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

Formats: - HTML - YAML - JSON - 2026-04-29T21:50:40.239357

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, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 1, -1, -2, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, -1], [0, 0, 0, 0, 0, 0, 0, 0], [4, 0, -2, -4, 4, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -2, 0, 0, 0, 1, 2, -1], [0, 0, 0, 0, 0, 0, 0, 0], [-3, 0, -2, -2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, -1, 1, 2], [0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0], [2, 0, 3, -2, 5, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 0, 0, 0, 0, 0, -2], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, -4, -2, -1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, -1, 1], [0, 0, 0, 0, 0, 0, 0, 0], [-8, 0, 7, -1, -7, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 0, 0, 0, -1, -2, 3], [0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 1, 4, 4, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -3, 0, 0, 0, -2, -2, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 1, -4, 4, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 4, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0], [10, 0, 2, -8, 2, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 0, 0, 0, 2, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0], [-6, 0, 0, -1, -3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -2, 0, 0, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 4, -4, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 0, 0, 0, 3, -3, 0], [0, 0, 0, 0, 0, 0, 0, 0], [2, 0, 11, 2, -9, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -2, 0, 0, 0, 1, -1, -1], [0, 0, 0, 0, 0, 0, 0, 0], [9, 0, 2, 4, 9, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, -2, 0, -2], [0, 0, 0, 0, 0, 0, 0, 0], [5, 0, -1, 1, 10, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -2, 0, 0, 0, -3, -2, 1], [0, 0, 0, 0, 0, 0, 0, 0], [-7, 0, -6, 0, 7, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -2, 0, 0, 0, -1, 1, -1], [0, 0, 0, 0, 0, 0, 0, 0], [3, 0, -5, -3, -2, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-8, 0, -9, -9, -16, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, -4, -2, 2], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -20, -10, 7, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, -3], [0, 0, 0, 0, 0, 0, 0, 0], [3, 0, -3, 0, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 0, 0, 0, 0, 0, 3], [0, 0, 0, 0, 0, 0, 0, 0], [-3, 0, -3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 0, 0, 0, -3, -5, 3], [0, 0, 0, 0, 0, 0, 0, 0], [-4, 0, 4, 9, -9, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 0, 0, 0, 3, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 6, 7, 6, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 0, 0, 0, 2, 4, 4], [0, 0, 0, 0, 0, 0, 0, 0]], 'ap': [[0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0], [-1, 0, 1, -1, -2, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, -1], [0, -2, 0, 0, 0, 