Database - mf_newforms

Formats: - HTML - YAML - JSON - 2026-10-23T07:53:02.292981

Query: /api/mf_newforms/?_offset=0

Table mf_newforms

Galois orbits of newforms

Column	Type	Example
Nk2	integer	14400
analytic_conductor	double precision	28.746144727660937
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[]	[[2, -1], [3, 1], [5, -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	[3600, 1, [3151, 901, 2801, 577], [1, 1, 1, 1]]
cm_discs	integer[]	[-15]
conrey_index	integer	1
dim	integer	2
embedded_related_objects	text[]
field_disc	numeric	5
field_disc_factorization	numeric[]	[[5, 1]]
field_poly	numeric[]	[-1, -1, 1]
field_poly_is_cyclotomic	boolean	False
field_poly_is_real_cyclotomic	boolean	True
field_poly_root_of_unity	integer	10
fricke_eigenval	smallint	1
has_non_self_twist	smallint	1
hecke_cutters	jsonb	[[7, [0, 1]], [11, [0, 1]], [13, [0, 1]], [17, [-20, 0, 1]]]
hecke_orbit	integer	45
hecke_orbit_code	bigint	198158383637859856
hecke_ring_generator_nbound	integer	17
hecke_ring_index	numeric	4
hecke_ring_index_factorization	numeric[]	[[2, 2]]
hecke_ring_index_proved	boolean	True
inner_twist_count	integer	4
inner_twists	integer[]	[[1, 1, 1, 1, 1, 1, 1], [1, 1, 15, 4, -1, 2, -15], [1, 1, 5, 2, 1, 2, 0], [1, 1, 3, 2, -1, 2, 0]]
is_cm	boolean	True
is_largest	boolean	True
is_maximal	boolean	False
is_polredabs	boolean	True
is_rm	boolean	False
is_self_dual	boolean	True
is_self_twist	boolean	True
is_twist_minimal	boolean	False
label	text	'3600.2.a.bs'
level	integer	3600
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	True
level_is_squarefree	boolean	False
level_primes	integer[]	[2, 3, 5]
level_radical	integer	30
minimal_twist	text	'45.2.b.a'
nf_label	text	'2.2.5.1'
prim_orbit_index	smallint	1
projective_field	numeric[]
projective_field_label	text
projective_image	text
projective_image_type	text
qexp_display	text	'q-\\beta q^{17}-4q^{19}+2\\beta q^{23}-8q^{31}+\\cdots'
related_objects	text[]	[]
relative_dim	integer	2
rm_discs	integer[]	[]
sato_tate_group	text	'1.2.1.d1'
self_twist_discs	integer[]	[-15]
self_twist_type	smallint	1
space_label	text	'3600.2.a'
trace_display	numeric[]	[0, 0, 0, 0]
trace_hash	bigint	1269535316095955268
trace_moments	numeric[]	[0.000, 1.865, 0.000, 22.024, 0.000, 290.515]
trace_zratio	numeric	0.761
traces	numeric[]	[2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -16, 0, ...
weight	smallint	2
weight_parity	smallint	1

