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

Formats: - HTML - YAML - JSON - 2026-05-01T01:30:56.662405

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, 0], [0, 0, 0, 0, 0, 0], [1, 0, 0, -1, 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, 0, 0, 0, 0, 0], [0, 1, -1, 1, -1, 0], [0, 0, 0, 0, 0, 0], [-2, 0, 0, 0, 1, -1], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, -1, -1, -1, -1], [0, 0, 0, 0, 0, 0], [-1, 0, -1, 1, 1, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [-3, 1, -2, 3, 1, -1], [0, 0, 0, 0, 0, 0], [0, 0, 0, -1, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [3, -2, -2, 0, 1, -1], [0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 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], [4, -1, 2, -4, -1, 1], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [-5, -2, -2, 0, 3, -3], [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, 0, 0, 0, 0], [2, 0, -2, -2, 2, 0], [0, 0, 0, 0, 0, 0], [-2, 1, -2, 3, 0, 1], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, -2, -2, -2, -2], [0, 0, 0, 0, 0, 0], [1, 0, 0, 0, -1, 1], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 1, -1, -5, -1, 0], [0, 0, 0, 0, 0, 0], [0, 0, 1, 0, -1, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [-2, 1, -1, 2, 0, -1], [0, 0, 0, 0, 0, 0], [0, 1, -1, 2, -1, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [7, 0, 0, 0, -1, 1], [0, 0, 0, 0, 0, 0], [0, -2, 1, 4, 1, -1], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [-3, 1, -3, 8, 0, -2], [0, 0, 0, 0, 0, 0], [3, -2, -1, -3, 3, 2], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [1, -1, -1, 0, -2, 2], [0, 0, 0, 0, 0, 0], [-1, -1, -1, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [1, 3, -1, -1, -2, -3], [0, 0, 0, 0, 0, 0], [-5, -1, 2, -3, 2, -1], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 1, 0, 1, 0, 1], [0, 0, 0, 0, 0, 0], [-4, 1, 1, 0, 1, -1], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0]], 'ap': [[0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [1, 0, 0, -1, 0, 0], [0, 0, 0, 0, -1, 0], [0, 1, -1, 1, -1, 0], [-2, 0, 0, 0, 1, -1], [0, 0, -1, -1, -1, -1], [-1, 0, -1, 1, 1, 0], [-3, 1, -2, 3, 1, -1], [3, -2, -2, 0, 1, -1], [0, 0, 0, 1, 0, 0], [4, -1, 2, -4, -1, 1], [-5, -2, -2, 0, 3, -3], [0, 1, 1, 0, 0, 0], [2, 0, -2, -2, 2, 0], [0, 0, -2, -2, -2, -2], [0, 1, -1, -5, -1, 0], [0, 0, 1, 0, -1, 0], [0, 1, -1, 2, -1, 0], [7, 0, 0, 0, -1, 1], [0, -2, 1, 4, 1, -1], [3, -2, -1, -3, 3, 2], [1, -1, -1, 0, -2, 2], [1, 3, -1, -1, -2, -3], [-4, 1, 1, 0, 