Database - mf_newforms

Formats: - HTML - YAML - JSON - 2026-10-22T21:35:15.823710

Query: /api/mf_newforms/?_offset=0

Table mf_newforms

Galois orbits of newforms

Column	Type	Example
Nk2	integer	154944
analytic_conductor	double precision	309.3085172696317
analytic_rank	smallint
analytic_rank_proved	boolean
artin_degree	integer
artin_field	numeric[]
artin_field_label	text
artin_image	text
atkin_lehner_eigenvals	integer[]	[[2, -1], [3, -1], [269, -1]]
atkin_lehner_string	text	'---'
char_conductor	integer	1
char_degree	integer	1
char_is_minimal	boolean	False
char_is_real	boolean	True
char_orbit_index	smallint	1
char_orbit_label	text	'a'
char_order	integer	1
char_parity	smallint	1
char_values	jsonb	[38736, 1, [14527, 9685, 21521, 24481], [17, 17, 17, 17]]
cm_discs	integer[]	[]
conrey_index	integer	1
dim	integer	3
embedded_related_objects	text[]
field_disc	numeric	3
field_disc_factorization	numeric[]	[[3, 1]]
field_poly	numeric[]	[1, -2, -1, 1]
field_poly_is_cyclotomic	boolean	False
field_poly_is_real_cyclotomic	boolean	True
field_poly_root_of_unity	integer	14
fricke_eigenval	smallint	-1
has_non_self_twist	smallint	-1
hecke_cutters	jsonb
hecke_orbit	integer	17
hecke_orbit_code	bigint	72057594071521104
hecke_ring_generator_nbound	integer
hecke_ring_index	numeric
hecke_ring_index_factorization	numeric[]
hecke_ring_index_proved	boolean
inner_twist_count	integer	-1
inner_twists	integer[]
is_cm	boolean	False
is_largest	boolean	False
is_maximal	boolean	False
is_polredabs	boolean	True
is_rm	boolean	False
is_self_dual	boolean	True
is_self_twist	boolean	False
is_twist_minimal	boolean
label	text	'38736.2.a.q'
level	integer	38736
level_is_powerful	boolean
level_is_prime	boolean	False
level_is_prime_power	boolean	False
level_is_prime_square	boolean
level_is_square	boolean	False
level_is_squarefree	boolean	False
level_primes	integer[]	[2, 3, 269]
level_radical	integer	1614
minimal_twist	text
nf_label	text	'3.3.49.1'
prim_orbit_index	smallint	1
projective_field	numeric[]
projective_field_label	text
projective_image	text
projective_image_type	text
qexp_display	text
related_objects	text[]	[]
relative_dim	integer	3
rm_discs	integer[]	[]
sato_tate_group	text	'1.2.3.c1'
self_twist_discs	integer[]	[]
self_twist_type	smallint	0
space_label	text	'38736.2.a'
trace_display	numeric[]	[0, 0, 7, 6]
trace_hash	bigint
trace_moments	numeric[]
trace_zratio	numeric
traces	numeric[]	[3, 0, 0, 0, 7, 0, 6, 0, 0, 0, -6, 0, -7, 0, 0, 0, 3, 0, 13, 0, 0, 0, 2, 0, 6, 0, 0, 0, 10, 0, 13, 0...
weight	smallint	2
weight_parity	smallint	1

