Database - mf_newforms

Formats: - HTML - YAML - JSON - 2026-10-24T13:42:09.353116

Query: /api/mf_newforms/?_offset=0

Table mf_newforms

Galois orbits of newforms

Column	Type	Example
Nk2	integer	84480
analytic_conductor	double precision	168.64404906894418
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], [5, 1], [11, 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	[21120, 1, [6271, 8581, 14081, 16897, 3841], [13, 13, 13, 13, 13]]
cm_discs	integer[]	[]
conrey_index	integer	1
dim	integer	1
embedded_related_objects	text[]
field_disc	numeric	1
field_disc_factorization	numeric[]	[]
field_poly	numeric[]	[0, 1]
field_poly_is_cyclotomic	boolean	False
field_poly_is_real_cyclotomic	boolean	False
field_poly_root_of_unity	integer	0
fricke_eigenval	smallint	-1
has_non_self_twist	smallint	-1
hecke_cutters	jsonb
hecke_orbit	integer	13
hecke_orbit_code	bigint	54043195562021504
hecke_ring_generator_nbound	integer	1
hecke_ring_index	numeric	1
hecke_ring_index_factorization	numeric[]	[]
hecke_ring_index_proved	boolean	True
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	'21120.2.a.m'
level	integer	21120
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, 5, 11]
level_radical	integer	330
minimal_twist	text
nf_label	text	'1.1.1.1'
prim_orbit_index	smallint	1
projective_field	numeric[]
projective_field_label	text
projective_image	text
projective_image_type	text
qexp_display	text	'q+q^{3}-q^{5}+q^{9}-q^{11}+2q^{13}-q^{15}+\\cdots'
related_objects	text[]	['EllipticCurve/Q/21120/m']
relative_dim	integer	1
rm_discs	integer[]	[]
sato_tate_group	text	'1.2.3.c1'
self_twist_discs	integer[]	[]
self_twist_type	smallint	0
space_label	text	'21120.2.a'
trace_display	numeric[]	[0, 1, -1, 0]
trace_hash	bigint
trace_moments	numeric[]
trace_zratio	numeric
traces	numeric[]	[1, 0, 1, 0, -1, 0, 0, 0, 1, 0, -1, 0, 2, 0, -1, 0, -6, 0, -4, 0, 0, 0, -4, 0, 1, 0, 1, 0, 6, 0, -4,...
weight	smallint	2
weight_parity	smallint	1