1, -1], [0, 3, -3, -3, -3, 0], [6, 1, 2, -6, -3, -1], [-3, -1, 2, 3, -1, 1], [0, 3, -2, -1, -2, 1], [10, 0, 0, 0, 2, -2], [0, -2, -2, 0, 3, -3], [8, -2, 2, -8, 0, 2], [0, -2, 1, -9, 1, -1], [-3, -3, -3, 0, -1, 1], [-6, 0, 0, 6, 0, 0], [0, -5, 4, -2, 4, -1], [0, 0, 2, 0, 2, 2], [-2, 2, 2, 2, -4, -2], [-3, 1, 1, 0, -2, 2], [2, 0, -2, -2, 2, 0], [0, -2, 4, 0, 4, 2], [9, 1, 1, 0, -3, 3], [-12, -4, 2, 12, 2, 4], [0, -6, 3, -8, 3, -3], [19, 1, 1, 0, 0, 0], [0, 5, -4, -2, -4, 1], [12, 3, 3, 0, -1, 1], [0, 4, 4, 0, 0, 0], [0, 2, 1, -13, 1, 3], [3, -4, 0, -3, 4, 4], [-12, 2, 2, 12, -4, -2], [14, 4, 4, 0, -4, 4], [0, -1, -2, -6, -2, -3], [-3, 6, 6, 0, -3, 3], [5, -1, 6, -5, -5, 1], [0, 4, 0, 2, 0, 4], [0, -4, 2, -12, 2, -2], [-16, -2, 3, 16, -1, 2], [0, 0, 1, 8, 1, 1], [22, 2, 2, 0, -2, 2], [0, -6, 3, 4, 3, -3], [-16, 2, 2, 0, 0, 0], [6, -2, -2, 0, 3, -3], [0, 1, 1, -15, 1, 2], [16, 3, 0, -16, -3, -3], [-17, -1, -2, 17, 3, 1], [3, 0, 4, -3, -4, 0], [6, 4, 4, 0, -3, 3], [0, 2, 0, 16, 0, 2], [0, -2, -2, 0, 0, 0], [0, -2, 1, -9, 1, -1], [-13, -1, 3, 13, -2, 1], [0, -3, -1, -18, -1, -4], [-8, -1, 5, 8, -4, 1], [-5, -6, -6, 0, 4, -4], [18, -2, 4, -18, -2, 2], [0, 5, -5, -13, -5, 0], [0, -1, 6, 0, -5, 1], [-2, 2, 4, 2, -6, -2], [0, 4, 2, -7, 2, 6], [-18, -2, -2, 0, 4, -4], [5, -5, -5, 0, 7, -7], [0, -4, 2, 0, 2, -2], [2, 0, 0, 0, 3, -3], [-12, 2, -9, 12, 7, -2], [-14, 0, -4, 14, 4, 0], [24, 2, 2, 0, 2, -2], [-6, -1, 3, 6, -2, 1], [-1, -4, -4, 0, -3, 3], [-16, -2, -2, 0, 1, -1], [14, 2, 0, -14, -2, -2], [0, 8, -4, -6, -4, 4], [0, -3, -3, -8, -3, -6], [0, -2, -2, 0, 4, -4], [-1, -2, 0, 1, 2, 2], [12, 0, 0, 0, 0, 0], [-14, 2, -8, 14, 6, -2], [0, -6, 2, -10, 2, -4], [30, -1, 3, -30, -2, 1], [17, -6, 2, -17, 4, 6], [16, 2, 2, 0, -6, 6], [0, 4, -4, -14, -4, 0], [0, 6, -10, -10, -10, -4], [-21, 1, -5, 21, 4, -1], [0, -1, 0, 23, 0, -1], [0, -3, -1, 0, -1, -4], [1, -5, -5, 0, 0, 0], [-3, 7, -2, 3, -5, -7], [0, 0, -6, 12, -6, -6], [-5, -7, -7, 0, 9, -9], [-12, -3, 1, 12, 2, 3], [0, 3, -2, -16, -2, 1], [4, 0, 0, 0, 8, -8], [0, 6, -6, 13, -6, 0], [26, 8, 8, 0, -10, 10], [0, 7, -3, -13, -3, 4], [-24, -2, -2, 0, 3, -3], [0, -8, -1, -11, -1, -9], [5, -3, -2, -5, 5, 3], [-4, -8, -8, 0, 8, -8], [0, 1, -6, -15, -6, -5], [-30, 2, 2, 0, 1, -1], [-3, -3, -6, 3, 9, 3], [0, -6, 5, 11, 5, -1], [-21, -4, 6, 21, -2, 4], [11, -8, -8, 0, 5, -5], [6, 6, 1, -6, -7, -6], [12, 2, 2, -12, -4, -2], [22, -7, -7, 0, 0, 0], [30, -1, -3, -30, 4, 1], [0, -9, 2, -3, 2, -7], [-9, -9, -9, 0, 6, -6], [19, -2, 4, -19, -2, 