# Stored data for newform 105.4.b.a, downloaded from the LMFDB on 24 April 2024.
{"label": "105.4.b.a", "space_label": "105.4.b", "level": 105, "weight": 4, "hecke_orbit": 1, "hecke_orbit_code": 68786585705, "dim": 16, "is_polredabs": true, "trace_hash": 777101065147461731, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[17, [-14231625894720, -2613586192416, -99699071472, 2696813856, 80245500, -673446, -17439, 36, 1]]], "qexp_display": "q+\\beta _{1}q^{2}+\\beta _{3}q^{3}+(-4+\\beta _{2})q^{4}-5q^{5}+\\cdots", "char_order": 2, "char_parity": 1, "char_degree": 1, "char_conductor": 21, "char_orbit_label": "b", "char_is_real": true, "Nk2": 1680, "analytic_conductor": 6.195200550602764, "hecke_ring_index": 27648, "level_radical": 105, "field_poly_is_cyclotomic": false, "field_poly_root_of_unity": 0, "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": {"__RealLiteral__": 0, "data": "0.512", "prec": 17}, "analytic_rank_proved": true, "char_values": [105, 2, [71, 22, 31], [1, 2, 1]], "hecke_ring_generator_nbound": 7, "inner_twist_count": 2, "level_primes": [3, 5, 7], "conrey_indexes": [41], "field_disc": 13675068095232196406986864551474830684812594446336, "field_disc_factorization": [[2, 16], [3, 10], [31, 2], [13577, 2], [141238467961289, 2]], "field_poly": [5760000, 0, 13209792, 0, 10461796, 0, 3791184, 0, 697017, 0, 68560, 0, 3618, 0, 96, 0, 1], "hecke_ring_index_factorization": [[2, 10], [3, 3]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "12.078", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "948.535", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "128484.562", "prec": 34}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 16, "sato_tate_group": "3.2.3.c2", "trace_display": [0, -2, -80, -4], "traces": [0, 16, 0, -2, -64, -80, -28, -4, 0, -22, 0, 0, -66, 0, -90, 10, 376, -72, -182, 0, 320, -74, -276, 0, 526, 400, 696, -128, 10, 0, 140, 0, 0, -502, 0, 20, 996, -812, -1200, -594, 0, -936, -1834, -548, 0, 110, 1224, 912, 1850, 328, 0, 750, 0, 0, -2950, 0, 1254, 432, 576, -552, 330, 0, -1860, -898, -4000, 0, 1378, 1004, 3828, 1988, 450, 0, 1988, 0, 0, -50, 0, 1152, 1446, 1292, -1880, -2950, 0, -1752, 1068, 360, 0, 1910, -912, 6096, 910, -552, 0, -1080, 0, 0, -9546, 0, -4824, 2530, -1600, -504, 1734, 0, -6252, 370, -5352, 0, 3378, 6100, 1380, 3392, 5846, 0, -3648, 0, 0, -7518, 0, -2664, -2630, -4084, -2460, 24, 0, -2000, 1648, 3440, 0, -376, -3480, 7800, 6732, -6204, 0, 640, 0, 0, -13016, 0, -50, 1554, 3396, 1500, 700, 0, -3732, 5122, 15020, 0, -700, 340, 27624, 10566, -3372, 0, -132, 0, 0, -10252, 0, -10716, -698, -2644, 12672, 2510, 0, -15816, 25744, 6676, 0, -9780, -8704, 6012, 12058, -100, 0, -1008, 0, 0, -4980, 0, -16524, -15696, -5640, 4060, 2940, 0, -18312, 15100, 