# Stored data for newform 14.4.c.b, downloaded from the LMFDB on 26 April 2024. {"label": "14.4.c.b", "space_label": "14.4.c", "level": 14, "weight": 4, "hecke_orbit": 2, "hecke_orbit_code": 4503737133432846, "dim": 2, "is_polredabs": true, "nf_label": "2.0.3.1", "trace_hash": 1802739313247737045, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[3, [1, -1, 1]]], "qexp_display": "q+(2-2\\zeta_{6})q^{2}+\\zeta_{6}q^{3}-4\\zeta_{6}q^{4}+(-7+\\cdots)q^{5}+\\cdots", "char_order": 3, "char_parity": 1, "char_degree": 2, "char_conductor": 7, "char_orbit_label": "c", "char_is_real": false, "Nk2": 224, "analytic_conductor": 0.8260267400803686, "hecke_ring_index": 1, "level_radical": 14, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 6, "field_poly_is_real_cyclotomic": false, "hecke_ring_index_proved": true, "self_twist_type": 0, "is_self_dual": false, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": 0, "analytic_rank_proved": true, "char_values": [14, 3, [3], [1]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 2, "level_primes": [2, 7], "conrey_indexes": [9, 11], "field_disc": -3, "field_disc_factorization": [[-1, 1], [3, 1]], "field_poly": [1, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.946", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "11.434", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "103.063", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "3.2.3.c3", "trace_display": [2, 1, -7, -20], "traces": [0, 2, 2, 1, -4, -7, 4, -20, -16, 26, 14, -35, 4, 132, 34, -14, -16, -59, -52, -137, 56, -37, -140, 7, -8, 76, 132, 106, 148, 212, -14, -75, 32, 35, -236, -119, -208, -11, 274, 66, 56, -996, -40, 520, -140, 182, -14, 171, -32, -286, 304, 59, -264, 417, 106, 490, 160, -274, 212, 17, 28, -51, -300, 442, 128, -462, -70, -439, -236, 14, -518, -1568, -208, -295, 22, -76, 1096, 1295, 264, 495, -112, -649, -996, 1864, 68, 826, 520, 106, 280, 873, 728, -1320, -56, 75, -342, -959, -32, -580, -1366, -1820, 304, 1085, -118, -1553, -1056, 140, 1668, -129, -212, 965, 490, -22, -272, -100, -274, 49, -424, 1716, 68, 2183, 112, 106, 102, -498, -300, -2814, 1924, 1872, 128, 260, 924, 755, -280, -2329, -1756, -371, 472, 2357, 14, 56, -560, 342, -1568, -2310, 416, -742, -1180, 397, 88, -2295, 152, 1109, 1096, -3068, 1400, 1050, 264, -1559, -990, -417, -448, 119, -2596, 2251, 1992, 245, 1864, 5576, 296, 4318, 826, 3562, -1040, -1579, 424, -2812, 1120, -17, -1746, -2451, 728, -2340, 2244, -102, -56, -77, -150, -2065, -1368, -1060, -3836, 1275, 64, -35, -580, -924, -1588, -5468, -1820, -2243, -608, 439, 4340, -2120, -472, 3486, 3106, -182, -1056, 9590, -238, 2344, 1668, -784, 258, -1820, -848, 2775, 3860, 295, -980, -3894, -22, 4048, -1184, 3952, -100, -2571, 548, -895, 196, 595, -1696, -1787, -3432, 1197, 68, 990, 2360, -10200, 112, 4177, -212, 2080, 408, 4781, -1992, -9042, 600, 932, -2814, -9360, 2080, -490, 1872, 413, -256, 1749, 1040, -187, 3696, 2756, -1510, 4473, -280, -5838, -10138, 1746, -1756, -1975, 742, 8439, 1888, -2442, 9428, 2660, -28, -527, 56, -3900, 952, -404, 342, 7949, 3136, 959, -9240, 9960, 1664, 1432, 1484, -290, -1180, 636, -572, -238, 88, -1855, 