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

Formats: - HTML - YAML - JSON - 2026-04-21T03:19:40.505281

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, 0, -1, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, -1, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0], [1, 1, 0, 0, -1, 1], [0, 0, 0, 0, 0, 0], [-1, 0, -1, 0, 0, 0], [0, 0, 0, 0, 0, 0], [1, 1, 1, 1, -2, 2], [0, 0, 0, 0, 0, 0], [0, 2, 0, -1, 0, 1], [0, 0, 0, 0, 0, 0], [0, -1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 2, 0, -2, 0], [0, 0, 0, 0, 0, 0], [1, -1, 2, 2, 0, 1], [0, 0, 0, 0, 0, 0], [0, 1, 0, 1, -1, 1], [0, 0, 0, 0, 0, 0], [-2, -2, -2, 0, 2, 0], [0, 0, 0, 0, 0, 0], [-1, -1, 0, -1, 2, -2], [0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [4, -1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [1, 1, 0, 1, -1, 2], [0, 0, 0, 0, 0, 0], [0, 1, 1, 2, -2, 1], [0, 0, 0, 0, 0, 0], [1, -2, -2, 1, 0, 1], [0, 0, 0, 0, 0, 0], [-1, -3, -2, -2, 4, -1], [0, 0, 0, 0, 0, 0], [1, 1, 2, 1, 0, 2], [0, 0, 0, 0, 0, 0], [-4, 0, 0, 2, 0, -2], [0, 0, 0, 0, 0, 0], [-4, 0, 0, -1, 0, 1], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -1, 0], [0, 0, 0, 0, 0, 0], [4, 2, 4, 0, -2, 0], [0, 0, 0, 0, 0, 0], [-1, 2, -5, -1, 0, -1], [0, 0, 0, 0, 0, 0], [2, 2, 2, 0, -2, 0], [0, 0, 0, 0, 0, 0], [2, 2, 4, 2, -3, 4], [0, 0, 0, 0, 0, 0], [4, -3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, -2, 0, 1, 0, -1], [0, 0, 0, 0, 0, 0], [1, 1, -3, 1, -2, 2], [0, 0, 0, 0, 0, 0], [6, 0, 4, -4, 2, -2], [0, 0, 0, 0, 0, 0], [-1, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0], [-8, 0, -6, 4, -2, 2], [0, 0, 0, 0, 0, 0], [-1, -1, -4, -1, 0, -2], [0, 0, 0, 0, 0, 0], [-2, -2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [-1, -1, 10, -1, 2, -2], [0, 0, 0, 0, 0, 0], [1, -1, 0, -2, 2, -1], [0, 0, 0, 0, 0, 0], [-8, 1, -12, -2, 1, -2], [0, 0, 0, 0, 0, 0], [-9, 2, -8, 2, -3, 1], [0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0], [-5, 4, 0, -1, 0, 1], [0, 0, 0, 0, 0, 0], [14, 2, 0, -2, 0, 2], [0, 0, 0, 0, 0, 0], [0, 0, -4, 0, -1, 0], [0, 0, 0, 0, 0, 0], [4, 2, 4, 0, -2, 0], [0, 0, 0, 0, 0, 0], [7, 1, -2, -2, 4, -3], [0, 0, 0, 0, 0, 0], [-1, 0, 0, 2, -1, 1], [0, 0, 0, 0, 0, 0], [-2, -2, 6, -2, 2, -4], [0, 0, 0, 0, 0, 0], [1, 0, 0, -1, 0, 1], [0, 0, 0, 0, 0, 0], [-1, 0, 0, 1, 0, -1], [0, 0, 0, 0, 0, 0]], 'ap': [[0, 0, 0, 0, 0, 0], [0, 