Formats: - HTML - YAML - JSON - 2026-10-12T01:44:11.116957
  • mf_newforms • Show schema
    {'Nk2': 80724, 'analytic_conductor': 161.14609631914595, 'atkin_lehner_eigenvals': [[3, 1], [7, -1], [31, 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': [20181, 1, [6728, 14416, 12496], [2, 2, 2]], 'cm_discs': [], 'conrey_index': 1, 'dim': 1, 'field_disc': 1, 'field_disc_factorization': [], 'field_poly': [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': -1, 'hecke_orbit': 2, 'hecke_orbit_code': 4503599660945109, 'hecke_ring_generator_nbound': 1, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': -1, 'is_cm': False, 'is_largest': False, 'is_maximal': False, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': False, 'label': '20181.2.a.b', 'level': 20181, 'level_is_prime': False, 'level_is_prime_power': False, 'level_is_square': False, 'level_is_squarefree': False, 'level_primes': [3, 7, 31], 'level_radical': 651, 'nf_label': '1.1.1.1', 'prim_orbit_index': 1, 'qexp_display': 'q-2q^{2}-q^{3}+2q^{4}+4q^{5}+2q^{6}+\\cdots', 'related_objects': ['EllipticCurve/Q/20181/b'], 'relative_dim': 1, 'rm_discs': [], 'sato_tate_group': '1.2.3.c1', 'self_twist_discs': [], 'self_twist_type': 0, 'space_label': '20181.2.a', 'trace_display': [-2, -1, 4, 1], 'traces': [1, -2, -1, 2, 4, 2, 1, 0, 1, -8, 2, -2, 1, -2, -4, -4, -4, -2, -7, 8, -1, -4, -6, 0, 11, -2, -1, 2, 0, 8, 0, 8, -2, 8, 4, 2, 3, 14, -1, 0, 2, 2, 5, 4, 4, 12, 4, 4, 1, -22, 4, 2, -2, 2, 8, 0, 7, 0, 12, -8, -6, 0, 1, -8, 4, 4, -4, -8, 6, -8, 10, 0, 5, -6, -11, -14, 2, 2, 0, -16, 1, -4, -16, -2, -16, -10, 0, 0, -10, -8, 1, -12, 0, -8, -28, -8, 5, -2, 2, 22], 'weight': 2, 'weight_parity': 1}
  • label 20181.2.a.b does not appear in mf_hecke_nf
  • mf_newspaces • Show schema
    {'ALdims': [113, 120, 111, 120, 127, 105, 97, 135], 'ALdims_eis_new': [0, 0, 0, 0, 0, 0, 0, 0], 'ALdims_eis_old': [15, 16, 16, 16, 16, 16, 16, 16], 'ALdims_old': [197, 214, 214, 200, 209, 206, 223, 190], 'Nk2': 80724, 'analytic_conductor': 161.14609631914595, 'char_conductor': 1, 'char_degree': 1, 'char_is_real': True, 'char_orbit_index': 1, 'char_orbit_label': 'a', 'char_order': 1, 'char_parity': 1, 'char_values': [20181, 1, [6728, 14416, 12496], [1, 1, 1]], 'conrey_index': 1, 'cusp_dim': 2581, 'dim': 928, 'eis_dim': 127, 'eis_new_dim': 0, 'hecke_orbit_code': 33574613, 'hecke_orbit_dims': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 5, 5, 6, 6, 6, 6, 7, 7, 8, 8, 9, 9, 9, 9, 12, 12, 14, 14, 16, 16, 16, 16, 18, 18, 28, 28, 28, 28, 28, 28, 36, 36, 36, 36, 36, 36, 48, 48, 64, 64], 'label': '20181.2.a', 'level': 20181, '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': [3, 7, 31], 'level_radical': 651, 'mf_dim': 2708, 'mf_new_dim': 928, 'num_forms': 80, 'plus_dim': 435, 'prim_orbit_index': 1, 'relative_dim': 928, 'sturm_bound': 5290, 'trace_display': [-4, 0, -8, -2], 'traces': [928, -4, 0, 928, -8, 4, -2, -12, 928, -8, 0, -8, -8, -2, 0, 920, -16, -4, 0, 0, 2, 16, 8, 12, 912, 16, 0, -6, -24, 0, 0, 12, 0, 24, 4, 928, -8, 64, 0, 24, -16, 2, -8, 40, -8, 8, 32, -32, 928, 36, 8, -24, -16, 4, -32, -18, 0, 16, 0, -16, -8, 0, -2, 