1, 2, -1], [-3, 0, -2, -2, 0, 0, 0, 0], [-1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 1], [0, -1, 0, 0, 0, 0, 0, -2], [0, 0, 0, 0, -3, 0, 0, 0], [0, 0, 0, 0, 0, 0, -1, 1], [1, 0, 1, 4, 4, 0, 0, 0], [-1, 0, 1, -4, 4, 0, 0, 0], [0, 1, 0, 0, 0, 4, 0, -1], [0, 2, 0, 0, 0, 2, 1, 1], [0, 0, 4, -4, 0, 0, 0, 0], [0, -2, 0, 0, 0, 1, -1, -1], [9, 0, 2, 4, 9, 0, 0, 0], [0, -2, 0, 0, 0, -3, -2, 1], [0, -2, 0, 0, 0, -1, 1, -1], [3, 0, -5, -3, -2, 0, 0, 0], [0, 0, 0, 0, 0, -4, -2, 2], [0, 0, 0, 0, 0, 0, 3, -3], [-3, 0, -3, 0, 0, 0, 0, 0], [-1, 0, 6, 7, 6, 0, 0, 0], [-10, 0, 0, -6, -5, 0, 0, 0], [0, -4, 0, 0, 0, 0, 2, -2], [0, 3, 0, 0, 0, 2, -2, 0], [3, 0, 1, 3, 2, 0, 0, 0], [9, 0, -2, -4, 9, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 2], [0, 0, 0, 0, 0, 4, 2, 0], [-5, 0, -2, -7, 2, 0, 0, 0], [0, -3, 0, 0, 0, 4, 8, -3], [-3, 0, -6, -3, -6, 0, 0, 0], [0, 0, 0, 0, 0, 0, 5, 5], [-10, 0, -6, 6, 0, 0, 0, 0], [0, 0, 0, 0, 0, 5, 5, -5], [0, 0, 0, 0, 0, 3, 0, 3], [3, 0, -12, 0, -3, 0, 0, 0], [0, 1, 0, 0, 0, -6, -6, 2], [-2, 0, 0, 0, -4, 0, 0, 0], [0, -3, 0, 0, 0, 2, 4, -3], [3, 0, 3, -4, -4, 0, 0, 0], [11, 0, -11, -10, 10, 0, 0, 0], [0, 1, 0, 0, 0, 6, 0, -1], [0, -1, 0, 0, 0, 2, -2, 0], [0, 0, 0, 0, 0, 1, 0, -1], [0, 6, 0, 0, 0, 3, -3, 3], [-19, 0, 13, 19, -6, 0, 0, 0], [-6, 0, 0, 0, -12, 0, 0, 0], [0, -4, 0, 0, 0, 4, 5, -5], [-3, 0, -2, -5, 2, 0, 0, 0], [0, -5, 0, 0, 0, -6, 0, 5], [14, 0, 0, -12, 7, 0, 0, 0], [0, 3, 0, 0, 0, 2, -2, 0], [-3, 0, -4, -8, -3, 0, 0, 0], [0, 2, 0, 0, 0, -3, -2, -1], [9, 0, 12, 0, -9, 0, 0, 0], [3, 0, -9, -3, -6, 0, 0, 0], [0, 1, 0, 0, 0, -6, -6, 2], [-1, 0, -16, -17, 16, 0, 0, 0], [0, 4, 0, 0, 0, 4, 1, 1], [0, 4, 0, 0, 0, 0, 6, 2], [-6, 0, 2, -2, 0, 0, 0, 0], [-7, 0, -11, -7, 4, 0, 0, 0], [0, -2, 0, 0, 0, 1, 3, 1], [0, 0, -10, -10, 0, 0, 0, 0], [0, -3, 0, 0, 0, 6, 12, -3], [5, 0, 5, -10, -10, 0, 0, 0], [-11, 0, 11, 4, -4, 0, 0, 0], [0, 8, 0, 0, 0, 8, 1, 1], [0, 3, 0, 0, 0, -2, 2, 0], [3, 0, 6, 12, 3, 0, 0, 0], [0, -4, 0, 0, 0, 5, -4, -9], [0, 6, 0, 0, 0, -3, -9, -3], [16, 0, 0, 0, 32, 0, 0, 0], [-5, 0, 6, 1, -6, 0, 0, 0], [-5, 0, -5, -22, -22, 0, 0, 0], [11, 0, -4, -15, -4, 0, 0, 0], [0, -9, 0, 0, 0, -4, 4, 0], [-1, 0, 17, -1, -18, 0, 0, 0], [0, 4, 0, 0, 0, -1, 4, 5], [3, 0, -16, 0, -3, 0, 0, 0], [0, -7, 0, 0, 0, 4, 4, -14], [0, 0, 0, 0, 0, -4, -2, 0], [17, 0, 2, 19, -2, 0, 0, 0], [-7, 0, 7, -6, 6, 0, 0, 0], [-13, 0, -2, 11, -2, 0, 0, 0], [0, -4, 0, 0, 0, -4, -1, -1], [0, 0, 0, 0, 0, 0, 6, 0], [0, 2, 0, 0, 0, -1, -2, 1], [0, -10, 0, 0, 0, -1, 9, -1], [0, -7, 0, 0, 0, 0, 0, -14], [0, 8, 0, 0, 0, -8, -5, 5], [0, -9, 0, 0, 0, 0, 0, -9], [5, 0, -5, -28, 28, 0, 0, 0], [-30, 0, 2, -2, 0, 0, 0, 0], [0, 3, 0, 0, 0, -4, 4, 0], [-5, 0, -3, 5, -8, 0, 0, 0], [0, 0, 0, 0, 0, -8, -4, 6], [-5, 0, -5, 14, 14, 0, 0, 0], [0, 7, 0, 0, 0, 0, 0, -7], [2, 0, 0, 12, 1, 0, 0, 0], [0, -4, 0, 0, 0, 0, -6, -2], [9, 0, 11, 9, -2, 0, 0, 0], [0, -6, 0, 0, 0, -3, -6, -3], [17, 0, 5, -17, 22, 0, 0, 0], [0, 0, 0, 0, 0, 12, 6, -6], [0, 0, 24, 12, 9, 0, 0, 0], [0, 