0, -1, 0, 0, 0], [0, -1, 0, 0, 1, 0], [1, 1, 0, 0, -1, 1], [1, 1, 1, 1, -2, 2], [0, 2, 0, -1, 0, 1], [0, 0, 2, 0, -2, 0], [1, -1, 2, 2, 0, 1], [-2, -2, -2, 0, 2, 0], [4, -1, 0, 0, 0, 0], [1, 1, 0, 1, -1, 2], [-1, -3, -2, -2, 4, -1], [-4, 0, 0, 2, 0, -2], [-4, 0, 0, -1, 0, 1], [4, 2, 4, 0, -2, 0], [2, 2, 4, 2, -3, 4], [1, 1, -3, 1, -2, 2], [6, 0, 4, -4, 2, -2], [-1, -1, -4, -1, 0, -2], [0, 2, 0, 0, 0, 0], [-1, -1, 10, -1, 2, -2], [-9, 2, -8, 2, -3, 1], [-5, 4, 0, -1, 0, 1], [4, 2, 4, 0, -2, 0], [1, 0, 0, -1, 0, 1], [2, 2, 8, 2, -2, 4], [5, -1, 4, -2, 2, -1], [8, -3, 9, 2, 2, 1], [-1, -1, 2, -1, 6, -2], [8, 0, 0, 0, 0, 0], [-6, 1, 0, 1, 0, -1], [0, -1, -1, -2, 2, -1], [0, 0, -4, 0, -2, 0], [-2, 2, 0, 1, 0, -1], [-4, 2, -4, 0, -2, 0], [0, 0, 4, 0, 5, 0], [-2, -2, 4, -2, 4, -4], [0, 4, -2, -4, -2, -2], [2, 4, 0, 2, 0, -2], [6, 0, 8, 4, -2, 2], [0, 0, -8, 0, -4, 0], [-10, 0, 0, 1, 0, -1], [0, 0, -4, -8, 4, -4], [2, 2, 5, 2, -8, 4], [12, -2, 0, 2, 0, -2], [0, 0, 12, 0, -4, 0], [-2, 0, 0, 2, 0, -2], [20, 1, 0, 0, 0, 0], [3, 3, 7, 3, 2, 6], [5, 7, 8, 6, -10, 3], [-12, 0, -14, -4, 2, -2], [2, 2, 0, 0, 0, 0], [3, 3, 11, 3, 2, 6], [-13, -4, 0, 1, 0, -1], [12, 2, 12, 0, -2, 0], [0, 0, 8, 0, -2, 0], [-2, -2, 4, -2, 5, -4], [-12, -3, -12, 0, 3, 0], [1, 1, 0, 1, -2, 2], [20, 2, 0, -2, 0, 2], [-1, -1, 18, -1, 2, -2], [8, -1, 0, 0, 0, 0], [0, -6, 0, -3, 0, 3], [2, 2, -4, 2, -8, 4], [-3, -2, -5, -4, 4, -2], [0, -3, 0, 0, 3, 0], [7, -3, 8, 2, 2, 1], [5, 0, 0, -4, 0, 4], [2, 2, -8, 2, 0, 4], [-18, -4, 0, 4, 0, -4], [4, 4, 0, 4, -8, 8], [-12, 2, -6, 12, -8, 6], [3, 3, 12, 3, -3, 6], [-5, -3, 0, 10, -2, 5], [-14, 0, 0, -1, 0, 1], [-2, -4, -6, -8, 8, -4], [4, 4, 8, 4, -2, 8], [3, 1, 4, 2, -2, 1], [-2, 2, -8, -12, 4, -6], [-2, -2, -1, -2, -4, -4], [-12, -8, 0, -2, 0, 2], [2, -6, 0, 5, 0, -5], [0, 0, 8, 0, 4, 0], [8, 4, 0, 1, 0, -1], [4, 5, 8, 8, -9, 4], [24, 3, 23, -2, -2, -1], [6, -10, 0, 2, 0, -2], [11, -2, 17, 12, -4, 6], [20, 2, 0, 0, 0, 0], [-6, 4, 0, -5, 0, 5], [8, 4, 4, -8, 0, -4], [2, 2, -16, 2, -2, 4], [-5, -5, -8, -5, -3, -10], [-13, 0, 0, 3, 0, -3], [-15, -3, -12, 6, 0, 3], [-14, -2, 0, 0, 0, 0], [4, 1, 0, -8, 3, -4], [2, 2, -2, 2, -4, 4], [-9, -15, -14, -10, 20, -5], [-11, 5, -12, -2, -4, -1], [-10, 2, 0, 2, 0, -2], [2, 2, 20, 2, -9, 4], [-9, -9, -3, -9, 18, -18], [-2, -6, 2, 8, 2, 4], [-5, -5, -18, -5, -2, -10], [0, 0, -17, 