Database - mf_newforms

Formats: - HTML - YAML - JSON - 2026-10-25T13:38:06.842407

Query: /api/mf_newforms/?_offset=0

Table mf_newforms

Galois orbits of newforms

Column	Type	Example
Nk2	integer	3172
analytic_conductor	double precision	1.5830342200718837
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	3172
char_degree	integer	2
char_is_minimal	boolean	True
char_is_real	boolean	False
char_orbit_index	smallint	29
char_orbit_label	text	'bc'
char_order	integer	6
char_parity	smallint	-1
char_values	jsonb	[3172, 6, [1587, 977, 1405], [3, 3, 5]]
cm_discs	integer[]	[-4]
conrey_index	integer	2027
dim	integer	2
embedded_related_objects	text[]
field_disc	numeric	-3
field_disc_factorization	numeric[]	[[-1, 1], [3, 1]]
field_poly	numeric[]	[1, -1, 1]
field_poly_is_cyclotomic	boolean	True
field_poly_is_real_cyclotomic	boolean	False
field_poly_root_of_unity	integer	6
fricke_eigenval	smallint
has_non_self_twist	smallint	1
hecke_cutters	jsonb	[[5, [3, 3, 1]]]
hecke_orbit	integer	1
hecke_orbit_code	bigint	1924162128996
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	4
inner_twists	integer[]	[[1, 1, 1, 1, 1, 1, 1], [1, 1, 4, 2, -1, 2, -4], [1, 1, 793, 20, 1, 6, 0], [1, 1, 3172, 29, -1, 6, 0...
is_cm	boolean	True
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	True
is_twist_minimal	boolean	True
label	text	'3172.1.bc.a'
level	integer	3172
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	False
level_primes	integer[]	[2, 13, 61]
level_radical	integer	1586
minimal_twist	text	'3172.1.bc.a'
nf_label	text	'2.0.3.1'
prim_orbit_index	smallint	29
projective_field	numeric[]	[578178, 81990, 1541, -2748, 388, -2, 1]
projective_field_label	text
projective_image	text	'D6'
projective_image_type	text	'Dn'
qexp_display	text	'q+\\zeta_{6}^{2}q^{2}-\\zeta_{6}q^{4}+(-1-\\zeta_{6})q^{5}+\\cdots'
related_objects	text[]	[]
relative_dim	integer	1
rm_discs	integer[]	[]
sato_tate_group	text
self_twist_discs	integer[]	[-4]
self_twist_type	smallint	1
space_label	text	'3172.1.bc'
trace_display	numeric[]	[-1, 0, -3, 0]
trace_hash	bigint	106985898314801539
trace_moments	numeric[]	[0.031, 2.082, 0.025, 19.089, -1.982, 214.942]
trace_zratio	numeric	0.641
traces	numeric[]	[2, -1, 0, -1, -3, 0, 0, 2, 2, 3, 0, 0, 1, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, -3, 0, 0, ...
weight	smallint	1
weight_parity	smallint	-1

{'Nk2': 18144, 'analytic_conductor': 36.22014235685278, 'analytic_rank': 1, 'analytic_rank_proved': True, 'atkin_lehner_eigenvals': [[2, 1], [3, -1], [7, -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': [4536, 1, [1135, 2269, 3809, 2593], [1, 1, 1, 1]], 'cm_discs': [], 'conrey_index': 1, 'dim': 3, 'field_disc': 81, 'field_disc_factorization': [[3, 4]], 'field_poly': [-1, -3, 0, 1], 'field_poly_is_cyclotomic': False, 'field_poly_is_real_cyclotomic': True, 'field_poly_root_of_unity': 18, 'fricke_eigenval': 1, 'has_non_self_twist': 0, 'hecke_cutters': [[5, [1, 0, -3, 1]], [11, [9, -9, 0, 1]]], 'hecke_orbit': 22, 'hecke_orbit_code': 94575592208339384, 'hecke_ring_generator_nbound': 5, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'id': 198455, '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': False, 'label': '4536.2.a.v', 'level': 4536, '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': '504.2.r.c', 'nf_label': '3.3.81.1', 'prim_orbit_index': 1, 'qexp_display': 'q+(1+\\beta _{1})q^{5}+q^{7}+(-\\beta _{1}+2\\beta _{2})q^{11}+\\cdots', 'related_objects': [], 'relative_dim': 3, 'rm_discs': [], 'sato_tate_group': '1.2.3.c1', 'self_twist_discs': [], 'self_twist_type': 0, 'space_label': '4536.2.a', 'trace_display': [0, 0, 3, 3], 'trace_hash': 1277197484737772193, 'trace_moments': [0, {'__RealLiteral__': 0, 'data': '2.903', 'prec': 14}, 0, {'__RealLiteral__': 0, 'data': '20.897', 'prec': 17}, {'__RealLiteral__': 0, 'data': '2.442', 'prec': 14}, {'__RealLiteral__': 0, 'data': '212.947', 'prec': 20}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.014', 'prec': 7}, 'traces': [3, 0, 0, 0, 3, 0, 3, 0, 0, 0, 0, 0, -3, 0, 0, 0, -6, 0, -9, 0, 0, 0, -6, 0, -6, 0, 0, 0, 3, 0, -9, 0, 0, 0, 3, 0, -15, 0, 0, 0, -6, 0, -15, 0, 0, 0, -9, 0, 3, 0, 0, 0, 6, 0, 0, 0, 0, 0, -3, 0, -12, 0, 0, 0, -15, 0, -12, 0, 0, 0, -21, 0, 3, 0, 0, 0, 0, 0, -15, 0, 0, 0, 6, 0, -15, 0, 0, 0, 18, 0, -3, 0, 0, 0, 6, 0, 15, 0, 0, 0, 9, 0, -6, 0, 0, 0, 3, 0, -9, 0, 0, 0, 12, 0, -9, 0, 0, 0, -6, 0, -15, 0, 0, 0, -6, 0, -30, 0, 0, 0, -3, 0, -9, 0, 0, 0, 33, 0, -3, 0, 0, 0, 0, 0, -18, 0, 0, 0, 18, 0, -3, 0, 0, 0, -21, 0, 9, 0, 0, 0, -6, 0, -6, 0, 0, 0, -21, 0, -12, 0, 0, 0, 27, 0, -6, 0, 0, 0, 3, 0, 21, 0, 0, 0, -3, 0, -9, 0, 0, 0, 9, 0, -9, 0, 0, 0, 51, 0, -18, 0, 0, 0, 3, 0, -24, 0, 0, 0, -9, 0, -21, 0, 0, 0, -27, 0, -9, 0, 0, 0, 24, 0, -3, 0, 0, 0, -33, 0, -45, 0, 0, 0, -9, 0, -6, 0, 0, 0, -39, 0, -12, 0, 0, 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