4590, 462, 608, -5200, 4436, -1085, -2192, -357, -3068, -16264, -2380, -3106, 1050, 929, -528, 209, -6236, -6734, -3960, -7131, 834, -3710, -448, -258, 518, 16166, -2596, 5016, -4502, -965, 7968, 2907, 980, 6571, -3728, 286, 5576, 6146, 320, -22932, 4318, -50, -1652, -2625, 14248, 12580, -4160, -49, 3158, 9777, 424, 23828, -3040, 6996, 1120, -9123, 34, 5488, -6984, 1003, -9804, -8149, -1456, -11910, -2340, 212, 9768, 4130, -102, -9671, 112, -12948, -308, -15429, -600, 4109, 4130, -1407, -1368, 13992, 1802, -6976, -3836, 936, -2550, -8717, 256, -4900, -140, 6760, 1160, -163, -924, -826, 2288, 1510, -5468, 3465, 3640, -999, -8972, 2740, -2432, 14757, -878, -4950, 4340, 9086, 3604, 770, -472, 133, -6972, -2357, 12424, -629, -728, -6524, 2112, 28, 9590, -12840, -1036, 20532, 2344, -4446, -3336, 4484, -3136, -867, 1032, 2310, 3640, 15213, -848, -2756, 3000, -1484, 3860, 959, -590, 2763, -3920, -17758, -15576, -5849, 44, 6111, 4048, -4590, -1280, 9164, 3952, 17430, 200, -1109, -10284, -7854, 2192, -11551, 1790, -3127, 196, -18988, 2590, -20320, -1696, 525, 3574, 1307, -13728, 16243, 4788, 1559, -136, -9100, 990, -20824, -4012, 21684, -10200, -18287, -224, -726, 16708, -140, -848, 2030, -4160, 14953, 408, 4502, 5558, 28704, -1992, -6254, 18084, 6370, 2400, 15680, 3728, 5531, 5628, 2788, -9360, 16800, -3536, -15190, -490, 2159, -3744, 2385, 1652, 10915, -1024, -7261, -3498, -10871, 1040, -11970, -814, -3158, 3696, 9153, -5512, 13807, -6040, -1292, 17892, -4425, 560, 12118, -5838, 884, -10960, -65736, 1746, -903, 3512, 2451, -7900, -13895, 2968, -8175, -16878, -1170, 1888, -13510, -2640, 9312, 9428, 1326, -5320, -14522, -112, 8415, -2108, 77, -112, -7003, -3900, 34320, 4144, -4130, -404, 19753, -684, 350, 31796, 24013, 12544, 6897, -1918, -24915, -9240, 2550, -16932, 1064, 1664, -127, -2864, 35, 5936, -18640, -1160, 14595, 2360, 12012, 636, 18088, -2732, 20550, -238, -2734, -176, 10701, -7420, -8260, 18360, 2243, -924, -20799, 608, -2804, 8840, -22828, 4436, 742, 2170, -6525, -8768, -3922, -1428, 11286, 6136, -15051, -16264, 6972, -10360, 22300, -3106, -3415, -2100, 371, 3716, 14841, -2112, 349, -418, 4795, -6236, 1298, -7280, -42368, -3960, 1172, 14262, -6552, 3336, -18876, -14840, -20384, 896, 10705, -258, 13720, 560, -3640, 16166, -14463, 5192, 595, 20064, 1275, -18008, -5979, 1930, 5285, 7968, -15340, 12654, -13880, 980, -13399, -13142, 3894, -14912, 35483, 1144, 742, -11152, 2024, 6146, 3570, -544, 59020, -22932, 4028, -8636, 26001, -200, 5800, -6608, 2571, 5250, 8805, 14248, -32998, 15658, -1790, -4160, 27522, 98, -28685, 12632, 18200, 39108, -196, -848, 29382, 23828, -3574, 5168, -6292, 6996, -1507, -2240, -1197, -36492, -40145, 136, -1259, -10976, -12870, -6984, -1050, 4366, 32340, -9804, -5100, 16298, -16425, -5824, -26401, -47640, -4177, 4680, 8056, 212, -12064, 10560, -30886, 4130, -15340, 204, -15243, -38684, 2002, 448, -15365, 25896, 10053, -308, -18084, -16680, 48768, -600, -16065, -8218, 24232, 16520, -2193, -5628, -11589, 2736, -4680, 13992, -15526, 7844, 29124, -6976, -245, 7672, 22765, 3744, -35705, -10200, 10738, 17434, 1122, 256, 7532, 8330, 3498, -140, 26861, -13520, 