0, -4, 0], [-15, 0, 0, 1, 0, -1], [26, 2, 22, -8, 2, -4], [2, 2, 26, 2, -4, 4], [3, -4, 0, 0, 0, 0], [7, 0, 8, 2, -1, 1], [0, 0, -22, 0, -2, 0], [-10, -4, 0, 4, 0, -4], [1, 1, 10, 1, -10, 2], [0, 13, 0, 0, 0, 0], [8, 8, 6, 8, -20, 16], [-2, -2, 0, 5, 0, -5], [-2, -2, -12, -2, -6, -4], [22, -7, 20, -4, 9, -2], [4, -8, 0, 6, 0, -6], [-1, -1, -4, -1, 12, -2], [-31, 0, 0, 6, 0, -6], [-32, -1, -32, 0, 1, 0], [-5, -5, -13, -5, 10, -10], [3, 13, 4, 2, -14, 1], [-12, 3, 0, -6, 0, 6], [-2, -4, -6, -8, 8, -4], [10, -4, 10, 0, 4, 0], [2, 11, 0, -5, 0, 5], [5, 1, 8, 6, -4, 3], [1, 1, -8, 1, -12, 2], [2, -4, 0, -4, 0, 4], [-3, -10, -4, -2, 11, -1], [8, 14, 0, -6, 0, 6], [-10, 2, -14, -8, 2, -4], [5, -8, 0, 6, 0, -6], [6, 6, 12, 6, -6, 12], [2, 2, 22, 2, -4, 4], [4, 1, 0, 6, 0, -6], [4, 4, -20, 4, -12, 8], [28, 6, 0, -8, 0, 8], [8, 13, 12, 8, -17, 4], [0, 0, 16, 0, 12, 0], [-21, -8, 0, -1, 0, 1], [-1, -1, -18, -1, 8, -2], [-10, -14, 0, 2, 0, -2], [12, 0, 0, 1, 0, -1], [6, 6, -6, 6, -8, 12], [0, 2, 2, 4, -4, 2], [10, -4, 14, 8, 0, 4], [10, -10, 8, -4, 12, -2], [-24, -6, 0, 2, 0, -2], [26, 0, 0, -5, 0, 5], [-2, -2, 6, 16, -6, 8], [5, 5, -6, 5, 4, 10], [-20, -2, 0, -2, 0, 2], [-29, 1, -24, 10, -6, 5], [-8, -2, -2, 12, -4, 6], [11, 0, 0, -8, 0, 8], [-2, -2, -20, -2, 3, -4], [-6, 6, -8, -4, -4, -2], [-18, 12, 0, -4, 0, 4], [18, 3, 0, -1, 0, 1], [12, -7, 13, 2, 6, 1], [-8, -8, -10, -8, 12, -16], [10, 10, 8, 10, -8, 20], [1, 1, -4, 1, -9, 2], [-3, -3, -26, -3, 14, -6]], 'char_orbit_index': 17, 'field_poly': [4, -18, 27, -19, 12, -3, 1], 'hecke_orbit_code': 49540695446258336, 'hecke_ring_character_values': [[127, [1, 0, 0, 0, 0, 0]], [421, [1, 0, 0, 0, 0, 0]], [449, [1, 0, 0, 0, 0, 0]], [577, [-1, 0, -1, 0, 0, 0]]], 'hecke_ring_cyclotomic_generator': 0, 'hecke_ring_denominators': [1, 1, 2, 1, 2, 1], 'hecke_ring_inverse_denominators': [1, 2, 2, 2, 2, 2], 'hecke_ring_inverse_numerators': [[1, 0, 0, 0, 0, 0], [1, 1, 0, 1, -2, 1], [-5, 3, 0, 1, -2, 1], [-5, -1, 6, -3, 8, -3], [27, -17, 12, -9, 18, -5], [49, -11, -34, 3, -28, 13]], 'hecke_ring_numerators': [[1, 0, 0, 0, 0, 0], [3, -1, 1, 0, 0, 0], [-18, 43, -28, 22, -5, 2], [22, -56, 37, -31, 7, -3], [50, -121, 82, -64, 15, -6], [24, -62, 44, -33, 8, -3]], 'hecke_ring_power_basis': False, 'hecke_ring_rank': 6, 'id': 47591, 'label': '672.2.q.l', 'level': 672, 'maxp': 997, 'weight': 2}