{'Nk2': 7220, 'analytic_conductor': 14.41299756484111, 'analytic_rank': 1, 'analytic_rank_proved': True, 'atkin_lehner_eigenvals': [[5, 1], [19, 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': [1805, 1, [362, 1446], [1, 1]], 'cm_discs': [], 'conrey_index': 1, 'dim': 4, 'field_disc': 2000, 'field_disc_factorization': [[2, 4], [5, 3]], 'field_poly': [5, 0, -5, 0, 1], 'field_poly_is_cyclotomic': False, 'field_poly_is_real_cyclotomic': True, 'field_poly_root_of_unity': 20, 'fricke_eigenval': 1, 'has_non_self_twist': 1, 'hecke_cutters': [[2, [5, 0, -5, 0, 1]], [3, [5, 0, -5, 0, 1]]], 'hecke_orbit': 12, 'hecke_orbit_code': 49539595934631693, 'hecke_ring_generator_nbound': 2, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'id': 131556, 'inner_twist_count': 2, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1], [1, 1, 19, 2, -1, 2, 0]], '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': '1805.2.a.l', 'level': 1805, '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': [5, 19], 'level_radical': 95, 'minimal_twist': '1805.2.a.l', 'nf_label': '4.4.2000.1', 'prim_orbit_index': 1, 'qexp_display': 'q+\\beta _{1}q^{2}+\\beta _{1}q^{3}+(1+\\beta _{2})q^{4}-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': '1805.2.a', 'trace_display': [0, 0, -4, -8], 'trace_hash': 801064477104425623, 'trace_moments': [0, {'__RealLiteral__': 0, 'data': '3.880', 'prec': 14}, 0, {'__RealLiteral__': 0, 'data': '77.403', 'prec': 17}, 0, {'__RealLiteral__': 0, 'data': '2114.346', 'prec': 24}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.519', 'prec': 10}, 'traces': [4, 0, 0, 2, -4, 10, -8, 0, -2, 0, -10, 0, 0, 0, 0, -14, 12, 0, 0, -2, 0, 0, -6, -10, 4, -10, 0, -14, 0, -10, 0, 0, 0, 0, 8, 4, 0, 0, -10, 0, 0, -30, 6, -20, 2, 0, 12, 0, 8, 0, 0, 0, 0, -30, 10, 0, 0, -10, 0, 0, -20, -10, -6, 8, 0, -40, 0, 16, 0, 0, 0, 0, -4, -10, 0, 0, 50, 0, 0, 14, -24, 30, -44, 0, -12, 0, -10, 0, 0, 0, 0, 22, -10, 0, 0, -20, 0, 0, -10, 2, 40, 40, 0, 0, 0, -40, 0, 0, 0, 0, -10, 38, 0, 0, 6, 0, 0, -80, -44, 10, 26, 0, 30, 0, -4, 0, 0, 0, 0, 10, -58, 0, 0, -50, 0, 0, 48, 10, -66, 14, 0, 30, 0, 2, 0, 0, 0, 0, 6, 10, 0, 0, 4, 0, 0, -20, 2, 40, -40, 0, -38, 0, -56, 0, 0, 0, 0, 10, -32, 0, 0, -2, 0, 0, -8, 50, -80, -10, 0, -4, 0, 50, 0, 0, 0, 0, -60, -14, 0, 0, 52, 0, 0, 20, 10, 44, -12, 0, 0, 0, -50, 0, 0, 0, 0, 60, 28, 0, 0, 30, 0, 0, 30, 50, -6, 40, 0, 30, 0, 20, 0, 0, 0, 0, -2, -60, 0, 0, -86, 0, 0, 50, 16, -10, -12, 0, 40, 0, 10, 0, 0, 0, 0, 30, -8, 0, 0, 10, 0, 0, -12, -8, -60, -30, 0, 14, 0, 10, 0, 0, 0, 0, -24, 10, 0, 0, -10, 0, 0, 30, 30, -52, 50, 0, -10, 0, -8, 0, 0, 0, 0, 10, -46, 0, 0, 70, 0, 0, -12, 10, 20, -2, 0, 60, 0, 50, 0, 0, 0, 0, -2, 40, 0, 0, 20, 0, 0, 80, 60, 10, -20, 0, -54, 0, 6, 0, 0, 0, 0, -8, 50, 0, 0, -32, 0, 0, 30, -20, 16, 40, 0, -12, 0, 30, 0, 0, 0, 0, -60, -16, 0, 0, -40, 0, 0, 20, 48, 30, 30, 0, 20, 0, 46, 0, 0, 0, 0, -10, 34, 0, 0, 60, 0, 0, 4, -10, 8, -4, 0, 10, 0, -10, 0, 0, 0, 0, -30, 70, 0, 0, -30, 0, 0, 30, -50, -20, -8, 0, -70, 0, 32, 0, 0, 0, 0, -10, 12, 0, 0, -14, 0, 0, 10, -10, 24, -50, 0, -20, 0, -30, 0, 0, 0, 0, 44, 50, 0, 0, 60, 0, 0, 40, -26, 10, 12, 0, -40, 0, 70, 0, 0, 0, 0, 30, 10, 0, 0, -10, 0, 0, 36, -60, -4, 30, 0, 10, 0, 44, 0, 0, 0, 0, 40, -110, 0, 0, 12, 0, 0, -22, -32, 180, 14, 0, 10, 0, 8, 0, 0, 0, 0, 90, 0, 0, 0, -72, 0, 0, -86, 20, -30, -10, 0, 88, 0, 10, 0, 0, 0, 0, 82, 40, 0, 0, 10, 0, 0, -100, -136, -2, 30, 0, 64, 0, -40, 0, 0, 0, 0, -40, 8, 0, 0, -20, 0, 0, 30, -50, 20, 0, 0, 40, 0, -34, 0, 0, 0, 0, 42, 40, 0, 0, -40, 0, 0, 80, -10, -60, -140, 0, 0, 0, 60, 0, 0, 0, 0, 14, 50, 0, 0, 40, 0, 0, 10, -58, -8, 0, 0, -38, 0, 70, 0, 0, 0, 0, 88, -80, 0, 0, -90, 0, 0, -110, -6, -34, 52, 0, -20, 0, 68, 0, 0, 0, 0, 20, 92, 0, 0, 80, 0, 0, 56, 90, 44, 28, 0, -60, 0, -10, 0, 0, 0, 0, -26, 70, 0, 0, -50, 0, 0, 12, 124, -10, -30, 0, 82, 0, 24, 0, 0, 0, 0, 50, 4, 0, 0, -74, 0, 0, -120, -60, 40, 0, 0, -70, 0, -80, 0, 0, 0, 0, -136, -54, 0, 0, 52, 0, 0, -10, 30, -78, -6, 0, 58, 0, 2, 0, 0, 0, 0, 80, -60, 0, 0, 40, 0, 0, 10, 50, -70, 120, 0, -100, 0, 4, 0, 0, 0, 0, -110, 40, 0, 0, -48, 0, 0, -16, 70, -10, -40, 0, 30, 0, 66, 0, 0, 0, 0, -14, -150, 0, 0, 70, 0, 0, -20, -70, 100, -30, 0, -40, 0, -160, 0, 0, 0, 0, -146, -2, 0, 0, -10, 0, 0, 140, 48, -20, 82, 0, 8, 0, -44, 0, 0, 0, 0, 10, -120, 0, 0, 180, 0, 0, -6, -10, 32, -100, 0, -10, 0, -22, 0, 0, 0, 0, -82, 80, 0, 0, -120, 0, 0, 26, -4, 10, 70, 0, 14, 0, -20, 0, 0, 0, 0, -30, -50, 0, 0, 20, 0, 0, 70, 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