5700, 4640, 220, -652, 68226, 1848, 27440, -826, 11236, 10928, 21826, 1510, 2097, 10936, -4473, 13860, 1000, 14560, -3366, 1998, -2919, -8972, -70668, -4658, -20178, -2432, -22698, -29514, -10325, -3512, -1813, -19800, 1975, -8680, -42535, 9086, 61352, 15688, 16878, 770, 15757, 944, -35620, 532, 29172, -27888, -37343, 4714, -2815, 12424, 5320, -680, -18552, -728, -18571, 13048, 527, 8448, -23423, 112, -19516, -19180, -3975, -12840, 58096, -1120, -26306, 20532, -202, -4688, -15113, -17784, 1802, -13344, -7949, -8968, 77, -3136, 64180, -3774, -49868, 1032, 24537, -4620, -20825, 14560, 18426, 60852, 22847, 1696, -11053, -2756, 2864, -5100, -34650, -1484, -28974, -7720, -7540, 3836, 28140, -2360, 42737, -5526, 318, -3920, 12324, -20644, 15496, -15576, -119, 11698, 25923, 176, -18720, 24444, -22715, -8096, 23427, -4590, 34314, 2176, 924, 9164, -7950, -7904, 24603, 69720, -9620, 800, 8190, 2218, -31935, -10284, 56420, -34188, 6816, 2192, -32620, 23102, 357, 7160, 12835, -12508, -13909, -392, -8132, -18988, -103488, 2800, -1672, -20320, 40378, 3392, 24537, 2100, 93571, 14296, -929, -2614, -14455, -13728, -65516, 17560, 418, 4788, 38561, -3118, -3486, -544, -6307, -36400, -39661, -1980, -19470, -20824, -14262, -17464, -93236, 21684, 8925, 20400, 3710, -73148, -87209, -896, 24166, 1452, 3354, 16708, 490, 238, 29632, -848, 8083, -4060, 16875, -16640, -560, 59812, -5016, -816, 15837, 4502, -61110, -8008, 50180, 28704, -9915, 3984, 19138, -25016, -3420, 72336, 1820, -12740, 43681, 2400, 13142, -26656, 31402, 3728, 47113, -11062, -583, 22512], "weight_parity": 1, "has_non_self_twist": 1, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": false, "level_is_squarefree": true, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 7, 3, 1, 3, 0]], "char_orbit_index": 3, "prim_orbit_index": 3, "minimal_twist": "14.4.c.b", "char_is_minimal": true, "conrey_index": 9, "id": null, "fricke_eigenval": null, "atkin_lehner_string": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "atkin_lehner_eigenvals": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0, 0], [1, 0], [2, -2], [0, 1], [0, -4], [-7, 7], [2, 0], [-19, 18], [-8, 0], [26, -26], [0, 14], [0, -35], [4, -4], [66, 0], [-2, 38], [-7, 0], [-16, 16], [0, -59], [0, -52], [-137, 137], [28, 0], [-18, -1], [-70, 0], [7, -7], [0, -8], [0, 76], [132, -132], [53, 0], [72, 4], [106, 0], [-14, 14], [0, -75], [0, 32], [35, -35], [-118, 0], [7, -133], [-104, 0], [-11, 11], [0, 274], [0, 66], [56, -56], [-498, 0], [-38, 36], [260, 0], [-140, 140], [0, 182], [0, -14], [171, -171], [-16, 0], [37, -360], [152, 0], [59, -59], [0, -264], [0, 417], [106, -106], [245, 0], [152, -144], [-137, 0], [212, -212], [0, 17], [0, 28], [-51, 51], [-150, 0], [-26, 494], [64, 0], [-462, 462], [0, -70], [0, -439], [-236, 236], [7, 0], [-252, -14], [-784, 0], [-208, 208], [0, -295], [0, 22], [-76, 76], [548, 0], [630, 35], [132, 0], [495, -495], [0, -112], [0, -649], [-996, 996], [932, 0], [-4, 76], [413, 0], [520, -520], [0, 106], [0, 280], [873, -873], [364, 0], [-1254, 1188], [-28, 0], [75, -75], [0, -342], [0, -959], [-32, 32], [-290, 0], [-646, -74], [-910, 0], [304, -304]]}