Database - mf_newforms

Formats: - HTML - YAML - JSON - 2026-10-23T13:57:03.406985

Query: /api/mf_newforms/?_offset=0

Table mf_newforms

Galois orbits of newforms

Column	Type	Example
Nk2	integer	3200
analytic_conductor	double precision	6.388032161702431
analytic_rank	smallint	0
analytic_rank_proved	boolean	True
artin_degree	integer
artin_field	numeric[]
artin_field_label	text
artin_image	text
atkin_lehner_eigenvals	integer[]
atkin_lehner_string	text
char_conductor	integer	20
char_degree	integer	2
char_is_minimal	boolean	True
char_is_real	boolean	False
char_orbit_index	smallint	14
char_orbit_label	text	'n'
char_order	integer	4
char_parity	smallint	1
char_values	jsonb	[800, 4, [351, 101, 577], [2, 4, 3]]
cm_discs	integer[]	[]
conrey_index	integer	543
dim	integer	2
embedded_related_objects	text[]
field_disc	numeric	-4
field_disc_factorization	numeric[]	[[-1, 1], [2, 2]]
field_poly	numeric[]	[1, 0, 1]
field_poly_is_cyclotomic	boolean	True
field_poly_is_real_cyclotomic	boolean	False
field_poly_root_of_unity	integer	4
fricke_eigenval	smallint
has_non_self_twist	smallint	1
hecke_cutters	jsonb	[[3, [8, -4, 1]], [7, [8, -4, 1]], [11, [0, 1]], [13, [2, -2, 1]]]
hecke_orbit	integer	10
hecke_orbit_code	bigint	40533290033087264
hecke_ring_generator_nbound	integer	9
hecke_ring_index	numeric	1
hecke_ring_index_factorization	numeric[]	[]
hecke_ring_index_proved	boolean	True
inner_twist_count	integer	2
inner_twists	integer[]	[[1, 1, 1, 1, 1, 1, 1], [1, 1, 20, 5, 1, 4, 0]]
is_cm	boolean	False
is_largest	boolean	False
is_maximal	boolean	False
is_polredabs	boolean	True
is_rm	boolean	False
is_self_dual	boolean	False
is_self_twist	boolean	False
is_twist_minimal	boolean	False
label	text	'800.2.n.j'
level	integer	800
level_is_powerful	boolean	True
level_is_prime	boolean	False
level_is_prime_power	boolean	False
level_is_prime_square	boolean	False
level_is_square	boolean	False
level_is_squarefree	boolean	False
level_primes	integer[]	[2, 5]
level_radical	integer	10
minimal_twist	text	'160.2.n.a'
nf_label	text	'2.0.4.1'
prim_orbit_index	smallint	5
projective_field	numeric[]
projective_field_label	text
projective_image	text
projective_image_type	text
qexp_display	text	'q+(2 i+2)q^{3}+(-2 i+2)q^{7}+5 i q^{9}+\\cdots'
related_objects	text[]	[]
relative_dim	integer	1
rm_discs	integer[]	[]
sato_tate_group	text	'1.2.3.c4'
self_twist_discs	integer[]	[]
self_twist_type	smallint	0
space_label	text	'800.2.n'
trace_display	numeric[]	[0, 4, 0, 4]
trace_hash	bigint	846542329289442432
trace_moments	numeric[]	[0.004, 1.957, 0.072, 11.506, 0.421, 94.835]
trace_zratio	numeric	0.253
traces	numeric[]	[2, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 2, 0, 0, 0, 10, 0, -8, 0, 16, 0, 4, 0, 0, 0, -8, 0, 0, 0, 0, 0,...
weight	smallint	2
weight_parity	smallint	1