6000, 0, -21698, -9368, 13824, 2970, 5444, 0, -8194, 0, 0, -15424, 0, -5124, -8352, 4680, 10896, -1376, 0, -13728, 9170, 2956, 0, -16684, -6456, 2740, 25954, -7944, 0, 9708, 0, 0, -26696, 0, -35862, -550, 10968, 9852, 21996, 0, -6120, 17546, -21708, 0, -8238, -4560, 29808, 24374, -2340, 0, -9250, 0, 0, -20942, 0, -1640, 20292, -8448, 31884, -16416, 0, -11160, 28746, 13104, 0, -3750, 18760, 23412, 14308, -6508, 0, 11110, 0, 0, -47992, 0, -31092, 10140, 4192, 21528, 14750, 0, -23124, 30006, 13248, 0, -17856, 9044, 55512, 19740, -6270, 0, -27402, 0, 0, -2160, 0, -23772, -42048, -6260, -2880, -20214, 0, -36348, 35600, 2760, 0, -16792, -11940, 28488, -1650, 13412, 0, 15996, 0, 0, -49890, 0, -61428, 2730, 9300, 22152, 16860, 0, -14988, 4490, -59456, 0, -8912, 20004, 20000, 34904, 24312, 0, 39504, 0, 0, -23458, 0, -204, -6890, -12128, -10212, -7580, 0, -5020, 9236, -11936, 0, -22000, -19140, 39912, 21252, -20332, 0, -9940, 0, 0, -77724, 0, -2250, 18324, 64968, 24912, -29856, 0, -83856, -8514, 32232, 0, -9940, 14728, 59124, 57672, 10272, 0, 4188, 0, 0, -45036, 0, -20856, 57780, -11308, 14484, 250, 0, -32076, 53672, -16232, 0, -1432, -28152, 41556, 57866, -5760, 0, -9104, 0, 0, -7230, 0, 11832, -5076, -26040, -6460, -52512, 0, 21972, 6612, 9400, 0, 20044, 18672, 70248, 14750, 16620, 0, 1680, 0, 0, -33184, 0, -1644, 18488, 8760, -5964, 17940, 0, -105168, -5340, -38044, 0, -26598, 73392, -1800, 7264, 53628, 0, 150, 0, 0, -90898, 0, -61092, -9550, -79528, 7584, 13020, 0, 4560, -17614, -66540, 0, 37668, -30480, 93960, 49076, -61094, 0, -4550, 0, 0, -47194, 0, 2760, 56748, 45568, -93636, -32316, 0, -55008, -19454, 55568, 0, 5400, 56400, 33324, 15384, -37820, 0, 34728, 0, 0, -79346, 0, -35844, 25132, 14376, 42720, 47730, 0, -29712, 14408, -128, 0, 51692, -65960, 56748, 38732, 24120, 0, -39024, 0, 0, -12650, 0, -13308, -74256, -83996, 8000, -14754, 0, -8088, 78182, 2520, 0, -18884, -67844, 21984, -8670, 26016, 0, -22644, 0, 0, -56256, 0, 8676, -44142, 31260, -7512, 79262, 0, 48816, -1850, 46800, 0, 50956, 40520, 26760, 51396, 75660, 0, 27024, 0, 0, 3728, 0, 31128, -16890, 63260, -32004, 15972, 0, -30500, 49242, 2204, 0, -13800, -6900, -1824, -8632, -8720, 0, -16960, 0, 0, 72, 0, -29230, 17202, -60396, 40968, -108360, 0, 145272, -77050, 67620, 0, 18240, 28592, 27336, 43022, -68400, 0, -3532, 0, 0, 20696, 0, 76068, -15918, -8808, -126444, 37590, 0, -46872, 84918, -8112, 0, -51820, -143132, -5088, -109868, 13320, 0, -70272, 0, 0, 13150, 0, -65448, -38744, -9040, 20420, -25440, 0, -113352, 26066, 12300, 0, 14748, 48356, -18264, -120, -19356, 0, 55458, 0, 0, 32108, 0, -2148, -29172, 10000, -57624, 143700, 0, 8448, -8240, 9596, 0, -31054, 112656, -17200, -60756, 13056, 0, 42196, 0, 0, -11828, 0, 78336, 1880, 29952, 