2], [12, 2, 2, 0, 4, -4], [-15, 1, 1, 15, -2, -1], [15, 7, 7, 0, -9, 9], [0, 10, -5, 3, -5, 5], [0, 10, -6, 6, -6, 4], [-3, 3, 3, 0, -12, 12], [0, -6, 0, -18, 0, -6], [2, 9, 9, 0, -9, 9], [-27, 3, -9, 27, 6, -3], [0, -1, 4, -24, 4, 3], [-8, 6, 6, 0, -4, 4], [0, -11, 4, -11, 4, -7], [25, -4, -4, 0, 1, -1], [2, 3, 3, 0, -12, 12], [0, 4, 1, 27, 1, 5], [20, -2, 9, -20, -7, 2], [4, -2, 12, -4, -10, 2], [-8, -2, -2, 8, 4, 2], [-14, 4, 4, 0, 0, 0], [-20, -5, -5, 0, -4, 4], [5, 7, -10, -5, 3, -7], [0, 2, -1, -2, -1, 1], [-3, 6, 6, 0, -3, 3], [1, 6, 0, -1, -6, -6], [-11, -1, 7, 11, -6, 1], [-10, 3, 3, 0, 0, 0], [0, 3, 5, 5, 5, 8], [-1, 5, 0, 1, -5, -5], [6, 4, 4, 0, -2, 2], [6, -9, -9, 0, 2, -2], [18, -4, 8, -18, -4, 4], [0, -12, 9, -15, 9, -3], [0, 4, -3, 11, -3, 1], [0, 3, 8, 3, 8, 11], [0, 0, 9, -14, 9, 9], [9, 10, 10, 0, -6, 6], [-23, -9, 8, 23, 1, 9], [0, -2, 6, 14, 6, 4], [-4, -9, -9, 0, 9, -9], [3, 9, -9, -3, 0, -9], [0, 5, -9, -22, -9, -4], [0, -8, 4, 1, 4, -4], [-22, 8, 8, 0, 0, 0], [21, 4, 4, 0, 0, 0], [0, 2, 2, -18, 2, 4], [-4, -10, -10, 0, 2, -2], [-15, 8, 6, 15, -14, -8], [22, -3, 6, -22, -3, 3], [21, -6, -6, 0, 3, -3], [-28, 0, 0, 0, -9, 9], [-10, -10, 12, 10, -2, 10], [0, -2, -2, 30, -2, -4], [0, 2, 2, 30, 2, 4], [0, -4, -2, 12, -2, -6], [0, 0, 3, 34, 3, 3], [-3, -4, 3, 3, 1, 4], [0, -3, 9, 27, 9, 6], [26, 3, -7, -26, 4, -3], [-13, 7, 7, 0, -4, 4], [0, -12, 4, 0, 8, 12], [-4, -8, 8, 4, 0, 8], [0, 0, -3, 33, -3, -3], [0, -8, 7, 15, 7, -1], [0, -8, -6, 3, -6, -14], [0, -10, -3, 0, 13, 10], [24, 10, 10, 0, -8, 8], [11, -5, 2, -11, 3, 5], [0, 8, 6, 4, 6, 14], [11, 2, 2, 0, -4, 4], [-10, -8, 6, 10, 2, 8], [0, -9, 10, 2, 10, 1], [21, 14, 14, 0, -13, 13], [0, 6, -4, 20, -4, 2], [-2, 10, -2, 2, -8, -10], [54, 0, 0, -54, 0, 0], [-12, 0, 0, 0, -6, 6], [0, -7, 2, -32, 2, -5], [20, -1, 13, -20, -12, 1], [-27, 6, 6, 0, -9, 9], [-54, 0, 0, 0, 2, -2], [-4, 6, 4, 4, -10, -6], [0, -7, -1, -15, -1, -8], [-35, 2, -7, 35, 5, -2], [0, 12, -10, -6, -10, 2], [0, -8, 4, 24, 4, -4], [-2, -4, -8, 2, 12, 4], [-18, 10, 10, 0, -8, 8], [1, 12, -15, -1, 3, -12], [-13, 3, 3, 0, 3, -3], [39, -1, 11, -39, -10, 1], [-34, -2, 0, 34, 2, 2], [-8, -10, -10, 0, 4, -4], [14, 5, 5, 0, 5, -5], [-32, 0, -4, 32, 4, 0], [0, -4, 10, 8, 10, 6], [-24, -7, 6, 24, 1, 7], [29, -9, 13, -29, -4, 9], [0, 8, 7, -18, 7, 15], [0, -6, -2, -10, -2, -8], [33, -5, -5, 0, 3, -3], [0, -3, -3, 9, -3, -6], [-24, -3, -3, 0, -4, 4], [0, 0, 3, 33, 3, 3], [-21, -12, 10, 21, 2, 12], [-19, 5, -18, 19, 13, -5], [-50, -6, -6, 0, 