912, -56, -8, -16, 16, 8, -12, -8, -12, -24, -16, -16, -16, 0, 8, 32, -48, 928, 8, 32, 6, 40, -64, -24, 40, 0, -8, 12, 32, 0, 48, 64, 68, -8, -4, 0, 848, -16, 8, -8, 80, 4, 104, 64, -8, -24, 80, -16, 2, -24, 24, 48, -40, -8, 80, -4, 48, 968, 48, 16, 0, -96, -2, 48, 132, 32, 88, 72, 56, 8, 96, 0, 56, -32, 8, 32, 44, 24, 96, 96, 920, -16, -16, 0, 24, 0, 92, -40, 144, -16, 0, 0, -16, -32, 56, 0, 200, -8, -4, 80, -16, -32, -32, 0, -6, 912, -40, 0, 32, 24, 8, 2, 16, 16, 8, 8, 0, -40, -44, -32, 16, -32, 0, 88, 88, 2, -40, 0, -120, 40, -40, 24, 928, 40, 16, -64, 108, 0, 16, 4, 24, -48, 32, 8, -56, -32, 20, -16, -16, -24, 0, 64, 12, 0, -56, -48, 32, -16, 48, -32, -58, 912, 56, -32, -32, -8, -128, -16, 16, 40, 16, -40, -152, -32, 28, -56, 32, 40, -52, 0, -136, -8, -80, -88, 0, 48, 40, 80, -6, 32, 72, -16, 904, -24, 24, 36, -120, -24, 176, 16, -8, -80, 40, 0, 96, -160, 0, 32, 96, 4, -40, 96, 104, -104, 48, 0, -60, 32, 32, 72, -88, -32, -40, 20, 12, 920, 48, 0, 40, 0, 4, 80, -64, 0, 24, 24, 8, -8, -96, 32, 80, -152, 24, -8, -16, 0, 0, -32, 88, 56, -24, 4, 120, 48, 88, 0, -144, -24, 8, 88, 928, -72, -16, -16, -40, -16, 8, -64, 160, -8, -112, 0, -2, -16, 20, 32, 88, 0, 64, -2, -184, 48, 8, 136, -136, -24, -30, 0, 64, 112, 16, -8, -32, 4, -8, 8, 24, 912, -64, 0, 76, 136, 40, 96, -88, -16, -96, -12, 0, 96, -256, -48, 80, -88, 2, 0, 16, -32, 88, -80, 28, 40, -232, -8, -184, -80, 80, 144, -12, 0, -224, -16, 40, 136, -288, 8, 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8, 280, -12, -144, 1056, -16, 40, 120, 56, -12, 232, 304, -80, -136, 208, 88, -8, -8, -8, 440, 120, 120, -128, -104, 0, 136, 208, -12, 64, 496, 0, 176, 40, 8, 72, 264, -24, 56, -40, -48, -184, 328, 80, -16, 0, -16, 64, 64, -40, -72, 136, 10, -72, -232, -16, 1160, 160, 8, -20, 56, 88, 0, -80, -16, 0, -2, 16, -72, 64, -48, -160, -48, 0, -184, 96, 120, 104, -160, 48, 134, -56, 8, -64, 24, 48, 40, 28, -176, -80, 320, 32, -24, 0, -60, 200, -176, 144, 144, -144, -48, -16, -44, -48, -440, -200, 36, 16, 12, 928, 40, 128, 0, 120, 160, 0, 72, 0, 8, 24, -32, -144, -108, 32, 0, 192, 40, 32, 16, -64, 208, -24, 328, 120, 80, 32, 6, -32, 240, -80, 312, 128, -144, -28, 56, 40, 0, -16, -144, 144, 24, -48, 520, 96, -64, 0, 0, 12, -56, -56, -40, -72, 224, -24, 920, 256, -64, -32, 8, 80, 240, 76, 40, 136, 56, 48, 32, -48, 40, -40, 356, 0, -224, 208, 48, 24, 0, -24, -112, 192, -8, -8, 12, -56, 152, 192, 32, 192, -144, 12, 40, -168, 24, -104, -64, 0, 40, 304, 32, -152, -240, -32, -248, -16, 40, 256, -368, 0, -56, 104, 4, 872, 136, -48, 0, -128, 48, 54, 0, -48, -24, -176, -248, -32, 60, 64, 88, 80, 112, 0, 240, 44, -56, 80, 68, -24, 304, 0, 0, -96, -152, 64, 96, -8, -16, -96, 0, -168, -304, 32, 240, -176, -4, 144, 80, -48, -104, 128, -96, 32, -184, 0, -128, 56, -152, -240, -146, -8, 0, 0, 848, -256, 208, -40, 176, -152, 136, -104, -48, -16, 56, -128, -48, 392, 104, 160, 216, 32, 8, 136, -816, 32, 88, 0, 0, -280, 248, -8, -80, -176, 0, 0, 464, 8, 32, 40, 80, -112, -72, -48, -216, -192, -136, 16, -360, 4, 400, -72, -32, -24, 288, -32, 4, 48, 104, -32, -16, -16, -48, -68, -96, 0, -1472, 64, 136, -2088, 48, 152, -204, 200, -1648, -24, -8, -88, 72, -16, -296, -1536, -304, 128, 0, -24, -40, 48, -112, -112, -2104, -16, -264, 48, 80, 8, 0, 128, 40, 64, 56, -1872, -16, -16, 344], 'weight': 2, 'weight_parity': 1}