40908, -70588, 0, 17400, -99384, 80392, 0, 26098, -39000, -82224, 75000, -128772, 0, -33660, 0, 0, 73722, 0, 31020, 11864, 56976, 93792, -61494, 0, -93336, -126492, -17264, 0, -3200, -40072, -96204, -140900, -16524, 0, -52806, 0, 0, 150288, 0, -80850, -36, -28832, 35304, 65080, 0, 215544, -6290, 43152, 0, -15220, -110808, -107364, 42056, 250, 0, -95736, 0, 0, -7770, 0, 117912, -53964, 1204, -16980, 22558, 0, 34464, 158730, -7500, 0, -63202, 132612, -93384, -3500, -25164, 0, 13248, 0, 0, 86154, 0, 18468, -12760, 18660, 150816, 234144, 0, 58872, -25610, -70824, 0, 65916, 119036, -75100, 25092, 116484, 0, 180984, 0, 0, 132672, 0, 31836, 3500, -149180, 69528, -34860, 0, -1700, 52476, -69284, 0, -109904, -138120, -60312, -264008, -8200, 0, -52830, 0, 0, 189234, 0, 16860, -67488, 314624, -92268, -243556, 0, 279996, -179488, 61728, 0, 660, -28008, -119232, 22160, -190028, 0, 36252, 0, 0, 90584, 0, 29928, 94900, 14880, 25512, 51260, 0, -120900, 49140, 116340, 0, -65712, -190188, -257016, -185784, 53580, 0, -67080, 0, 0, 3490, 0, -126888, 74316, -240744, 13220, -69672, 0, 313872, -68202, -63360, 0, 189196, -21064, -118116, -12550, -22932, 0, 164016, 0, 0, 204872, 0, 172752, -8724, 79080, -200448, 138828, 0, 31560, -128720, -23092, 0, -98962, 277040, -33380, -329958, 152980, 0, 111318, 0, 0, 251112, 0, -44424, 48900, 41280, 121596, -177066, 0, 43520, -126300, -283680, 0, 42702, -30060, -276756, -18992, 102912, 0, -60290, 0, 0, 127818, 0, 500, -86856, 131324, -237612, -94602, 0, -69240, -149942, -165908, 0, 5040, 183288, -131076, -235432, -35216, 0, 87742, 0, 0, 154120, 0, 305550, 103488, -292020, 66576, 24900, 0, 356952, -118720, 75000, 0, 166870, -287060, 44268, 53316, 82620, 0, -353820, 0, 0, 78480, 0, 175092, 72792, -121004, 28200, 22314, 0, -58392, 50016, -20300, 0, -78222, 409284, -202440, -14700, 17400, 0, -43788, 0, 0, 132408, 0, -118800, -34086, 91560, 25392, 275448, 0, 216816, -75500, 108408, 0, 43464, 211176, -30000, 98108, 157992, 0, 173204, 0, 0, 136066, 0, 246072, 108490, 11200, -236928, -129692, 0, 46840, 83992, -51280, 0, 24396, -69120, -142392, -229050, -80364, 0, -14850, 0, 0, 151336, 0, -27220, 27190, 301860, 230616, -397752, 0, 193692, -342258, -27192, 0, 40970, -27656, -540492, 96728, -244824, 0, 35748, 0, 0, 220616, 0], "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, 21, 3, 1, 2, 0]], "char_orbit_index": 2, "prim_orbit_index": 3, "minimal_twist": "105.4.b.a", "char_is_minimal": true, "conrey_index": 41, "id": null, "nf_label": 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-4, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, -4, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0], [0, -5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0], [-4, -3, 