3, 0, 0, 0, 2, 4, 3], [-23, 0, 23, 14, -14, 0, 0, 0], [3, 0, -18, -21, -18, 0, 0, 0], [0, -8, 0, 0, 0, -8, -3, -3], [0, 4, 0, 0, 0, -9, -5, 9], [-5, 0, 12, 0, 5, 0, 0, 0], [0, -2, 0, 0, 0, 1, 3, 1], [0, -5, 0, 0, 0, 6, 6, -10], [0, 0, 16, 8, -21, 0, 0, 0], [0, -9, 0, 0, 0, 8, 16, -9], [-15, 0, -15, -10, -10, 0, 0, 0], [-14, 0, 0, 24, -7, 0, 0, 0], [42, 0, 2, -2, 0, 0, 0, 0], [0, -2, 0, 0, 0, 1, -1, -1], [0, 8, 0, 0, 0, 9, 8, -1], [-8, 0, 18, 18, -16, 0, 0, 0], [17, 0, 4, 21, -4, 0, 0, 0], [0, 3, 0, 0, 0, -6, 0, -3], [0, -16, 0, 0, 0, 0, 12, -8], [9, 0, -7, 9, 16, 0, 0, 0], [0, 14, 0, 0, 0, -9, -14, 5], [0, -4, 0, 0, 0, 7, -4, -11], [0, 1, 0, 0, 0, 2, 2, 2], [0, 0, -40, -20, 15, 0, 0, 0], [1, 0, 22, 23, -22, 0, 0, 0], [7, 0, -7, -12, 12, 0, 0, 0], [-19, 0, -32, -13, -32, 0, 0, 0], [0, -2, 0, 0, 0, -1, -3, 1], [17, 0, -18, 0, -17, 0, 0, 0], [0, 0, -20, -10, 27, 0, 0, 0], [0, -6, 0, 0, 0, 6, -1, 1], [35, 0, -35, -16, 16, 0, 0, 0], [0, 7, 0, 0, 0, 4, 0, -7], [0, -4, 0, 0, 0, -4, 7, 7], [6, 0, 0, 20, 3, 0, 0, 0], [0, 0, 0, 0, 0, -9, -9, 9], [23, 0, -17, -23, 6, 0, 0, 0], [-12, 0, 18, 18, -24, 0, 0, 0], [0, 0, 0, 0, 0, 20, 10, -4], [0, -4, 0, 0, 0, 4, -1, 1], [5, 0, 30, 25, 30, 0, 0, 0], [38, 0, 0, 0, 19, 0, 0, 0], [0, -4, 0, 0, 0, 0, 18, -2], [0, 3, 0, 0, 0, 0, 0, 0], [0, -1, 0, 0, 0, 0, 0, -2], [0, 0, 0, 0, 0, 8, 4, -18], [0, 1, 0, 0, 0, 2, 4, 1], [-1, 0, 16, 17, 16, 0, 0, 0], [12, 0, -20, 20, 0, 0, 0, 0], [-9, 0, 15, -9, -24, 0, 0, 0], [0, 4, 0, 0, 0, -5, -4, -1], [-9, 0, 6, 0, 9, 0, 0, 0], [0, 8, 0, 0, 0, -8, -9, 9], [0, 15, 0, 0, 0, -8, -16, 15], [17, 0, -17, 8, -8, 0, 0, 0], [0, -4, 0, 0, 0, -4, 1, 1], [0, 9, 0, 0, 0, 10, -10, 0], [1, 0, 18, 36, 1, 0, 0, 0]], 'char_orbit_index': 47, 'field_poly': [169, -182, 128, -12, -25, 24, -4, -2, 1], 'hecke_orbit_code': 40535557775819584, 'hecke_ring_character_values': [[703, [-1, 0, 0, 0, 0, 0, 0, 0]], [261, [1, 0, 0, 0, 0, 0, 0, 0]], [769, [0, 0, -1, 0, 0, 0, 0, 0]]], 'hecke_ring_cyclotomic_generator': 0, 'hecke_ring_denominators': [1, 284739, 284739, 284739, 5811, 284739, 284739, 21903], 'hecke_ring_inverse_denominators': [1, 2, 1, 2, 1, 2, 1, 2], 'hecke_ring_inverse_numerators': [[1, 0, 0, 0, 0, 0, 0, 0], [0, -1, 0, 1, -1, -1, -1, 0], [1, 0, 3, 0, -1, -1, 0, 0], [-13, -2, 7, 13, -6, -2, -3, -3], [0, 6, 8, 4, -5, -2, 2, 0], [-89, 3, -29, 60, -29, -1, -4, -1], [9, 32, -27, -27, 18, 0, 29, 16], [-322, -31, -322, 111, 111, 81, 31, 50]], 'hecke_ring_numerators': [[1, 0, 0, 0, 0, 0, 0, 0], [-531206, 395140, -349865, -1634, 99650, -23026, -2179, 836], [-155675, -30938, 62854, -17057, 29525, -8251, -5146, 2105], [328068, 58801, -11896, 42834, 19645, -7692, 80, 2365], [-4576, 6246, -3968, 2168, 773, -716, 84, 62], [41938, -398868, 98255, -157403, 50698, 10331, -19554, 3277], [1041560, -813003, 434146, 95639, -168580, 40087, 17697, -4786], [-34032, 29692, 16736, -18930, 11278, -1080, -1777, 856]], 'hecke_ring_power_basis': False, 'hecke_ring_rank': 8, 'id': 55172, 'label': '832.2.bu.j', 'level': 832, 'maxp': 997, 'weight': 2}