LMFDB - Database - mf_hecke

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Query: /api/mf_hecke_nf/?_offset=0

Table mf_hecke_nf

Hecke eigenvalues of Galois orbits of newforms

Column	Type	Example
an	jsonb	[[1, 0, 0], [0, 1, 0], [1, 0, 0], [1, 0, 1], [-1, -1, 1], [0, 1, 0], [0, -2, 1], [1, 0, 1], [1, 0, 0...
ap	jsonb	[[0, 1, 0], [1, 0, 0], [-1, -1, 1], [0, -2, 1], [1, 0, 0], [-3, 1, 1], [0, 0, 0], [0, 0, -2], [-4, 0...
char_orbit_index	smallint	1
field_poly	numeric[]	[2, -4, -1, 1]
hecke_orbit_code	bigint	103582791463085377
hecke_ring_character_values	jsonb
hecke_ring_cyclotomic_generator	integer	0
hecke_ring_denominators	numeric[]	[1, 1, 1]
hecke_ring_inverse_denominators	numeric[]	[1, 1, 1]
hecke_ring_inverse_numerators	numeric[]	[[1, 0, 0], [0, 1, 0], [3, 0, 1]]
hecke_ring_numerators	numeric[]	[[1, 0, 0], [0, 1, 0], [-3, 0, 1]]
hecke_ring_power_basis	boolean	False
hecke_ring_rank	integer	3
label	text	'9537.2.a.x'
level	integer	9537
maxp	integer	2999
weight	smallint	2

