Database - mf_newforms

Formats: - HTML - YAML - JSON - 2026-10-25T08:03:24.897954

Query: /api/mf_newforms/?_offset=0

Table mf_newforms

Galois orbits of newforms

Column	Type	Example
Nk2	integer	37076
analytic_conductor	double precision	74.01333763352478
analytic_rank	smallint	1
analytic_rank_proved	boolean	True
artin_degree	integer
artin_field	numeric[]
artin_field_label	text
artin_image	text
atkin_lehner_eigenvals	integer[]	[[13, 1], [23, 1], [31, 1]]
atkin_lehner_string	text	'+++'
char_conductor	integer	1
char_degree	integer	1
char_is_minimal	boolean	True
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	[9269, 1, [4279, 3225, 8373], [1, 1, 1]]
cm_discs	integer[]	[]
conrey_index	integer	1
dim	integer	2
embedded_related_objects	text[]
field_disc	numeric	12
field_disc_factorization	numeric[]	[[2, 2], [3, 1]]
field_poly	numeric[]	[-3, 0, 1]
field_poly_is_cyclotomic	boolean	False
field_poly_is_real_cyclotomic	boolean	True
field_poly_root_of_unity	integer	12
fricke_eigenval	smallint	1
has_non_self_twist	smallint	0
hecke_cutters	jsonb	[[2, [-2, 2, 1]], [3, [-2, -2, 1]], [5, [-2, -2, 1]]]
hecke_orbit	integer	6
hecke_orbit_code	bigint	22517998170416181
hecke_ring_generator_nbound	integer	2
hecke_ring_index	numeric	1
hecke_ring_index_factorization	numeric[]	[]
hecke_ring_index_proved	boolean	True
inner_twist_count	integer	1
inner_twists	integer[]	[[1, 1, 1, 1, 1, 1, 1]]
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	True
label	text	'9269.2.a.f'
level	integer	9269
level_is_powerful	boolean	False
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	True
level_primes	integer[]	[13, 23, 31]
level_radical	integer	9269
minimal_twist	text	'9269.2.a.f'
nf_label	text	'2.2.12.1'
prim_orbit_index	smallint	1
projective_field	numeric[]
projective_field_label	text
projective_image	text
projective_image_type	text
qexp_display	text	'q+(-1+\\beta )q^{2}+(1-\\beta )q^{3}+(2-2\\beta )q^{4}+\\cdots'
related_objects	text[]	[]
relative_dim	integer	2
rm_discs	integer[]	[]
sato_tate_group	text	'1.2.3.c1'
self_twist_discs	integer[]	[]
self_twist_type	smallint	0
space_label	text	'9269.2.a'
trace_display	numeric[]	[-2, 2, 2, 0]
trace_hash	bigint	1151324931339429853
trace_moments	numeric[]	[0.000, 2.061, 0.000, 9.996, 0.000, 66.987]
trace_zratio	numeric	0.016
traces	numeric[]	[2, -2, 2, 4, 2, -8, 0, -12, 2, 4, -8, 16, -2, 12, -4, 16, 10, -14, -2, -8, -12, 2, -2, -24, -2, 2, ...
weight	smallint	2
weight_parity	smallint	1

