -1], [0, -1, 0, -1, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 1, 0, 0, 1, 0, 0], [1, -2, 0, -2, -1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, -1, 0, 0, 0], [1, 0, -1, 0, 0, -1, 0, 0, 0, 0], [-1, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, -2, 0, 1, 0], [1, 0, 0, 0, 0, 0, -1, 0, 0, 1], [3, 0, -2, 0, -1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, -1, 0, 0, 0, 1], [0, 0, 2, 1, 0, 1, -4, -1, 2, -1], [0, 0, -1, 0, 0, -1, 1, 0, -1, 1], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 2, 0, 0, 0, 0, 1, 0, 1, 0], [0, 0, -1, 3, 0, 0, 0, -1, -1, 0], [0, 0, 0, 1, 0, 0, 0, -1, 0, 0], [0, 0, 0, -3, 0, 1, 1, 1, 0, -1], [-1, -1, 0, -1, 1, 1, 0, 0, 0, 0], [-1, 2, 0, 0, 1, 0, 1, 1, 0, -1], [0, 0, -1, -1, 0, 0, -1, -1, -1, 0], [-1, 1, 1, 1, 0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 5, 0, -2, -1, -1, 1, 2], [-1, 2, 1, 2, 0, 1, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0, 1, 0, -1, 1], [-2, -2, 1, -2, 0, -1, 0, 0, 0, 0], [-2, 4, 0, 0, 1, 0, 2, 1, -1, -1], [1, 0, 0, 0, 0, 0, -1, 0, 1, 0], [0, -3, 0, 0, -1, 0, 0, -1, -1, 2], [0, 0, 2, -1, 0, -1, -1, 1, 2, 1], [2, 0, -1, 0, 0, 0, 0, 0, 0, 0], [3, 1, 0, -1, -1, 0, -1, 0, 1, 1], [7, 1, -2, 1, 1, -1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 0, 0, -1], [-8, -2, 0, 0, 0, 0, 8, 0, -2, -1], [-4, -1, 0, 0, -1, 0, 4, -1, 1, -2], [-3, 0, 0, 0, 1, 0, 3, 1, -2, 0], [1, 0, -2, 0, 0, -1, 0, 0, 0, 0], [10, -1, 0, 0, -1, 0, -10, -1, 3, -1], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 1, -1, 0, 1, -6, 1, 1, -1], [-2, -3, 1, -3, 1, -1, 0, 0, 0, 0], [4, -1, -2, -1, -1, -1, 0, 0, 0, 0], [0, 0, 0, 3, 0, 2, -5, 1, 0, -2], [6, -1, 0, 0, 0, 0, -6, 0, 0, 1], [-1, 0, 1, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, -3, 0, 0, 2, 1, 0, 0], [0, 0, -1, -1, 0, -1, -4, 1, -1, 1], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, -3, 0, 0, -1, 0, 0, -1, -1, -1], [-16, 3, 0, 0, 0, 0, 16, 0, -4, 1], [0, 0, -1, 2, 0, 0, -1, 0, -1, 0], [0, 0, -1, -3, 0, 2, 8, 1, -1, -2], [0, 0, -1, 0, 0, -2, 1, 0, -1, 2], [0, -3, 1, -3, -1, 0, 0, 0, 0, 0], [1, -1, 0, 0, -1, 0, -1, -1, 2, 2], [0, 0, 1, -4, 0, 0, -6, 1, 1, 0], [0, -1, 0, -1, -1, 0, 0, 0, 0, 0], [9, -2, -2, -2, 0, 2, 0, 0, 0, 0], [0, 0, 1, 1, 0, 1, 6, 1, 1, -1], [-1, 