{'an': [[1, 0, 0, 0, 0, 0, 0, 0], [-1, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, -1, 0], [2, -1, 1, 0, 0, 0, 0, 0], [-2, 0, -1, 0, 0, -1, 0, 0], [-1, -1, 0, -1, 0, 1, 2, 0], [0, 0, 1, 1, 1, 0, 0, 0], [-3, 1, -2, 1, 0, 0, 0, 0], [1, -1, 0, 0, -1, 1, 1, 0], [2, -3, 0, -1, -1, 0, 1, -1], [-2, 0, -1, -1, -1, 1, 1, 1], [0, 1, -1, 1, 0, -2, -3, 1], [-1, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 2, 0, 1, 0, 0], [0, -1, 2, 0, 1, 1, 3, -1], [2, -3, 2, -1, 1, 0, 0, 0], [-2, 0, 1, -1, 1, 1, 1, -1], [-3, 2, 0, 1, 2, -2, -3, 1], [-1, -1, -2, -1, -2, -2, 1, -1], [-5, 3, -2, 0, 0, -1, -2, 1], [-2, -1, -1, -1, 0, -2, 1, 0], [2, -2, 1, -1, 1, -1, -3, 0], [0, 0, 2, -1, 1, 1, 0, 1], [1, -2, 1, -1, -1, 2, 4, -3], [2, 0, 3, 0, 0, 4, 1, 0], [1, -1, 0, 0, 0, 0, 0, 0], [-1, 3, -2, 2, -1, -2, -2, 0], [3, 0, 2, 0, 1, 0, -1, 1], [1, 0, 2, 2, 0, -1, -2, 1], [1, 5, -2, 5, 0, -3, -7, 2], [-1, 0, 0, 0, 0, 0, 0, 0], [-5, 2, -2, -1, -2, 1, 0, 0], [-2, 3, 2, 0, 1, 1, -1, -1], [4, 0, -1, 1, -1, -1, -3, 2], [0, -1, -2, -3, -2, 1, -1, 0], [3, -4, 1, -2, -1, 4, 6, -3], [-3, 3, 0, 2, 1, 2, 0, 2], [0, -2, -2, -2, -1, -4, 0, -1], [0, 0, 0, 0, 0, 0, 1, 0], [7, -3, 4, -2, 1, 3, 3, 0], [-2, -1, 0, -2, -1, -2, -1, 1], [0, -2, -3, -1, -3, -1, 0, -2], [0, 0, -1, -2, -2, 0, 2, -3], [-7, 0, -3, -1, -1, 2, 5, -3], [-6, 5, -1, 1, 2, -3, -4, 3], [-1, 2, -2, 1, -1, 2, -1, 0], [-3, 0, 0, 3, 3, 2, 1, -2], [0, 4, 0, 2, 2, -4, -4, 3], [0, 3, 2, 1, 0, 2, -2, 1], [-1, 6, 1, 4, 4, -1, -6, 4], [-4, 3, -2, 0, 1, -1, 1, 3], [-2, 1, -1, 0, 0, 0, 0, 0], [-1, -1, 1, -1, 0, -1, 1, -2], [8, -5, 5, -2, 1, 1, 6, -2], [3, 2, 1, 5, 1, -2, -2, 1], [-5, 2, -2, -3, -1, 1, 2, -1], [0, 1, 1, 4, 1, 1, -1, 0], [-4, 1, -1, 2, 1, 3, 5, -2], [0, -1, -1, -1, -2, -3, -1, -2], [5, -6, 5, -4, 0, 7, 11, -3], [1, -1, -1, 2, 1, 2, 0, -2], [1, -1, 0, 0, 0, 0, 0, 0], [-4, 1, 1, -2, 1, 0, 2, 0], [7, -1, 0, -1, 0, -2, -1, 1], [2, 0, 1, 0, 0, 1, 0, 0], [11, -1, 2, 1, 0, 1, 1, 2], [2, -1, 1, 0, 1, 1, 1, 1], [-5, 0, -1, -1, -1, 2, 5, -1], [-3, 2, 1, -2, 2, -1, 0, 2], [-4, -3, -1, -6, 0, -1, 1, 1], [-1, 0, -1, 0, -2, -2, 2, 1], [0, 6, -3, 3, -1, -6, -10, 5], [3, -2, -3, 0, 0, -1, -1, 0], [10, -3, 7, 2, 3, 3, -2, 0], [-3, 5, -7, 0, -3, -4, -7, 3], [-3, 0, -2, -2, -1, 2, 2, -1], [-6, -3, -4, -2, -3, -3, 2, -3], [1, 1, 0, 1, 0, -1, -2, 0], [4, 0, -2, -2, 0, -4, 0, 1], [-3, 8, -2, 5, 0, 0, -5, 1], [3, -6, 1, -2, 0, 2, 4, -4], [-3, -3, -5, -3, -3, 1, 4, -3], [-1, 0, 1, 2, -2, 1, 1, 1], [0, -1, 1, -2, 1, -1, -1, 1], [3, 0, -1, 3, -1, -2, -4, -1], [5, 1, -1, -1, 0, -7, -4, 3], [4, -5, -1, -1, -2, -2, 2, -1], [11, -1, 2, 3, 0, -7, -6, 5], [-3, -3, 1, -4, 1, 0, 2, -2], [14, -11, 4, -4, -4, 9, 11, -6], [0, 0, -1, -1, -1, 0, 0, 0], [6, -4, 3, 0, 2, -2, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0], [6, -2, 5, 4, 2, 0, -4, 4], [4, 6, 5, 1, 3, 4, -2, 3], [3, 0, 0, 0, -2, 5, 4, -1], [-3, 0, -2, -2, 0, 0, -1, -2], [6, 0, 4, 1, 3, 3, 2, 1], [6, -3, -1, 0, 1, -1, 3, 0], [5, -6, 2, -1, -1, 6, 11, -5]], 'ap': [[-1, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, -1, 