1, -4, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0], [1, -4, 1, 2, 0, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0], [-5, -1, 2, -1, -1, 0, 0, -1, 0, -1, 1, 0, 0, 0, 0, 1], [0, 0, 0, -5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [25, 0, -4, 3, 0, -3, -1, 1, 1, 1, 0, 2, -1, 0, 1, 0], [-4, 0, 2, 3, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, -1, 1], [-12, -6, 2, -1, 0, 0, 2, -1, 0, 0, 0, -2, 0, 0, 1, 0], [1, 5, 1, -1, -2, 0, -2, 0, 0, -1, 1, 1, -1, -1, 0, 0], [20, 0, -5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-4, 10, 1, 0, -1, 0, 0, 0, 0, 1, -1, 0, 1, 1, 1, 2], [-18, 0, 0, 3, 0, 2, -2, 2, 2, 0, 0, 0, 0, 0, 1, 0], [-2, -7, -2, -6, 1, 1, 0, 0, 0, 2, 2, 2, 0, 0, 0, -1], [34, -11, -8, -1, 2, -2, 0, 1, 0, 2, -3, 3, 0, -2, 0, 1], [25, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [44, 0, -4, 3, 0, 1, -2, 0, 0, 0, 3, -3, 0, 0, 2, 1], [-10, 16, -1, -4, 0, 1, 4, 0, -2, 0, -4, -2, -1, -1, -1, -3], [1, -9, 3, 3, 2, 2, -2, 0, -1, -1, 0, -3, 4, -2, 1, 2], [2, -3, 2, -5, 1, -3, -1, 2, -2, -2, 2, 2, 0, 0, 0, 1], [10, 0, 0, 0, 0, -5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 8, 1, 5, -3, -1, -2, -2, 2, -1, 2, 2, 5, 3, 0, 3], [0, 27, 0, 21, -4, 3, 4, -3, 3, 0, 4, 4, 0, 4, 0, 0], [-32, -4, 1, 0, 4, 2, 1, 0, 2, 2, -4, 2, -1, 3, 0, -2], [0, -21, 0, -3, 3, 4, 0, -1, 1, 0, -1, -1, -6, 0, 0, -3], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5, 0, 0, 0, 0], [62, -11, -3, -2, 3, 2, -2, 3, -1, 0, -5, -7, 2, -2, 1, 3], [-52, 0, 6, 6, 0, -9, 2, -2, -2, 0, 3, -3, 0, 0, -3, -7], [-78, 0, 20, -6, 0, -1, 2, -1, -1, 0, 6, -6, 0, 0, 1, 0], [-38, -8, -3, 0, -1, -2, 8, 0, -2, 0, -6, 0, -1, 0, -3, 0], [0, 20, 0, 5, -5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-65, 0, 3, -3, 0, 0, 1, 2, 2, -1, 4, -6, 1, 0, 2, -6], [-115, -5, 16, 1, -2, 2, -2, -2, -1, -1, -7, -2, 6, 0, -4, 1], [-36, 0, -12, 0, 0, 9, 0, 0, 0, -2, -6, 2, 2, 0, -5, 1], [-3, -13, -3, -21, -1, 3, -3, 1, -1, 3, 10, 10, -5, 0, 0, -4], [5, -5, -5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0], [73, 0, -7, -33, 0, -7, 13, -3, -3, 1, -2, 4, -1, 0, -1, 0], [51, 0, -15, 0, 0, -3, 4, 0, 0, -1, -1, -1, 1, 0, -7, -7], [125, 65, -14, 19, -9, -1, -7, 1, 4, -3, -4, 12, -5, 2, 1, 0], [24, 25, 1, 25, 0, 17, -10, -4, 2, -3, -2, -2, 5, 3, -3, 5], [0, 25, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [43, -4, -8, -9, 2, -2, 0, -2, -4, 5, 1, -7, -4, -1, -2, -8], [-2, 64, -2, -8, 0, -4, 4, 5, -5, 2, -3, -3, 0, 0, 0, -1], [-2, 17, -2, 14, 1, -5, 12, 6, -6, 2, 4, 4, 0, -2, 0, -1], [-179, -20, 27, -5, 3, -4, -3, 2, 1, -5, -6, 6, 1, -4, 0, 2], [0, -5, 0, -5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0], [85, -22, -22, -12, 2, -8, -20, 7, 4, 1, 3, 10, 2, -2, 0, 7], [22, 20, 8, 4, -2, 7, 8, -4, 