{'Nk2': 29624, 'analytic_conductor': 59.13720773696025, 'analytic_rank': 0, 'analytic_rank_proved': True, 'atkin_lehner_eigenvals': [[2, -1], [7, 1], [23, 1]], 'atkin_lehner_string': '-++', 'char_conductor': 1, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 1, 'char_orbit_label': 'a', 'char_order': 1, 'char_parity': 1, 'char_values': [7406, 1, [2117, 3179], [1, 1]], 'cm_discs': [], 'conrey_index': 1, 'dim': 4, 'field_disc': 4352, 'field_disc_factorization': [[2, 8], [17, 1]], 'field_poly': [2, -4, -6, 0, 1], 'field_poly_is_cyclotomic': False, 'field_poly_is_real_cyclotomic': False, 'field_poly_root_of_unity': 0, 'fricke_eigenval': -1, 'has_non_self_twist': 0, 'hecke_cutters': [[3, [2, -4, -6, 0, 1]], [5, [-14, 20, -2, -4, 1]], [11, [2, -4, 1]]], 'hecke_orbit': 29, 'hecke_orbit_code': 126100789599935726, 'hecke_ring_generator_nbound': 3, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'id': 242129, 'inner_twist_count': 1, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1]], 'is_cm': False, 'is_largest': False, 'is_maximal': False, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': False, 'is_twist_minimal': True, 'label': '7406.2.a.bc', 'level': 7406, 'level_is_powerful': False, '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, 7, 23], 'level_radical': 322, 'minimal_twist': '7406.2.a.bb', 'nf_label': '4.4.4352.1', 'prim_orbit_index': 1, 'qexp_display': 'q+q^{2}+(-\\beta _{1}+\\beta _{3})q^{3}+q^{4}+(1-\\beta _{2}+\\cdots)q^{5}+\\cdots', 'related_objects': [], 'relative_dim': 4, 'rm_discs': [], 'sato_tate_group': '1.2.3.c1', 'self_twist_discs': [], 'self_twist_type': 0, 'space_label': '7406.2.a', 'trace_display': [4, 0, 4, -4], 'trace_hash': 557207147853501900, 'trace_moments': [{'__RealLiteral__': 0, 'data': '0.008', 'prec': 4}, {'__RealLiteral__': 0, 'data': '3.883', 'prec': 14}, {'__RealLiteral__': 0, 'data': '0.111', 'prec': 10}, {'__RealLiteral__': 0, 'data': '40.537', 'prec': 17}, {'__RealLiteral__': 0, 'data': '8.054', 'prec': 14}, {'__RealLiteral__': 0, 'data': '646.426', 'prec': 20}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.026', 'prec': 7}, 'traces': [4, 4, 0, 4, 4, 0, -4, 4, 0, 4, 8, 0, -4, -4, 0, 4, 4, 0, 8, 4, 0, 8, 0, 0, 0, -4, 12, -4, -4, 0, 0, 4, 4, 4, -4, 0, -8, 8, -8, 4, 0, 0, 8, 8, 16, 0, 0, 0, 4, 0, 0, -4, 0, 12, 12, -4, 24, -4, 8, 0, 12, 0, 0, 4, 16, 4, 32, 4, 0, -4, 8, 0, 4, -8, 4, 8, -8, -8, 16, 4, -8, 0, -20, 0, -12, 8, -20, 8, 28, 16, 4, 0, -12, 0, 8, 0, -16, 4, 8, 0, 12, 0, -8, -4, 0, 0, 0, 12, 32, 12, 12, -4, 40, 24, 0, -4, 12, 8, -4, 0, -20, 12, -40, 0, -12, 0, -24, 4, -48, 16, -28, 4, -8, 32, 32, 4, 0, 0, 24, -4, 12, 8, 0, 0, -4, 4, 0, -8, 16, 4, 32, 8, -16, -8, -32, -8, 48, 16, 44, 4, 0, -8, -24, 0, 16, -20, 16, 0, -12, -12, 24, 8, 40, -20, 0, 8, 12, 28, -16, 16, 56, 4, 40, 0, 12, -12, 4, 0, -12, 8, 8, 0, -16, -16, -8, 4, 0, 8, 16, 0, 12, 12, 4, 0, -24, -8, 0, -4, 24, 0, -16, 0, -16, 0, 40, 12, 0, 32, 32, 12, -24, 12, 20, -4, 12, 40, 72, 24, 8, 0, -4, -4, -12, 12, 8, 8, 4, -4, 0, 0, -12, -20, -24, 12, 4, -40, -24, 0, -8, -12, 48, 0, 0, -24, -4, 4, 0, -48, 8, 16, -20, -28, -24, 4, -36, -8, -72, 32, 40, 32, 36, 4, 8, 0, -8, 0, 12, 24, -44, -4, 0, 12, 16, 8, 56, 0, 0, 0, -48, -4, -40, 4, -20, 0, 40, -8, 32, 16, 0, 4, -8, 32, -8, 8, 12, -16, 4, -8, -40, -32, 36, -8, -28, 48, -16, 16, -44, 44, 8, 4, -40, 0, 8, -8, -4, -24, 4, 0, 0, 16, -40, -20, 32, 16, 52, 0, 8, -12, 4, -12, -12, 24, -4, 8, 0, 40, -16, -20, 0, 0, 24, 8, 60, 12, 24, 28, 0, -16, 40, 16, -12, 56, 16, 4, 80, 40, 28, 0, -64, 12, 0, -12, 32, 4, 0, 0, 40, -12, -8, 8, -80, 8, -4, 0, -12, -16, -16, -16, 72, -8, 0, 4, -28, 0, -52, 8, -52, 16, -24, 0, -96, 12, -32, 12, -56, 4, -24, 0, 4, -24, -20, -8, -8, 0, 0, -4, -28, 24, -8, 0, -8, -16, 20, 0, -8, -16, -12, 0, -16, 40, 0, 12, -8, 0, -24, 32, 0, 32, 84, 12, 0, -24, 0, 12, -20, 20, -68, -4, -28, 12, -8, 40, 88, 72, -16, 24, 72, 8, -8, 0, 16, -4, 48, -4, -36, -12, 24, 12, -32, 8, 0, 8, 8, 4, 8, -4, 8, 0, 32, 0, 8, -12, 0, -20, -52, -24, -32, 12, -40, 4, 24, -40, -4, -24, 36, 0, -8, -8, -40, -12, 28, 48, 24, 0, 8, 0, 8, -24, 56, -4, -4, 4, 8, 0, -32, -48, -28, 8, 64, 16, -40, -20, -16, -28, -4, -24, 32, 4, 0, -36, 44, -8, 8, -72, -16, 32, -16, 40, 8, 32, 52, 36, 40, 4, 44, 8, 8, 0, 40, -8, -48, 0, -16, 12, 16, 24, 56, -44, 64, -4, -8, 0, 48, 12, 12, 16, 8, 8, -40, 56, 32, 0, -48, 0, 0, 0, -20, -48, 32, -4, 20, -40, 0, 4, -48, -20, -56, 0, -24, 40, 0, -8, 32, 32, 12, 16, -88, 0, 96, 4, -44, -8, 32, 32, -4, -8, 8, 8, 20, 12, -32, -16, -56, 4, -88, -8, -56, -40, -20, -32, 0, 36, -28, -8, -72, -28, 72, 48, -28, -16, 56, 16, 0, -44, 32, 44, -4, 8, 0, 4, 0, -40, 16, 0, -104, 8, -56, -8, 28, -4, 12, -24, -88, 4, -88, 0, 108, 0, -48, 16, -20, -40, -8, -20, -8, 32, 0, 16, -92, 52, 60, 0, -20, 8, -4, -12, -28, 4, 16, -12, -16, -12, 40, 24, 36, -4, 72, 8, -80, 0, 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