0], [-2, 0, -1, 0, 0, -1, 0, 0], [0, 0, 1, 1, 1, 0, 0, 0], [-2, 0, -1, -1, -1, 1, 1, 1], [-1, 0, 0, 0, 0, 0, 0, 0], [-2, 0, 1, -1, 1, 1, 1, -1], [-1, -1, -2, -1, -2, -2, 1, -1], [0, 0, 2, -1, 1, 1, 0, 1], [1, 0, 2, 2, 0, -1, -2, 1], [-1, 0, 0, 0, 0, 0, 0, 0], [-3, 3, 0, 2, 1, 2, 0, 2], [-2, -1, 0, -2, -1, -2, -1, 1], [0, 0, -1, -2, -2, 0, 2, -3], [-3, 0, 0, 3, 3, 2, 1, -2], [-1, -1, 1, -1, 0, -1, 1, -2], [0, -1, -1, -1, -2, -3, -1, -2], [1, -1, -1, 2, 1, 2, 0, -2], [2, -1, 1, 0, 1, 1, 1, 1], [-1, 0, -1, 0, -2, -2, 2, 1], [3, -2, -3, 0, 0, -1, -1, 0], [4, 0, -2, -2, 0, -4, 0, 1], [-1, 0, 1, 2, -2, 1, 1, 1], [-3, -3, 1, -4, 1, 0, 2, -2], [-3, 0, -2, -2, 0, 0, -1, -2], [-1, -4, -1, 0, 2, 2, -3, -1], [-1, -1, 3, 4, 5, 3, 0, -2], [-5, -4, 1, -1, 3, 3, 2, -2], [1, -2, 1, -1, -3, -1, -5, 2], [-6, 3, -2, 0, -3, 0, 1, 0], [1, 3, -1, -1, 0, -3, -2, -2], [-1, 1, 0, -1, 0, 5, 1, 2], [0, 0, 2, 2, 0, -2, -5, 2], [-3, 2, 2, 2, 6, 1, -4, 4], [-5, 3, 6, 1, 0, 5, 0, 0], [5, 4, 1, 3, 1, 4, -2, 2], [-2, 3, 2, -2, 1, -2, -3, 1], [-4, 2, -4, 2, 0, -1, -2, 3], [4, 1, 6, 1, 0, 4, -5, 5], [-9, 5, -3, 3, -2, -1, 2, 1], [-2, 1, -2, -6, -5, -1, 3, -3], [-3, 0, -3, 2, 0, -3, 3, -4], [7, -7, -5, -1, 0, -6, 3, -2], [-6, 1, -1, -1, -2, -3, 4, 0], [-6, 1, 0, 3, 2, 2, -3, 2], [5, -3, 0, -2, -1, -2, 3, -6], [-1, -4, 2, -4, 0, -2, 0, -1], [2, 1, 1, 2, 1, -7, -2, -2], [0, -10, 6, -1, 1, 1, 2, -1], [3, -3, -4, -6, -5, -4, 5, -2], [5, 2, 0, -1, -3, -1, -9, 9], [3, 6, 6, 5, 5, 2, -8, 4], [5, -4, 3, -5, -3, -2, 3, 5], [7, 3, -1, 4, 3, -2, 3, 0], [-7, 4, -2, 7, 1, 1, 2, 2], [2, -2, -1, 3, -5, -3, -2, 3], [-16, 3, -7, -1, -2, -2, 2, 1], [-6, 5, -7, 1, 2, 0, -2, 3], [4, -3, 2, 3, -4, 0, 2, 3], [-5, 2, -2, 1, 3, -3, 1, -6], [0, -1, 2, -2, 7, 3, 0, -3], [-18, 3, -3, -5, 2, 2, 2, -3], [3, -5, 1, -2, 1, -1, 4, -2], [3, 0, 3, -2, -2, 2, -3, -3], [-1, -5, -4, -7, 0, -1, 5, -2], [-13, -4, 0, 4, 8, 0, 0, -1], [8, 3, 0, 1, -6, 6, 2, 3], [-7, 6, -5, -6, -6, -3, 9, 2], [19, 3, 1, 4, -1, -6, -5, -5], [8, 1, 5, 4, 3, 1, -6, 7], [-2, -10, 1, -5, -1, 1, 4, 2], [-10, 8, -5, 2, 2, 5, 2, 3], [-3, -4, 2, -4, 4, -1, -1, 2], [-7, 7, -3, 2, -5, -7, 0, -3], [9, 6, 0, -2, -2, -3, -9, 6], [-7, 5, -5, 2, -1, -2, 8, -3], [-1, 5, 4, 5, 4, 9, 2, 4], [-7, 0, 2, 1, -1, 7, 7, 1], [-4, -3, -3, 1, -2, -2, 2, -7], [4, 0, -8, 2, 0, -6, -5, -4], [8, -2, 4, 0, -2, -3, 4, -8], [-6, 1, 3, -4, -5, -2, 6, -1], [1, -5, 8, 2, 11, 8, 0, -4], [-5, 7, -4, 2, 3, 0, 6, -5], [9, 3, 5, -6, -3, -3, -6, 5], [-14, 6, -3, -6, 0, 3, -2, 2], [9, -1, 5, 3, 2, 1, -4, 4], [-2, -11, -2, -1, 4, -4, 7, -9], [2, 2, 3, 4, -2, -2, 6, 2], [0, 1, 1, -6, -7, 1, -6, 2], [-6, 3, -1, 3, 4, -9, -5, -4], [0, -5, -6, -6, -5, -6, -2, 6], [-4, -3, -1, 2, 3, 3, 6, -3], [5, -1, -1, 1, 0, 5, -2, -2], [-2, 3, -6, -3, -6, -8, 0, 3], [-6, 5, 0, 5, -2, 7, 4, -1], [-16, -3, -2, -3, -2, 0, -2, -2], [6, 6, 2, 12, 0, -4, -10, 3], [-1, 7, -3, 3, 2, -3, -4, -3], [5, -2, -9, -4, -8, -4, -2, -2], [9, 0, 3, 15, 5, 3, -8, 3], [-1, -3, 0, 4, 3, 8, 5, 6], [-4, 6, 1, 18, 8, 1, -7, 2], [4, 2, 0, 0, 0, 0, -1, -4], [-10, 