3, 0, 3, 1, -1, 0, 0, 0, 0], [-1, -1, 0, 0, 1, 0, 1, 1, -1, -4], [-10, -2, 4, -2, 0, 1, 0, 0, 0, 0], [1, 1, 0, 0, -1, 0, -1, -1, 0, -1], [0, 5, 0, 0, 1, 0, 0, 1, 1, -1], [-2, 0, 0, 0, 2, 0, 2, 2, 0, -2], [0, 0, 0, 2, 0, -1, -1, -1, 0, 1], [4, 2, 1, 2, 0, 1, 0, 0, 0, 0], [6, 3, 1, 5, 1, 0, -3, -1, 2, 0], [1, 1, 1, 1, -1, 0, 0, 0, 0, 0], [0, 0, -1, 7, 0, -3, 4, -1, -1, 3], [1, -4, 0, 0, 0, 0, -1, 0, 1, 2], [1, -1, 0, 0, 0, 0, -1, 0, 1, -1], [-1, 1, 0, 0, -1, 0, 1, -1, -3, 2], [-5, -6, -1, -6, 0, 1, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0, 1, 0, 0, 0], [-2, -2, 0, -2, 2, -3, 0, 0, 0, 0], [0, 0, -2, 0, 0, 0, 0, -2, -2, 0], [1, -5, -1, -5, -1, 2, 0, 0, 0, 0], [6, 4, 0, 4, 0, 1, 0, 0, 0, 0], [0, 0, -1, 5, 0, -3, -1, -2, -1, 3], [1, -2, 0, 0, 0, 0, -1, 0, 1, -1], [-3, 10, 1, 10, 2, -2, 0, 0, 0, 0], [0, 0, -2, -1, 0, 0, 7, -1, -2, 0], [0, 0, 1, 0, 0, 1, -1, 0, 1, -1], [0, 0, -2, 0, 0, 1, 1, 0, -2, -1], [1, 6, 0, 0, 2, 0, -1, 2, 3, 0], [2, 2, 0, 0, 0, 0, -2, 0, 1, 1], [0, 0, 1, -4, 0, 0, -11, 2, 1, 0], [0, 0, 3, -3, 0, -1, -2, 1, 3, 1], [0, 0, 1, 4, 0, -1, -2, -1, 1, 1], [-2, 2, 1, 2, 0, 0, 0, 0, 0, 0], [-11, 5, 0, 0, -1, 0, 11, -1, 0, -2], [0, 0, -1, 0, 0, 0, 1, 0, -1, 0], [-7, 4, 0, 4, 2, 1, 0, 0, 0, 0]], 'ap': [[0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, -1], [0, 1, 0, 0, 1, 0, 0, 1, 0, 0], [-1, 0, 1, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, -1, 0, 0, 1], [0, 0, -1, 0, 0, -1, 1, 0, -1, 1], [-1, 2, 0, 0, 0, 0, 1, 0, 1, 0], [-1, -1, 0, -1, 1, 1, 0, 0, 0, 0], [-1, 2, 1, 2, 0, 1, 0, 0, 0, 0], [-2, -2, 1, -2, 0, -1, 0, 0, 0, 0], [3, 1, 0, -1, -1, 0, -1, 0, 1, 1], [-4, -1, 0, 0, -1, 0, 4, -1, 1, -2], [1, 0, -2, 0, 0, -1, 0, 0, 0, 0], [-2, -3, 1, -3, 1, -1, 0, 0, 0, 0], [0, 0, -1, -1, 0, -1, -4, 1, -1, 1], [0, 0, -1, 0, 0, -2, 1, 0, -1, 2], [1, -1, 0, 0, -1, 0, -1, -1, 2, 2], [-1, -1, 0, 0, 1, 0, 1, 1, -1, -4], [-2, 0, 0, 0, 2, 0, 2, 2, 0, -2], [4, 2, 1, 2, 0, 1, 0, 0, 0, 0], [-1, 1, 0, 0, -1, 0, 1, -1, -3, 2], [0, 0, -2, 0, 0, 0, 0, -2, -2, 0], [0, 0, -2, -1, 0, 0, 7, -1, -2, 0], [-2, 2, 1, 2, 0, 0, 0, 0, 0, 0], [6, -3, 1, -3, -1, 0, 0, 0, 0, 0], [3, -1, 0, -1, -1, 1, 0, 0, 0, 0], [2, 2, 0, 0, -2, 0, -2, -2, 0, 0], [0, 0, -1, 0, 0, 0, 0, -2, -1, 0], [0, 0, -2, -4, 