2, -2], [41, -8, -8, 0, 5, -5], [0, -8, -7, 7, -7, -15], [-23, -18, 15, 23, 3, 18], [0, 17, -9, 32, -9, 8], [6, 10, 5, -6, -15, -10], [6, 0, 0, 0, -12, 12], [36, 2, -4, -36, 2, -2], [20, -9, -9, 0, 12, -12], [0, 3, -9, -9, -9, -6], [0, -3, 0, 34, 0, -3], [-44, 0, 0, 0, 2, -2], [36, 16, 16, 0, -21, 21], [-42, 4, -20, 42, 16, -4], [0, -2, -2, 18, -2, -4], [19, 15, 15, 0, -11, 11], [0, -4, 2, 30, 2, -2], [31, 3, -7, -31, 4, -3], [0, 3, 6, 7, 6, 9], [0, 3, -7, -48, -7, -4], [-27, -13, -13, 0, 14, -14], [-16, 10, -6, 16, -4, -10], [0, 8, -15, -4, -15, -7], [-34, -6, -6, 0, 4, -4], [0, -10, 4, -33, 4, -6], [-4, -6, -6, 0, 3, -3], [0, 2, -4, 12, -4, -2], [7, 6, -6, -7, 0, -6], [-9, -4, -4, 0, -1, 1], [22, 8, 8, 0, 4, -4], [-12, 7, 7, 0, -15, 15], [0, 16, -11, 15, -11, 5], [-43, 6, -1, 43, -5, -6], [0, -9, 4, -16, 4, -5], [0, -6, 3, 22, 3, -3], [-1, -4, 10, 1, -6, 4], [-34, -6, -6, 0, 6, -6], [58, -2, -2, -58, 4, 2], [65, 1, 2, -65, -3, -1], [0, -18, 6, -41, 6, -12], [-13, 4, -15, 13, 11, -4], [-14, 12, -10, 14, -2, -12], [0, 10, 2, 22, 2, 12], [0, -21, 12, -23, 12, -9], [42, -2, -2, 0, 10, -10], [13, -3, -3, 0, -5, 5], [-38, 2, -10, 38, 8, -2], [3, 1, 7, -3, -8, -1], [0, -2, 3, -18, 3, 1], [3, 3, 3, 0, -12, 12], [0, -1, 2, 13, 2, 1], [-3, -14, -14, 0, 7, -7], [0, -14, -2, -30, -2, -16], [0, 22, -12, 26, -12, 10], [37, 15, -10, -37, -5, -15], [-35, 0, 0, 0, -1, 1], [-26, -7, -7, 0, -6, 6], [0, 12, -12, 24, -12, 0], [-39, 2, -3, 39, 1, -2], [23, -1, -1, 0, 12, -12], [-27, -1, -1, 27, 2, 1], [32, -1, -1, 0, 8, -8], [32, 10, 0, -32, -10, -10], [-4, 12, -14, 4, 2, -12], [0, -3, -4, 18, -4, -7]], 'char_orbit_index': 19, 'field_poly': [1, 5, 24, 7, 6, -1, 1], 'hecke_orbit_code': 31526434375730412, 'hecke_ring_character_values': [[631, [1, 0, 0, 0, 0, 0]], [281, [1, 0, 0, 0, 0, 0]], [757, [1, 0, 0, 0, 0, 0]], [1081, [-1, 0, 0, 1, 0, 0]]], 'hecke_ring_cyclotomic_generator': 0, 'hecke_ring_denominators': [1, 149, 149, 149, 149, 149], 'hecke_ring_inverse_denominators': [1, 3, 1, 3, 1, 3], 'hecke_ring_inverse_numerators': [[1, 0, 0, 0, 0, 0], [0, 1, -2, 0, 1, -1], [0, 1, 0, -3, 0, 1], [-12, 8, 8, 0, -13, 13], [-19, -2, 10, 19, -8, 2], [0, -98, 31, 126, 31, -67]], 'hecke_ring_numerators': [[1, 0, 0, 0, 0, 0], [416, 179, 144, -67, 36, -6], [386, -114, 168, -103, 42, -7], [155, 744, 174, 186, -31, 30], [405, 2093, 719, 486, -81, 88], [49, 2053, 527, 625, -129, 96]], 'hecke_ring_power_basis': False, 'hecke_ring_rank': 6, 'id': 72212, 'label': '1260.2.s.h', 'level': 1260, 'maxp': 1999, 'weight': 2}