1, -1, -3, -6, 2, 0, -1], [2, 2, -2, 1, -1, 1, -3, 5], [4, -6, 3, 6, -2, 6, -4, 5], [-10, 9, -4, 3, -4, 3, 1, 5], [-12, 7, 11, -7, -2, 9, 1, 2], [10, -4, 5, 8, 10, -2, 4, -2], [10, 2, 14, -8, 0, -4, -5, 1], [-3, -10, -6, -4, -2, 3, 7, -7], [-14, 0, -9, 1, -5, -5, 0, 0], [-7, 1, 6, 5, 2, 3, 1, -5], [-15, 1, -8, -8, -3, 2, 9, 3], [1, -5, 0, -2, 7, 2, 2, 1], [4, 0, 7, 3, 1, 11, -3, 15], [2, 13, -3, 7, 2, 6, -4, 5], [4, -1, 1, -5, -4, -4, -5, 6], [13, -6, -12, -3, -5, -15, -7, -8], [-8, -4, 6, 4, 4, 7, 8, 0], [-6, -3, -8, -1, 2, 2, 7, -8], [-23, 2, 0, -7, -3, -2, 3, -3], [-6, 7, -1, -1, -2, -1, 4, 4], [-18, 2, -5, -6, -8, -9, 2, -1], [13, -4, 2, -8, -12, -2, 6, -8], [-10, 2, 2, 3, 5, 9, 0, 4], [0, 7, -4, 3, 4, 0, -5, -3], [-4, 5, 1, 2, -3, 4, -8, 13], [-20, 8, -3, 13, 5, 6, 2, 1], [-16, -2, -8, -9, -9, -7, 8, -1], [24, -1, 9, -2, 3, 1, -4, -2], [-2, -3, 5, -6, -9, 0, -4, -2], [17, 2, 5, -5, 3, -2, -4, 2], [-7, 0, -2, -5, 3, 12, 6, -5], [-19, -1, 0, -13, -4, 6, 0, -3], [-9, -3, 7, -5, 2, 9, -1, 0], [-14, -8, -4, -1, 5, 9, 7, 0], [-4, 1, 3, -6, -9, -3, -5, 0], [23, -7, -7, -10, -7, -6, -2, -3], [-4, 7, -4, -6, 3, 9, 7, -7], [-5, -9, 11, -4, 7, 6, 3, 4], [0, -16, -3, 4, 6, 4, 1, -8], [-1, 0, 2, 6, -4, -5, -2, 1], [3, 6, -1, 6, -4, -3, -6, -1], [4, 5, 9, 11, 8, 8, -10, 3], [-4, 9, 6, 11, 14, 12, -2, 6], [-9, -4, -2, -10, -2, 5, 15, -3], [13, -1, 3, 18, 7, -6, -11, 10], [9, -10, 6, -1, 1, 10, 3, -1], [2, 7, -6, -5, -8, -3, -7, 8], [1, -3, 0, 6, 5, -12, -13, -6], [-1, -2, 5, 4, -4, 11, 3, 9], [2, 5, -9, 9, -2, -7, 0, -5], [-21, 6, -5, 3, 1, 3, 4, 4], [-4, 5, -9, 1, -4, -12, 8, -4], [2, -7, -5, -7, 2, -4, 10, -11], [8, 1, -1, 2, 3, -7, 1, -8], [6, -5, -3, -1, -2, 10, 6, -1], [-14, 8, 5, -4, 0, 14, 8, 5], [21, -3, 4, 16, 3, 0, -8, 5], [-1, -5, -2, -11, -4, -15, -4, -2], [15, 4, -5, 5, 5, 0, -4, -2], [5, 4, -1, 3, 3, -14, -11, 0], [-6, 6, -12, 0, -2, -13, -4, 8], [-13, -8, -9, 7, 5, -8, -5, -5], [-24, 5, -24, -3, -12, -8, 3, 4], [-3, 5, 7, 10, 3, 13, -10, 2]], 'char_orbit_index': 1, 'field_poly': [1, -1, -29, -31, 21, 19, -7, -3, 1], 'hecke_orbit_code': 13510798915666323, 'hecke_ring_cyclotomic_generator': 0, 'hecke_ring_denominators': [1, 1, 1, 1, 1, 1, 1, 1], 'hecke_ring_inverse_denominators': [1, 1, 1, 1, 1, 1, 1, 1], 'hecke_ring_inverse_numerators': [[1, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0], [3, 1, 1, 0, 0, 0, 0, 0], [3, 5, 1, 1, 0, 0, 0, 0], [15, 9, 6, 3, 1, 0, 0, 0], [27, 30, 12, 12, 3, 1, 0, 0], [90, 69, 43, 36, 13, 4, -1, 1], [205, 201, 109, 114, 40, 19, -3, 4]], 'hecke_ring_numerators': [[1, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0], [-3, -1, 1, 0, 0, 0, 0, 0], [0, -4, -1, 1, 0, 0, 0, 0], [3, 9, -3, -3, 1, 0, 0, 0], [0, 3, 9, -3, -3, 1, 0, 0], [2, -9, -30, 3, 21, -3, -4, 1], [2, -20, -34, 18, 20, -7, -3, 1]], 'hecke_ring_power_basis': False, 'hecke_ring_rank': 8, 'id': 33483, 'label': '403.2.a.d', 'level': 403, 'maxp': 997, 'weight': 2}

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Table mf_hecke_nf

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