0, 2, -8, 2, -2, -2], [0, 0, -1, 0, 0, -1, -2, 2, -1, 1], [0, 0, 0, 2, 0, 2, 2, 2, 0, -2], [8, -3, -1, -3, -1, -2, 0, 0, 0, 0], [0, 0, 1, 6, 0, 1, 6, 0, 1, -1], [-2, 5, 1, 5, 1, 2, 0, 0, 0, 0], [-4, -3, 0, 0, 1, 0, 4, 1, 2, 0], [0, 0, 0, 3, 0, -3, -4, 1, 0, 3], [0, 0, 3, -1, 0, 5, 0, -1, 3, -5], [-8, 3, 0, 0, -1, 0, 8, -1, 3, -1], [0, 0, 2, 2, 0, -1, -8, 0, 2, 1], [-3, 2, -3, 2, 0, 2, 0, 0, 0, 0], [-5, 5, 0, 0, -1, 0, 5, -1, -1, 1], [-4, 1, -1, 1, -1, -1, 0, 0, 0, 0], [-6, -1, 0, -1, -1, -1, 0, 0, 0, 0], [0, 0, -1, 2, 0, 3, 1, 0, -1, -3], [3, -5, -1, -5, -3, -2, 0, 0, 0, 0], [0, -9, 0, -9, -1, 0, 0, 0, 0, 0], [-5, 3, 3, 3, 1, 0, 0, 0, 0, 0], [6, 5, 0, 0, 3, 0, -6, 3, 3, 1], [-8, 1, 0, 0, 1, 0, 8, 1, 4, -3], [5, 0, -1, 0, -4, -3, 0, 0, 0, 0], [0, 0, 2, -3, 0, -1, -11, -3, 2, 1], [2, 3, 0, 0, 3, 0, -2, 3, -2, 0], [7, 3, 2, 3, 3, 3, 0, 0, 0, 0], [0, 0, -2, 2, 0, 1, 6, -2, -2, -1], [-7, 0, 0, 0, -2, 0, 7, -2, 3, 2], [-1, 2, 5, 2, 2, 0, 0, 0, 0, 0], [0, 0, -4, 4, 0, -3, -7, 0, -4, 3], [2, 0, 0, 0, 4, 0, -2, 4, 2, -5], [0, 0, 3, -4, 0, 3, 1, 4, 3, -3], [7, 1, 0, 0, 3, 0, -7, 3, 3, -4], [-3, 1, 0, 0, -3, 0, 3, -3, 0, 8], [10, 5, 0, 5, 1, -2, 0, 0, 0, 0], [0, 0, -2, 8, 0, -2, 2, 0, -2, 2], [0, 0, 2, -10, 0, -2, 1, 2, 2, 2], [0, 0, -2, -2, 0, 1, 2, 0, -2, -1], [0, 0, -1, -3, 0, -4, -5, 5, -1, 4], [-7, -6, 0, 0, -2, 0, 7, -2, -4, -4], [0, -6, -4, -6, -2, 0, 0, 0, 0, 0], [0, 0, 3, 2, 0, 5, -9, -4, 3, -5], [0, 0, 2, 3, 0, 0, 5, 1, 2, 0], [1, 3, 2, 3, 3, 7, 0, 0, 0, 0], [-13, 4, 0, 0, 0, 0, 13, 0, -2, -1], [-1, 1, 0, 0, -1, 0, 1, -1, -3, 7], [0, 0, 0, 12, 0, 2, 4, 0, 0, -2], [15, 1, 0, 0, -1, 0, -15, -1, 2, 1], [7, 6, 0, 0, 2, 0, -7, 2, 3, 1], [8, 0, -1, 0, -2, 6, 0, 0, 0, 0], [11, -5, 0, -5, -5, 1, 0, 0, 0, 0], [0, 0, 0, -2, 0, 0, -3, 2, 0, 0], [0, 0, 3, 5, 0, -7, 0, -3, 3, 7], [4, -6, 2, -6, 2, 3, 0, 0, 0, 0], [17, -6, 0, 0, 2, 0, -17, 2, 1, 0], [6, -11, -1, -11, 3, 0, 0, 0, 0, 0], [8, -12, 0, 0, -2, 0, -8, -2, -1, -5], [7, -6, -3, -6, -4, 0, 0, 0, 0, 0], [-21, -2, 0, 0, 0, 0, 21, 0, -3, -4], [5, 2, 0, 0, 0, 0, -5, 0, 7, -1], [0, 0, -3, -4, 0, -2, 9, 0, -3, 2], [-7, -4, 0, 0, -4, 0, 7, -4, 0, 5], [-7, 1, 0, 1, -5, 3, 0, 0, 0, 0], [0, 0, 3, -3, 0, 3, 0, -3, 3, -3], [22, 5, -1, 5, -1, 1, 0, 0, 0, 0], [8, -1, 