  • source_label 20181.2.a.b does not appear in mf_twists_nf
  • hecke_orbit_code 4503599660945109 does not appear in mf_hecke_charpolys
  • label 20181.2.a.b does not appear in mf_newform_portraits
  • mf_hecke_traces • Show schema
    • id: 120028542
      {'hecke_orbit_code': 4503599660945109, 'n': 1, 'trace_an': 1}
    • id: 120028543
      {'hecke_orbit_code': 4503599660945109, 'n': 2, 'trace_an': -2}
    • id: 120028544
      {'hecke_orbit_code': 4503599660945109, 'n': 3, 'trace_an': -1}
    • id: 120028545
      {'hecke_orbit_code': 4503599660945109, 'n': 4, 'trace_an': 2}
    • id: 120028546
      {'hecke_orbit_code': 4503599660945109, 'n': 5, 'trace_an': 4}
    • id: 120028547
      {'hecke_orbit_code': 4503599660945109, 'n': 6, 'trace_an': 2}
    • id: 120028548
      {'hecke_orbit_code': 4503599660945109, 'n': 7, 'trace_an': 1}
    • id: 120028549
      {'hecke_orbit_code': 4503599660945109, 'n': 8, 'trace_an': 0}
    • id: 120028550
      {'hecke_orbit_code': 4503599660945109, 'n': 9, 'trace_an': 1}
    • id: 120028551
      {'hecke_orbit_code': 4503599660945109, 'n': 10, 'trace_an': -8}
    • id: 120028552
      {'hecke_orbit_code': 4503599660945109, 'n': 11, 'trace_an': 2}
    • id: 120028553
      {'hecke_orbit_code': 4503599660945109, 'n': 12, 'trace_an': -2}
    • id: 120028554
      {'hecke_orbit_code': 4503599660945109, 'n': 13, 'trace_an': 1}
    • id: 120028555
      {'hecke_orbit_code': 4503599660945109, 'n': 14, 'trace_an': -2}
    • id: 120028556
      {'hecke_orbit_code': 4503599660945109, 'n': 15, 'trace_an': -4}
    • id: 120028557
      {'hecke_orbit_code': 4503599660945109, 'n': 16, 'trace_an': -4}
    • id: 120028558
      {'hecke_orbit_code': 4503599660945109, 'n': 17, 'trace_an': -4}
    • id: 120028559
      {'hecke_orbit_code': 4503599660945109, 'n': 18, 'trace_an': -2}
    • id: 120028560
      {'hecke_orbit_code': 4503599660945109, 'n': 19, 'trace_an': -7}
    • id: 120028561
      {'hecke_orbit_code': 4503599660945109, 'n': 20, 'trace_an': 8}
    • id: 120028562
      {'hecke_orbit_code': 4503599660945109, 'n': 21, 'trace_an': -1}
    • id: 120028563
      {'hecke_orbit_code': 4503599660945109, 'n': 22, 'trace_an': -4}
    • id: 120028564
      {'hecke_orbit_code': 4503599660945109, 'n': 23, 'trace_an': -6}
    • id: 120028565
      {'hecke_orbit_code': 4503599660945109, 'n': 24, 'trace_an': 0}
    • id: 120028566
      {'hecke_orbit_code': 4503599660945109, 'n': 25, 'trace_an': 11}
    • id: 120028567
      {'hecke_orbit_code': 4503599660945109, 'n': 26, 'trace_an': -2}
    • id: 120028568
      {'hecke_orbit_code': 4503599660945109, 'n': 27, 'trace_an': -1}
    • id: 120028569
      {'hecke_orbit_code': 4503599660945109, 'n': 28, 'trace_an': 2}
    • id: 120028570
      {'hecke_orbit_code': 4503599660945109, 'n': 29, 'trace_an': 0}
    • id: 120028571
      {'hecke_orbit_code': 4503599660945109, 'n': 30, 'trace_an': 8}
    • id: 120028572