{'Nk2': 4608, 'analytic_conductor': 9.1987663128515, 'analytic_rank': 0, 'analytic_rank_proved': True, 'char_conductor': 8, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 4, 'char_orbit_label': 'd', 'char_order': 2, 'char_parity': 1, 'char_values': [1152, 2, [127, 901, 641], [2, 1, 2]], 'cm_discs': [], 'conrey_index': 577, 'dim': 2, 'field_disc': -4, 'field_disc_factorization': [[-1, 1], [2, 2]], 'field_poly': [1, 0, 1], 'field_poly_is_cyclotomic': True, 'field_poly_is_real_cyclotomic': False, 'field_poly_root_of_unity': 4, 'has_non_self_twist': 1, 'hecke_cutters': [[5, [0, 1]], [7, [4, 1]], [17, [-2, 1]]], 'hecke_orbit': 1, 'hecke_orbit_code': 206191985792, 'hecke_ring_generator_nbound': 11, 'hecke_ring_index': 4, 'hecke_ring_index_factorization': [[2, 2]], 'hecke_ring_index_proved': True, 'id': 106826, 'inner_twist_count': 2, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1], [1, 1, 8, 2, 1, 2, 0]], 'is_cm': False, 'is_largest': False, 'is_maximal': False, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': False, 'is_self_twist': False, 'is_twist_minimal': False, 'label': '1152.2.d.a', 'level': 1152, 'level_is_powerful': True, 'level_is_prime': False, 'level_is_prime_power': False, 'level_is_prime_square': False, 'level_is_square': False, 'level_is_squarefree': False, 'level_primes': [2, 3], 'level_radical': 6, 'minimal_twist': '384.2.d.a', 'nf_label': '2.0.4.1', 'prim_orbit_index': 2, 'qexp_display': 'q-4 q^{7}+\\beta q^{11}-\\beta q^{13}+2 q^{17}+\\cdots', 'related_objects': [], 'relative_dim': 2, 'rm_discs': [], 'sato_tate_group': '1.2.3.c2', 'self_twist_discs': [], 'self_twist_type': 0, 'space_label': '1152.2.d', 'trace_display': [0, 0, 0, -8], 'trace_hash': 1543917248941261866, 'trace_moments': [{'__RealLiteral__': 0, 'data': '0.021', 'prec': 7}, {'__RealLiteral__': 0, 'data': '1.972', 'prec': 14}, {'__RealLiteral__': 0, 'data': '0.141', 'prec': 10}, {'__RealLiteral__': 0, 'data': '15.745', 'prec': 17}, {'__RealLiteral__': 0, 'data': '1.657', 'prec': 14}, {'__RealLiteral__': 0, 'data': '157.308', 'prec': 20}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.515', 'prec': 10}, 'traces': [2, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 16, 0, 10, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, -16, 0, 18, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -16, 0, 12, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 28, 0, 0, 0, 0, 0, -16, 0, -10, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, -64, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, -40, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 32, 0, -36, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, 0, 0, -32, 0, 0, 0, 0, 0, -40, 0, 0, 0, 0, 0, 0, 0, 0, 0, -44, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, -32, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, -48, 0, -26, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -64, 0, -44, 0, 0, 0, 0, 0, 64, 0, 0, 0, 0, 0, 0, 0, 0, 0, 64, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, -68, 0, 0, 0, 0, 0, 48, 0, 6, 0, 0, 0, 0, 0, 72, 0, 0, 0, 0, 0, 0, 0, 0, 0, -64, 0, 0, 0, 0, 0, -32, 0, 0, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 68, 0, 0, 0, 0, 0, 32, 0, 52, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 20, 0, 0, 0, 0, 0, -48, 0, 28, 0, 0, 0, 0, 0, -24, 0, 0, 0, 0, 0, 0, 0, 0, 0, -28, 0, 0, 0, 0, 0, 0, 0, 20, 0, 0, 0, 0, 0, -40, 0, 0, 0, 0, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, -16, 0, -32, 0, 0, 0, 0, 0, -40, 0, 0, 0, 0, 0, 0, 0, 0, 0, 64, 0, 0, 0, 0, 0, 48, 0, 0, 0, 0, 0, 0, 0, -48, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 16, 0, 82, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -64, 0, -32, 0, 0, 0, 0, 0, -32, 0, 0, 0, 0, 0, 0, 0, 0, 0, -20, 0, 0, 0, 0, 0, 80, 0, 36, 0, 0, 0, 0, 0, -64, 0, 0, 0, 0, 0, 0, 0, 0, 0, -36, 0, 0, 0, 0, 0, 48, 0, 44, 0, 0, 0, 0, 0, 56, 0, 0, 0, 0, 0, 0, 0, 0, 0, 20, 0, 0, 0, 0, 0, 48, 0, 50, 0, 0, 0, 0, 0, 88, 0, 0, 0, 0, 0, 0, 0, 0, 0, 36, 0, 0, 0, 0, 0, -48, 0, 96, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 96, 0, -68, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 64, 0, 0, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, -32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 64, 0, 0, 0, 0, 