1, -1, -3, -1, 0, 0, 0, 0], [3, 8, 0, 0, 2, 0, -3, 2, -5, 6], [0, 0, -4, -7, 0, 1, -17, 3, -4, -1], [0, 0, 1, -12, 0, -5, -1, 6, 1, 5], [0, -9, 0, 0, -3, 0, 0, -3, -3, -3], [2, -5, 0, 0, -5, 0, -2, -5, 2, 6], [-18, 0, 7, 0, -2, -4, 0, 0, 0, 0], [-13, -5, 1, -5, 5, 0, 0, 0, 0, 0], [0, 0, 0, -8, 0, -3, -20, -2, 0, 3], [20, -8, 6, -8, -2, 4, 0, 0, 0, 0], [-7, 0, 1, 0, 6, -3, 0, 0, 0, 0], [0, 0, 1, 0, 0, 3, 8, 2, 1, -3], [0, 0, -9, 3, 0, 3, 10, 3, -9, -3], [6, 3, 0, 0, -1, 0, -6, -1, -1, 5], [-14, 3, -3, 3, 5, -6, 0, 0, 0, 0], [8, 4, 0, 0, -2, 0, -8, -2, 0, -4], [0, 0, -2, 6, 0, 2, 13, -2, -2, -2], [0, 0, -1, -3, 0, -1, -6, 1, -1, 1], [0, 0, 3, -10, 0, 1, -5, 0, 3, -1], [0, 0, -5, 0, 0, -8, -5, 2, -5, 8], [-12, 7, -4, 7, 3, -8, 0, 0, 0, 0], [0, 0, -3, 9, 0, 2, 15, -7, -3, -2], [0, 0, 4, -7, 0, 6, 3, 1, 4, -6], [-22, -1, 0, -1, 3, -6, 0, 0, 0, 0], [1, -3, 0, 0, 1, 0, -1, 1, 2, 9], [1, 8, 0, 0, 2, 0, -1, 2, 3, 1], [-18, 1, 0, 0, 5, 0, 18, 5, -1, 1], [-3, -1, 0, 0, -3, 0, 3, -3, 5, 5], [-9, 1, 0, 0, -3, 0, 9, -3, -4, -3], [7, -4, -1, -4, 0, 13, 0, 0, 0, 0], [0, 0, -4, -9, 0, 5, -3, -1, -4, -5], [0, 0, -4, 6, 0, -3, 5, -6, -4, 3], [0, 0, 6, -4, 0, 2, -2, 4, 6, -2], [14, -11, 2, -11, 1, 4, 0, 0, 0, 0], [0, 0, 1, -7, 0, -11, -2, -1, 1, 11], [15, 2, 0, 0, 2, 0, -15, 2, -8, 5], [9, 3, 0, 0, 1, 0, -9, 1, 9, 0], [8, -3, 5, -3, -5, 9, 0, 0, 0, 0], [-17, -7, 0, 0, 1, 0, 17, 1, -10, -5], [-3, 8, 2, 8, 0, -1, 0, 0, 0, 0], [0, 0, 1, 5, 0, -3, 11, 5, 1, 3], [0, 0, 0, 7, 0, -4, -9, -3, 0, 4], [8, -3, -6, -3, -3, 2, 0, 0, 0, 0], [13, -2, 0, 0, 0, 0, -13, 0, 1, -1], [-16, 1, 4, 1, 5, -2, 0, 0, 0, 0], [0, 0, 7, 6, 0, 10, -1, -6, 7, -10], [0, 5, 0, 0, 3, 0, 0, 3, -3, 9], [4, -8, 0, 0, 0, 0, -4, 0, 0, 4], [-18, -8, 0, 0, 4, 0, 18, 4, -8, -4], [0, 0, -7, -4, 0, -5, -4, 6, -7, 5], [2, -12, 0, 0, 2, 0, -2, 2, -2, -10], [0, 0, -6, -2, 0, -1, 29, -2, -6, 1], [0, 0, 7, -9, 0, 5, 14, 3, 7, -5], [0, 0, 2, 6, 0, -7, -4, 6, 2, 7], [-6, 8, 0, 8, 0, 1, 0, 0, 0, 0], [-18, -6, 3, -6, -4, -3, 0, 0, 0, 0], [0, 0, 5, 4, 0, 4, 13, 0, 5, -4], [26, -2, 3, -2, 0, -4, 0, 0, 0, 0], [7, 5, 0, 0, -1, 0, -7, -1, 12, 6], [26, 1, 0, 0, -1, 0, -26, -1, -3, 1], [-3, -1, 0, -1, 3, -7, 0, 0, 0, 0], [8, 10, 0, 0, 4, 0, -8, 4, -1, 5], [18, -7, -5, -7, 5, -1, 