      {'hecke_orbit_code': 4503599660945109, 'n': 31, 'trace_an': 0}
    • id: 120028573
      {'hecke_orbit_code': 4503599660945109, 'n': 32, 'trace_an': 8}
    • id: 120028574
      {'hecke_orbit_code': 4503599660945109, 'n': 33, 'trace_an': -2}
    • id: 120028575
      {'hecke_orbit_code': 4503599660945109, 'n': 34, 'trace_an': 8}
    • id: 120028576
      {'hecke_orbit_code': 4503599660945109, 'n': 35, 'trace_an': 4}
    • id: 120028577
      {'hecke_orbit_code': 4503599660945109, 'n': 36, 'trace_an': 2}
    • id: 120028578
      {'hecke_orbit_code': 4503599660945109, 'n': 37, 'trace_an': 3}
    • id: 120028579
      {'hecke_orbit_code': 4503599660945109, 'n': 38, 'trace_an': 14}
    • id: 120028580
      {'hecke_orbit_code': 4503599660945109, 'n': 39, 'trace_an': -1}
    • id: 120028581
      {'hecke_orbit_code': 4503599660945109, 'n': 40, 'trace_an': 0}
    • id: 120028582
      {'hecke_orbit_code': 4503599660945109, 'n': 41, 'trace_an': 2}
    • id: 120028583
      {'hecke_orbit_code': 4503599660945109, 'n': 42, 'trace_an': 2}
    • id: 120028584
      {'hecke_orbit_code': 4503599660945109, 'n': 43, 'trace_an': 5}
    • id: 120028585
      {'hecke_orbit_code': 4503599660945109, 'n': 44, 'trace_an': 4}
    • id: 120028586
      {'hecke_orbit_code': 4503599660945109, 'n': 45, 'trace_an': 4}
    • id: 120028587
      {'hecke_orbit_code': 4503599660945109, 'n': 46, 'trace_an': 12}
    • id: 120028588
      {'hecke_orbit_code': 4503599660945109, 'n': 47, 'trace_an': 4}
    • id: 120028589
      {'hecke_orbit_code': 4503599660945109, 'n': 48, 'trace_an': 4}
    • id: 120028590
      {'hecke_orbit_code': 4503599660945109, 'n': 49, 'trace_an': 1}
    • id: 120028591
      {'hecke_orbit_code': 4503599660945109, 'n': 50, 'trace_an': -22}
    • id: 120028592
      {'hecke_orbit_code': 4503599660945109, 'n': 51, 'trace_an': 4}
    • id: 120028593
      {'hecke_orbit_code': 4503599660945109, 'n': 52, 'trace_an': 2}
    • id: 120028594
      {'hecke_orbit_code': 4503599660945109, 'n': 53, 'trace_an': -2}
    • id: 120028595
      {'hecke_orbit_code': 4503599660945109, 'n': 54, 'trace_an': 2}
    • id: 120028596
      {'hecke_orbit_code': 4503599660945109, 'n': 55, 'trace_an': 8}
    • id: 120028597
      {'hecke_orbit_code': 4503599660945109, 'n': 56, 'trace_an': 0}
    • id: 120028598
      {'hecke_orbit_code': 4503599660945109, 'n': 57, 'trace_an': 7}
    • id: 120028599
      {'hecke_orbit_code': 4503599660945109, 'n': 58, 'trace_an': 0}
    • id: 120028600
      {'hecke_orbit_code': 4503599660945109, 'n': 59, 'trace_an': 12}
    • id: 120028601
      {'hecke_orbit_code': 4503599660945109, 'n': 60, 'trace_an': -8}
    • id: 120028602
      {'hecke_orbit_code': 4503599660945109, 'n': 61, 'trace_an': -6}
    • id: 120028603
      {'hecke_orbit_code': 4503599660945109, 'n': 62, 'trace_an': 0}
    • id: 120028604
      {'hecke_orbit_code': 4503599660945109, 'n': 63, 'trace_an': 1}
    • id: 120028605
      {'hecke_orbit_code': 4503599660945109, 'n': 64, 'trace_an': -8}
    • id: 120028606
      {'hecke_orbit_code': 4503599660945109, 'n': 65, 'trace_an': 4}
    • id: 120028607