{'Nk2': 672, 'analytic_conductor': 1.3414867539575104, 'analytic_rank': 0, 'analytic_rank_proved': True, 'char_conductor': 168, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 9, 'char_orbit_label': 'i', 'char_order': 2, 'char_parity': 1, 'char_values': [168, 2, [127, 85, 113, 73], [2, 1, 1, 1]], 'cm_discs': [-24], 'conrey_index': 125, 'dim': 4, 'field_disc': 576, 'field_disc_factorization': [[2, 6], [3, 2]], 'field_poly': [4, 0, 2, 0, 1], 'field_poly_is_cyclotomic': False, 'field_poly_is_real_cyclotomic': False, 'field_poly_root_of_unity': 0, 'has_non_self_twist': 1, 'hecke_cutters': [[5, [12, 0, 1]], [11, [-32, 0, 1]], [13, [0, 1]]], 'hecke_orbit': 2, 'hecke_orbit_code': 4504149416738984, 'hecke_ring_generator_nbound': 3, 'hecke_ring_index': 4, 'hecke_ring_index_factorization': [[2, 2]], 'hecke_ring_index_proved': True, 'id': 26642, 'inner_twist_count': 8, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1], [1, 1, 24, 8, -1, 2, -24], [1, 1, 3, 2, -1, 2, 0], [1, 1, 7, 2, -1, 2, 0], [1, 1, 8, 2, 1, 2, 0], [1, 1, 21, 3, 1, 2, 0], [1, 1, 56, 8, -1, 2, 0], [1, 1, 168, 9, 1, 2, 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': True, 'label': '168.2.i.b', 'level': 168, '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, 3, 7], 'level_radical': 42, 'minimal_twist': '168.2.i.b', 'nf_label': '4.0.576.2', 'prim_orbit_index': 9, 'qexp_display': 'q+\\beta _{1}q^{2}-\\beta _{2}q^{3}+2q^{4}+2\\beta _{2}q^{5}+\\cdots', 'related_objects': [], 'relative_dim': 4, 'rm_discs': [], 'sato_tate_group': '1.2.1.d2', 'self_twist_discs': [-24], 'self_twist_type': 1, 'space_label': '168.2.i', 'trace_display': [0, 0, 0, 4], 'trace_hash': 1621340388845770727, 'trace_moments': [{'__RealLiteral__': 0, 'data': '0.020', 'prec': 7}, {'__RealLiteral__': 0, 'data': '3.707', 'prec': 14}, {'__RealLiteral__': 0, 'data': '0.148', 'prec': 10}, {'__RealLiteral__': 0, 'data': '172.701', 'prec': 20}, 0, {'__RealLiteral__': 0, 'data': '8888.399', 'prec': 24}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.881', 'prec': 10}, 'traces': [4, 0, 0, 8, 0, 0, 4, 0, -12, 0, 0, 0, 0, 0, 24, 16, 0, 0, 0, 0, 0, -32, 0, 0, -28, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, -24, 0, 0, 0, 0, 0, -24, 0, 0, 0, 0, 0, 0, -20, 0, 0, 0, 0, 0, 0, 0, 0, -16, 0, 48, 0, 0, -12, 32, 0, 0, 0, 0, 0, 48, 0, 0, 0, 0, 0, 0, 0, 0, 40, 0, 36, 0, 0, 0, 0, 0, 0, -64, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -56, 0, 0, 0, 0, 24, 80, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 84, 0, 0, 0, 0, 0, -88, 0, 0, 0, 0, 0, 0, 0, -72, 0, 0, 0, 0, 0, 0, 0, 0, -48, 0, 0, 0, 0, 0, 0, -8, 0, 0, -32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -48, -52, 0, 0, 0, 0, 0, -28, 0, -72, 0, 0, 0, 0, 0, 0, 0, 0, 48, 0, 0, 0, 0, 0, 0, 104, 0, 0, -40, 0, 96, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -64, 0, 0, 48, 0, 0, 0, 0, 0, 0, 0, 84, 0, 0, 0, 0, 0, 96, -32, 0, 0, 0, 0, 0, 0, 0, 96, 0, 0, 0, 0, 0, 0, 0, 0, -120, 0, 0, -24, 0, 0, 0, 64, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 96, 0, 0, 0, 0, 0, 0, 0, 0, -68, 0, 0, 0, 0, -48, 144, 0, 0, 16, 0, 0, 0, 0, -24, 0, 0, 0, 0, 0, 0, -96, 0, 0, 0, 0, 0, 80, 0, 0, 64, 0, 0, 0, 0, 72, 0, 0, 0, 0, 0, -192, 0, 0, 0, 0, 0, 0, -88, 0, 0, 0, 0, 0, -68, 0, 0, 0, 0, 0, 0, 0, 0, -128, 0, 0, 0, 0, 0, 64, 0, 0, -76, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -48, 0, 0, 72, 0, 0, 0, 0, 0, 0, -192, 0, 0, 0, 0, 0, 0, 0, 24, -80, 0, 0, 0, 0, 0, -112, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 240, 0, 0, 0, 0, 48, 0, 0, 0, 160, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -96, 0, 0, 60, 0, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, 0, 0, 0, 152, 0, 0, 0, 0, 0, -104, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 168, 0, 0, -8, 0, 0, 96, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 48, 0, 0, -176, 0, 0, -96, 0, 0, 0, 0, 0, 0, 0, 120, 0, 0, 48, 0, 0, 0, 0, 0, 0, 92, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -144, 0, 0, 0, 0, 0, 0, 0, 0, 0, 224, 0, 0, 40, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 36, 0, 0, 0, 0, 0, 0, 0, 0, -96, 0, 0, 0, 0, 0, 192, -320, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 48, 0, 0, 0, 0, 0, 0, -64, 0, 144, 0, 0, 0, 0, 0, 0, -44, 0, 0, 0, 0, -144, -200, 0, 0, -176, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -48, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -96, 136, 0, 0, -104, 0, 0, 192, 0, -72, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -160, 0, 0, 0, 0, 0, -56, 0, 0, 0, 0, 0, 0, 0, -144, 0, 0, -120, 0, 0, 0, 0, 0, 0, 0, 0, 0, 144, 0, 0, 0, 0, 0, 0, 0, -108, 192, 0, 0, 0, 0, -120, 0, 0, 0, 0, 0, 0, 80, 0, 96, 0, 0, 0, 0, 0, 0, 40, 0, 216, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 208, 0, 0, 0, 0, 0, 176, 0, 0, 0, 0, 0, -80, 0, 0, 0, 0, 0, 0, 0, 192, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -72, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 184, 0, 0, -144, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -84, 0, 0, 0, 0, 0, 84, 0, 0, 0, 0, 0, 0, 0, 0, -128, 0, 0, 0, 0, 0, 0, 0, 0, -240, 0, 0, 96, 0, -96, 0, 0, 0, 0, 0, 0, 0, 0, 216, 0, 0, 0, 0, 0, 0, 160, 0, 0, -88, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 168, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 200, 0, 0, 0, 0, 192, 0, 0, 0, -64, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -72, 0, 0, 0, 0, 0, 0, 0, 0, -240, 0, 0, 0, 0, 0, 192, 28, 0, 0, 0, 0, 0, 248, 0, 0, -384, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -128, 0, 0, 0, 0, 0, 0, 0, 0, -232, 0, 0, 0, 0, -240, 0, 0, 0, 0], 'weight': 2, 'weight_parity': 1}