Database - mf_newforms

Formats: - HTML - YAML - JSON - 2026-10-23T10:45:41.684991

Query: /api/mf_newforms/?_offset=0

Table mf_newforms

Galois orbits of newforms

Column	Type	Example
Nk2	integer	192556
analytic_conductor	double precision	384.3918502902416
analytic_rank	smallint
analytic_rank_proved	boolean
artin_degree	integer
artin_field	numeric[]
artin_field_label	text
artin_image	text
atkin_lehner_eigenvals	integer[]	[[7, 1], [13, 1], [23, -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	[48139, 1, [20632, 22219, 14288], [33, 33, 33]]
cm_discs	integer[]	[]
conrey_index	integer	1
dim	integer	32
embedded_related_objects	text[]
field_disc	numeric
field_disc_factorization	numeric[]
field_poly	numeric[]
field_poly_is_cyclotomic	boolean
field_poly_is_real_cyclotomic	boolean
field_poly_root_of_unity	integer
fricke_eigenval	smallint	-1
has_non_self_twist	smallint	-1
hecke_cutters	jsonb
hecke_orbit	integer	33
hecke_orbit_code	bigint	144115188109458443
hecke_ring_generator_nbound	integer
hecke_ring_index	numeric
hecke_ring_index_factorization	numeric[]
hecke_ring_index_proved	boolean
inner_twist_count	integer	-1
inner_twists	integer[]
is_cm	boolean	False
is_largest	boolean	False
is_maximal	boolean	False
is_polredabs	boolean
is_rm	boolean	False
is_self_dual	boolean	True
is_self_twist	boolean	False
is_twist_minimal	boolean
label	text	'48139.2.a.bg'
level	integer	48139
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[]	[7, 13, 23]
level_radical	integer	2093
minimal_twist	text
nf_label	text
prim_orbit_index	smallint	1
projective_field	numeric[]
projective_field_label	text
projective_image	text
projective_image_type	text
qexp_display	text
related_objects	text[]	[]
relative_dim	integer	32
rm_discs	integer[]	[]
sato_tate_group	text	'1.2.3.c1'
self_twist_discs	integer[]	[]
self_twist_type	smallint	0
space_label	text	'48139.2.a'
trace_display	numeric[]	[0, -7, 10, -32]
trace_hash	bigint
trace_moments	numeric[]
trace_zratio	numeric
traces	numeric[]	[32, 0, -7, 36, 10, -10, -32, 6, 29, -10, 11, -6, -32, 0, 6, 36, 1, -33, 12, -4, 7, -19, 0, 6, 50, 0...
weight	smallint	2
weight_parity	smallint	1

{'Nk2': 736, 'analytic_conductor': 0.3673118492978898, 'analytic_rank': 0, 'analytic_rank_proved': True, 'char_conductor': 736, 'char_degree': 4, 'char_is_minimal': True, 'char_is_real': False, 'char_orbit_index': 16, 'char_orbit_label': 'p', 'char_order': 8, 'char_parity': -1, 'char_values': [736, 8, [415, 645, 97], [8, 7, 4]], 'cm_discs': [-23], 'conrey_index': 45, 'dim': 8, 'field_disc': 5308416, 'field_disc_factorization': [[2, 16], [3, 4]], 'field_poly': [1, 0, 0, 0, -1, 0, 0, 0, 1], 'field_poly_is_cyclotomic': True, 'field_poly_is_real_cyclotomic': False, 'field_poly_root_of_unity': 24, 'has_non_self_twist': 1, 'hecke_cutters': [[3, [1, -8, 22, -20, 18, -16, 10, -4, 1]]], 'hecke_orbit': 2, 'hecke_orbit_code': 4504630436299488, 'hecke_ring_generator_nbound': 2, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'id': 78789, 'inner_twist_count': 4, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1], [1, 1, 23, 2, -1, 2, -23], [1, 1, 32, 7, 1, 8, 0], [1, 1, 736, 16, -1, 8, 0]], 'is_cm': True, 'is_largest': True, 'is_maximal': False, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': False, 'is_self_twist': True, 'is_twist_minimal': True, 'label': '736.1.p.b', 'level': 736, '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, 23], 'level_radical': 46, 'minimal_twist': '736.1.p.b', 'nf_label': '8.0.5308416.1', 'prim_orbit_index': 16, 'projective_field': [2888, 0, -18752, 0, 32016, 0, 41472, 0, 31668, 0, 25184, 0, 19128, 0, 10000, 0, 3572, 0, 880, 0, 152, 0, 16, 0, 1], 'projective_image': 'D24', 'projective_image_type': 'Dn', 'qexp_display': 'q-\\zeta_{24}^{5}q^{2}+(\\zeta_{24}-\\zeta_{24}^{8})q^{3}+\\zeta_{24}^{10}q^{4}+\\cdots', 'related_objects': [], 'relative_dim': 2, 'rm_discs': [], 'self_twist_discs': [-23], 'self_twist_type': 1, 'space_label': '736.1.p', 'trace_display': [0, 4, 0, 0], 'trace_hash': 1749188791141136552, 'trace_moments': [{'__RealLiteral__': 0, 'data': '-0.027', 'prec': 7}, {'__RealLiteral__': 0, 'data': '7.767', 'prec': 14}, {'__RealLiteral__': 0, 'data': '-0.062', 'prec': 7}, {'__RealLiteral__': 0, 'data': '587.455', 'prec': 20}, {'__RealLiteral__': 0, 'data': '22.911', 'prec': 17}, {'__RealLiteral__': 0, 'data': '84944.187', 'prec': 27}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.792', 'prec': 10}, 'traces': [8, 0, 4, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 4, -8, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, -4, 0, -4, 0, 4, 0, 0, 0, 8, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, -4, 8, 0, 0, -4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 8, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, -8, 0, -12, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, -4, 4, 0, 0, 0, 8, 0, 4, 0, 0, 0, -8, 0, 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