      {'hecke_orbit_code': 4503599660945109, 'n': 66, 'trace_an': 4}
    • id: 120028608
      {'hecke_orbit_code': 4503599660945109, 'n': 67, 'trace_an': -4}
    • id: 120028609
      {'hecke_orbit_code': 4503599660945109, 'n': 68, 'trace_an': -8}
    • id: 120028610
      {'hecke_orbit_code': 4503599660945109, 'n': 69, 'trace_an': 6}
    • id: 120028611
      {'hecke_orbit_code': 4503599660945109, 'n': 70, 'trace_an': -8}
    • id: 120028612
      {'hecke_orbit_code': 4503599660945109, 'n': 71, 'trace_an': 10}
    • id: 120028613
      {'hecke_orbit_code': 4503599660945109, 'n': 72, 'trace_an': 0}
    • id: 120028614
      {'hecke_orbit_code': 4503599660945109, 'n': 73, 'trace_an': 5}
    • id: 120028615
      {'hecke_orbit_code': 4503599660945109, 'n': 74, 'trace_an': -6}
    • id: 120028616
      {'hecke_orbit_code': 4503599660945109, 'n': 75, 'trace_an': -11}
    • id: 120028617
      {'hecke_orbit_code': 4503599660945109, 'n': 76, 'trace_an': -14}
    • id: 120028618
      {'hecke_orbit_code': 4503599660945109, 'n': 77, 'trace_an': 2}
    • id: 120028619
      {'hecke_orbit_code': 4503599660945109, 'n': 78, 'trace_an': 2}
    • id: 120028620
      {'hecke_orbit_code': 4503599660945109, 'n': 79, 'trace_an': 0}
    • id: 120028621
      {'hecke_orbit_code': 4503599660945109, 'n': 80, 'trace_an': -16}
    • id: 120028622
      {'hecke_orbit_code': 4503599660945109, 'n': 81, 'trace_an': 1}
    • id: 120028623
      {'hecke_orbit_code': 4503599660945109, 'n': 82, 'trace_an': -4}
    • id: 120028624
      {'hecke_orbit_code': 4503599660945109, 'n': 83, 'trace_an': -16}
    • id: 120028625
      {'hecke_orbit_code': 4503599660945109, 'n': 84, 'trace_an': -2}
    • id: 120028626
      {'hecke_orbit_code': 4503599660945109, 'n': 85, 'trace_an': -16}
    • id: 120028627
      {'hecke_orbit_code': 4503599660945109, 'n': 86, 'trace_an': -10}
    • id: 120028628
      {'hecke_orbit_code': 4503599660945109, 'n': 87, 'trace_an': 0}
    • id: 120028629
      {'hecke_orbit_code': 4503599660945109, 'n': 88, 'trace_an': 0}
    • id: 120028630
      {'hecke_orbit_code': 4503599660945109, 'n': 89, 'trace_an': -10}
    • id: 120028631
      {'hecke_orbit_code': 4503599660945109, 'n': 90, 'trace_an': -8}
    • id: 120028632
      {'hecke_orbit_code': 4503599660945109, 'n': 91, 'trace_an': 1}
    • id: 120028633
      {'hecke_orbit_code': 4503599660945109, 'n': 92, 'trace_an': -12}
    • id: 120028634
      {'hecke_orbit_code': 4503599660945109, 'n': 93, 'trace_an': 0}
    • id: 120028635
      {'hecke_orbit_code': 4503599660945109, 'n': 94, 'trace_an': -8}
    • id: 120028636
      {'hecke_orbit_code': 4503599660945109, 'n': 95, 'trace_an': -28}
    • id: 120028637
      {'hecke_orbit_code': 4503599660945109, 'n': 96, 'trace_an': -8}
    • id: 120028638
      {'hecke_orbit_code': 4503599660945109, 'n': 97, 'trace_an': 5}
    • id: 120028639
      {'hecke_orbit_code': 4503599660945109, 'n': 98, 'trace_an': -2}
    • id: 120028640
      {'hecke_orbit_code': 4503599660945109, 'n': 99, 'trace_an': 2}
    • id: 120028641
      {'hecke_orbit_code': 4503599660945109, 'n': 100, 'trace_an': 22}