{'Nk2': 3200, 'analytic_conductor': 6.388032161702431, 'analytic_rank': 0, 'analytic_rank_proved': True, 'char_conductor': 40, 'char_degree': 2, 'char_is_minimal': False, 'char_is_real': False, 'char_orbit_index': 15, 'char_orbit_label': 'o', 'char_order': 4, 'char_parity': 1, 'char_values': [800, 4, [351, 101, 577], [2, 2, 3]], 'cm_discs': [-8], 'conrey_index': 143, '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': [[3, [8, 4, 1]], [7, [0, 1]]], 'hecke_orbit': 1, 'hecke_orbit_code': 962106229536, 'hecke_ring_generator_nbound': 9, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'id': 83656, 'inner_twist_count': 4, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1], [1, 1, 8, 4, -1, 2, -8], [1, 1, 5, 3, -1, 4, 0], [1, 1, 40, 11, 1, 4, 0]], 'is_cm': True, 'is_largest': False, 'is_maximal': False, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': False, 'is_self_twist': True, 'is_twist_minimal': False, 'label': '800.2.o.a', 'level': 800, '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, 5], 'level_radical': 10, 'minimal_twist': '200.2.k.a', 'nf_label': '2.0.4.1', 'prim_orbit_index': 11, 'qexp_display': 'q+(2 i-2)q^{3}-5 i q^{9}+6 q^{11}+(4 i+4)q^{17}+\\cdots', 'related_objects': [], 'relative_dim': 1, 'rm_discs': [], 'sato_tate_group': '1.2.1.d4', 'self_twist_discs': [-8], 'self_twist_type': 1, 'space_label': '800.2.o', 'trace_display': [0, -4, 0, 0], 'trace_hash': 422585341881309718, 'trace_moments': [0, {'__RealLiteral__': 0, 'data': '1.959', 'prec': 14}, {'__RealLiteral__': 0, 'data': '0.188', 'prec': 10}, {'__RealLiteral__': 0, 'data': '16.973', 'prec': 17}, {'__RealLiteral__': 0, 'data': '4.148', 'prec': 14}, {'__RealLiteral__': 0, 'data': '180.607', 'prec': 20}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.625', 'prec': 10}, 'traces': [2, 0, -4, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, -24, 0, 0, 0, 0, 0, 0, 0, -12, 0, -12, 0, 0, 0, 0, 0, 0, 0, -32, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, -2, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, -28, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 50, 0, 24, 0, 0, 0, 0, 0, 0, 0, 36, 0, 0, 0, 0, 0, -32, 0, 0, 0, 0, 0, 0, 0, 0, 0, -28, 0, 0, 0, 0, 0, 40, 0, 0, 0, 0, 0, 0, 0, 0, 0, 36, 0, 0, 0, 0, 0, 0, 0, 20, 0, 0, 0, 0, 0, -24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 48, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, -48, 0, 0, 0, 0, 0, 0, 0, 0, 0, -28, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, -52, 0, -20, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, -72, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -36, 0, 36, 0, 0, 0, 0, 0, 0, 0, -96, 0, 0, 0, 0, 0, 48, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, -48, 0, 0, 0, 0, 0, 0, 0, 112, 0, -16, 0, 0, 0, 0, 0, 0, 0, 52, 0, 0, 0, 0, 0, 48, 0, 0, 0, 0, 0, 0, 0, 0, 0, 52, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, 0, 0, 30, 0, -100, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 60, 0, 0, 0, 0, 0, -72, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 128, 0, 0, 0, 0, 0, -88, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, 70, 0, -4, 0, 0, 0, 0, 0, 0, 0, -72, 0, 0, 0, 0, 0, 48, 0, 0, 0, 0, 0, 0, 0, 0, 0, -44, 0, 0, 0, 0, 0, -72, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -84, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 52, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, -12, 0, 36, 0, 0, 0, 0, 0, 0, 0, 60, 0, 0, 0, 0, 0, 72, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -192, 0, -52, 0, 0, 0, 0, 0, 0, 0, -44, 0, 0, 0, 0, 0, 48, 0, 0, 0, 0, 0, 0, 0, 0, 0, -68, 0, 0, 0, 0, 0, 64, 0, 0, 0, 0, 0, 0, 0, -92, 0, 60, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -56, 0, 0, 0, 0, 0, 0, 0, 0, 0, -48, 0, 0, 0, 0, 0, 56, 0, 0, 0, 0, 0, 0, 0, 84, 0, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -120, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 72, 0, 0, 0, 0, 0, 0, 0, 16, 0, -44, 0, 0, 0, 0, 0, 0, 0, 92, 0, 0, 0, 0, 0, -48, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 104, 0, 0, 0, 0, 0, 0, 0, -96, 0, 0, 0, 0, 0, 72, 0, 0, 0, 0, 0, 0, 0, 0, 0, 20, 0, 0, 0, 0, 0, -24, 0, 0, 0, 0, 0, 0, 0, 108, 0, 0, 0, 0, 0, 0, 0, 0, 0, 64, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 36, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 180, 0, 144, 0, 0, 0, 0, 0, 0, 0, 76, 0, 0, 0, 0, 0, -24, 0, 0, 0, 0, 0, 0, 0, 0, 0, -28, 0, 0, 0, 0, 0, -56, 0, 0, 0, 0, 0, 0, 0, -58, 0, 72, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -32, 0, 0, 0, 0, 0, 0, 0, 0, 0, -60, 0, 0, 0, 0, 0, 120, 0, 0, 0, 0, 0, 0, 0, -36, 0, -84, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -84, 0, 0, 0, 0, 0, -24, 0, 0, 0, 0, 0, 0, 0, -48, 0, 0, 0, 0, 0, 0, 0, 0, 0, -28, 0, 0, 0, 0, 0, -72, 0, 0, 0, 0, 0, 0, 0, 0, 0, 76, 0, 0, 0, 0, 0, 64, 0, 0, 0, 0, 0, 0, 0, 62, 0, -140, 0, 0, 0, 0, 0, 0, 0, -108, 0, 0, 0, 0, 0, 88, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -104, 0, 0, 0, 0, 0, 0, 0], 'weight': 2, 'weight_parity': 1}