0, -2, -6, -6, 6, 8, -3, -1], [48, 0, -4, 27, 0, -20, -6, 1, 1, 6, 3, 9, -6, 0, -1, 3], [-33, 0, 25, -3, 0, -16, 1, 4, 4, 5, 6, 4, -5, 0, 6, 0], [20, 15, -5, 20, -5, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0], [-2, 13, -2, 40, -3, 5, 10, -4, 4, 2, -13, -13, 0, 0, 0, -1], [-119, 0, 17, 15, 0, 16, -5, -5, -5, -5, 5, -15, 5, 0, -6, 1], [-48, -7, 21, 2, -9, 7, -21, 2, 0, -8, 1, -4, -3, -3, 4, -1], [-258, 0, 31, -42, 0, 24, 8, -8, -8, -6, 6, -18, 6, 0, 6, 8], [-5, 20, -5, -10, 0, 0, 0, 0, 0, 5, 0, 0, 5, 0, 0, 0], [91, -65, -27, -18, -4, -1, 5, -7, 0, -5, 5, 13, -5, 4, 2, -1], [42, 0, -2, -42, 0, -1, 14, 6, 6, 0, 6, -6, 0, 0, 1, -7], [237, 0, -23, -21, 0, 1, 5, -2, -2, 1, 7, -5, -1, 0, 3, 7], [126, 73, -2, -2, 2, -4, -3, -4, 2, 2, 1, -5, 6, -1, 6, 4], [25, 5, -10, 5, 5, 0, 0, 5, 0, 5, -5, 0, 0, 0, 0, -5], [4, -32, 4, 48, -9, -1, 3, -6, 6, -4, 4, 4, 10, 3, 0, 7], [130, 47, -32, 19, 0, -16, -12, 9, 11, 12, -11, 11, -8, 4, 7, -9], [-9, 28, -9, -29, 10, 2, -3, 0, 0, 9, -1, -1, 5, -10, 0, -2], [-1, -129, -1, 63, 15, 3, 25, 0, 0, 1, 1, 1, -5, -8, 0, -3], [0, 0, 0, 25, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-3, -177, -3, -45, 15, -7, -5, 7, -7, 3, -4, -4, 3, -12, 0, 0], [75, 32, -33, -38, -2, -13, -8, -8, -4, -3, -1, -3, 11, 8, -1, -1], [106, -28, 16, 63, -7, 16, -12, -5, 8, -16, -14, -4, -4, -4, -2, 4], [103, 0, -15, 54, 0, -18, -18, -2, -2, 5, 9, 1, -5, 0, 8, 4], [-125, 0, 20, -15, 0, 15, 5, -5, -5, -5, 0, -10, 5, 0, -5, 0], [-206, 0, 8, -20, 12, 5, 25, 10, 0, 5, 11, -11, -2, 3, 5, -5], [-11, -104, -11, -59, 16, -6, 7, 10, -10, 11, 16, 16, 3, 8, 0, -4], [-103, 0, -1, -39, 0, -16, 13, 0, 0, 7, -7, 21, -7, 0, 2, 12], [84, -194, 10, 24, 15, 7, -21, 3, 7, -2, -12, 5, -5, 2, 2, 8], [20, 0, -10, -15, 0, -5, 5, 0, 0, 0, 0, 0, 0, 0, 5, -5], [13, 25, 13, -29, -5, 9, -21, -3, 3, -13, 6, 6, -25, 0, 0, -6], [122, -50, -45, 10, -4, 18, -9, 2, -4, -6, -13, -19, 5, 5, -6, 12], [-78, 0, 32, -114, 0, -15, 38, -3, -3, 4, 10, -2, -4, 0, 7, 4], [385, 0, -31, 21, 0, 12, -15, 10, 10, 1, -2, 4, -1, 0, 10, 6], [60, 30, -10, 5, 0, 0, -10, 5, 0, 0, 0, 10, 0, 0, -5, 0], [-16, 101, 16, -7, 4, 5, -26, 10, -6, -6, -7, -1, -14, -1, 3, 3], [4, 77, 4, 50, -9, -5, -4, -7, 7, -4, -8, -8, 20, -12, 0, 12], [-52, -29, 40, 20, -19, 2, -34, -8, 0, -4, 21, 15, 12, -2, -3, 16], [11, 105, 11, 54, -3, 14, 9, -4, 4, -11, 12, 12, -31, 0, 0, -10], [-5, -25, -5, 5, 10, 0, 10, 0, 0, 5, -5, -5, 5, 5, 0, 0], [-592, 160, 82, 9, -25, 15, 4, -18, -5, -4, 17, 5, 0, -6, 0, 13], [-2, -98, -2, 55, -24, -6, 7, -2, 2, 2, 6, 6, 18, 0, 0, 8], [-315, 12, 7, -127, 19, 22, -15, 1, -11, 1, 9, -13, -15, -4, 1, -13], [158, 25, -19, -55, 0, -23, 15, 6, -8, 12, 14, 28, -7, -16, 11, 3], [-100, 0, 25, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]}