0, -48, 0, -32, 0, 0, 0, 0, 0, 56, 0, 0, 0, 0, 0, 0, 0, 0, 0, -96, 0, 0, 0, 0, 0, -32, 0, 0, 0, 0, 0, 0, 0, -88, 0, 0, 0, 0, 0, 0, 0, 0, 0, -20, 0, 0, 0, 0, 0, -96, 0, 92, 0, 0, 0, 0, 0, 40, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -112, 0, -96, 0, 0, 0, 0, 0, -32, 0, 0, 0, 0, 0, 0, 0, 0, 0, -52, 0, 0, 0, 0, 0, 0, 0, -32, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 36, 0, 0, 0, 0, 0, -48, 0, -70, 0, 0, 0, 0, 0, 40, 0, 0, 0, 0, 0, 0, 0, 0, 0, 44, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, 0, 0, 96, 0, 0, 0, 0, 0, 0, 0, 0, 0, 28, 0, 0, 0, 0, 0, 96, 0, 32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -32, 0, 0, 0, 0, 0, -72, 0, 0, 0, 0, 0, 0, 0, 0, 0, -28, 0, 0, 0, 0, 0, 0, 0, 44, 0, 0, 0, 0, 0, 96, 0, 0, 0, 0, 0, 0, 0, 0, 0, -84, 0, 0, 0, 0, 0, -48, 0, -30, 0, 0, 0, 0, 0, -24, 0, 0, 0, 0, 0, 0, 0, 0, 0, -60, 0, 0, 0, 0, 0, -32, 0, 0, 0, 0, 0, 0, 0, 40, 0, 0, 0, 0, 0, 0, 0, 0, 0, -128, 0, 0, 0, 0, 0, 64, 0, -36, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 60, 0, 0, 0, 0, 0, 96, 0, -20, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 116, 0, 0, 0, 0, 0, 0, 0, -96, 0, 0, 0, 0, 0, -88, 0, 0, 0, 0, 0, 0, 0, 0, 0, -64, 0, 0, 0, 0, 0, 32, 0, -128, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 84, 0, 0, 0, 0, 0, -96, 0, 0, 0, 0, 0, 0, 0, -64, 0, 0, 0, 0, 0, 0, 0, 0, 0, -96, 0, 0, 0, 0, 0, 144, 0, -76, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, -96, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -80, 0, -32, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, -108, 0, 0, 0, 0, 0, 32, 0, 4, 0, 0, 0, 0, 0, -32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 60, 0, 0, 0, 0, 0, 64, 0, 90, 0, 0, 0, 0, 0, -136, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, -64, 0, 36, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 48, 0, 96, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 20, 0, 0, 0, 0, 0, 0, 0, -68, 0, 0, 0, 0, 0, -24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 64, 0, 0, 0, 0, 0, -48, 0, -108, 0, 0, 0, 0, 0, 104, 0, 0, 0, 0, 0, 0, 0, 0, 0, -128, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 144, 0, 0, 0, 0, 0, 0, 0, 0, 0, -60, 0, 0, 0, 0, 0, 0, 0, 42, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 32, 0, -32, 0, 0, 0, 0, 0, 72, 0, 0, 0, 0, 0, 0, 0, 0, 0, 100, 0, 0, 0, 0, 0, 0, 0, -32, 0, 0, 0, 0, 0, 56, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, -80, 0, 96, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, -64, 0, 0, 0, 0, 0, -128, 0, 0, 0, 0, 0, 0, 0, -40, 0, 0, 0, 0, 0, 0, 0, 0, 0, 84, 0, 0, 0, 0, 0, -16, 0, 28, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -48, 0, -24, 0, 0, 0, 0, 0, 72, 0, 0, 0, 0, 0, 0, 0, 0, 0, 160, 0, 0, 0, 0, 0, 0, 0, 128, 0, 0, 0, 0, 0, 120, 0, 0, 0, 0, 0, 0, 0, 0, 0, -100, 0, 0, 0, 0, 0, -48, 0, 160, 0, 0, 0, 0, 0, -56, 0, 0, 0, 0, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, 0, 0, -32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 124, 0, 0, 0, 0, 0, -48, 0, 108, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 176, 0, -128, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, -76, 0, 0, 0, 0, 0, 88, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 96, 0, -10, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 36, 0, 0, 0, 0, 0, -96, 0, 0, 0, 0, 0, 0, 0, -192, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, -32, 0, 128, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 76, 0, 0, 0, 0, 0, -120, 0, 0, 0, 0, 0, 0, 0, 0, 0, -192, 0, 0, 0, 0, 0, -80, 0, 100, 0, 0, 0, 0, 0, 72, 0, 0, 0, 0, 0, 0, 0, 0, 0, 160, 0, 0, 0, 0, 0, 16, 0, 76, 0, 0, 0, 0, 0, -160, 0, 0, 0, 0, 0, 0, 0, 0, 0, 64, 0, 0, 0, 0, 0, 48, 0, 60, 0, 0, 0, 0, 0, -152, 0, 0, 0, 0, 0, 0, 0, 0, 0, -128, 0, 0, 0, 0, 0, 48, 0, 54, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -32, 0, -68, 0, 0, 0, 0, 0, 120, 0, 0, 0, 0, 0, 0, 0, 0, 0, 60, 0, 0, 0, 0, 0, 0, 0, -96, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 52, 0, 0, 0, 0, 0, 64, 0, 56, 0, 0, 0, 0, 0, -96, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 192, 0, 0, 0, 0, 0, 0, 0, 88, 0, 0, 0, 0, 0, 0, 0, 0, 0, 64, 0, 0, 0, 0, 0, 48, 0, -32, 0, 0, 0, 0, 0, 40, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -32, 0, -140, 0, 0, 0, 0, 0, 136, 0], 'weight': 2, 'weight_parity': 1}