0, 0, 0, 0], [13, -7, -11, -7, 3, -8, 0, 0, 0, 0], [22, 2, 0, 0, -6, 0, -22, -6, -2, 1], [0, 0, 1, 8, 0, 4, -8, -2, 1, -4], [0, 0, -8, -3, 0, 8, 3, 1, -8, -8], [0, 0, 5, 9, 0, 5, -20, -3, 5, -5], [0, 0, -2, 6, 0, -2, -2, 2, -2, 2], [-2, -2, 0, 0, 4, 0, 2, 4, 1, 7], [0, 0, -3, 11, 0, 9, 6, -3, -3, -9], [0, 0, -2, 3, 0, -1, 23, -3, -2, 1], [0, 0, -9, -1, 0, 1, 22, 1, -9, -1], [10, 1, 3, 1, -5, 3, 0, 0, 0, 0], [0, 0, -7, 5, 0, 1, 18, 1, -7, -1]], 'char_orbit_index': 5, 'field_poly': [9, -42, 199, -40, 127, -12, 67, -2, 9, 0, 1], 'hecke_orbit_code': 4503874538831983, 'hecke_ring_character_values': [[38, [1, 0, 0, 0, 0, 0, 0, 0, 0, 0]], [76, [-1, 0, 0, 0, 0, 0, 1, 0, 0, 0]]], 'hecke_ring_cyclotomic_generator': 0, 'hecke_ring_denominators': [1, 1, 1536868, 1536868, 1536868, 1536868, 4610604, 2305302, 4610604, 1536868], 'hecke_ring_inverse_denominators': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'hecke_ring_inverse_numerators': [[1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, -4, 0, 1, 0], [1, -6, 0, -6, -1, 1, 0, 0, 0, 0], [-24, 1, 0, 0, 1, 0, 24, 1, -8, 1], [0, 0, 1, 40, 0, -9, -10, -9, 1, 9], [161, -12, -58, -12, -10, -8, 0, 0, 0, 0], [-88, 277, 0, 0, 68, 0, 88, 68, -14, -66], [0, 0, 411, 116, 0, 52, -1120, -82, 411, -52], [741, -1942, -146, -1942, -493, 463, 0, 0, 0, 0]], 'hecke_ring_numerators': [[1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [6161881, -398034, 1876446, -162941, 994032, -71604, 111041, -6318, 14742, -777], [330792, -1557847, 98901, -790705, 52392, -3774, 3116, -333, 777, 1601], [-6528107, 1352484, -6375996, 2477663, -3377632, 243304, -453567, 21468, -50092, -2833], [-6080223, 1226610, -5782590, -729699, -3063280, 220660, -434871, 19470, -45430, 6773], [4568151, -21645833, 2038445, -13846352, 1311846, -7378340, 219529, -990045, 4803, -110264], [9626169, -45575618, 11276363, -28353989, 2598834, -13585958, 412939, -1808988, -5415, -195107], [-213039, -85389230, 7135046, -54896585, 2265288, -29298548, 544993, -3941226, -25014, -438725], [-117819, -27043556, 1577650, -19195081, -1272056, -10288740, -124643, -1405052, -51426, -154917]], 'hecke_ring_power_basis': False, 'hecke_ring_rank': 10, 'id': 12621, 'label': '111.2.e.b', 'level': 111, 'maxp': 997, 'weight': 2}