# Stored data for newform 189.3.d.a, downloaded from the LMFDB on 24 April 2024.
{"label": "189.3.d.a", "space_label": "189.3.d", "level": 189, "weight": 3, "hecke_orbit": 1, "hecke_orbit_code": 206208762045, "dim": 2, "is_polredabs": true, "nf_label": "2.0.3.1", "trace_hash": 461531312625178106, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[2, [1, 1]]], "qexp_display": "q-q^{2}-3q^{4}+(1-2\\zeta_{6})q^{5}+(-7+7\\zeta_{6})q^{7}+\\cdots", "char_order": 2, "char_parity": -1, "char_degree": 1, "char_conductor": 7, "char_orbit_label": "d", "char_is_real": true, "Nk2": 1701, "analytic_conductor": 5.149876996409612, "hecke_ring_index": 1, "level_radical": 21, "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": {"__RealLiteral__": 0, "data": "0.505", "prec": 17}, "analytic_rank_proved": true, "char_values": [189, 2, [29, 136], [2, 1]], "hecke_ring_generator_nbound": 7, "inner_twist_count": 2, "level_primes": [3, 7], "conrey_indexes": [55], "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": "1.903", "prec": 17}, {"__RealLiteral__": 0, "data": "0.037", "prec": 17}, {"__RealLiteral__": 0, "data": "15.121", "prec": 20}, {"__RealLiteral__": 0, "data": "0.760", "prec": 17}, {"__RealLiteral__": 0, "data": "152.142", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "2.2.3.c2", "trace_display": [-2, 0, 0, -7], "traces": [0, 2, -2, 0, -6, 0, 0, -7, 14, 0, 0, 34, 0, 0, 7, 0, 10, 0, 0, 0, 0, 0, -34, 64, 0, 44, 0, 0, 21, 4, 0, 0, -66, 0, 0, 21, 0, 16, 0, 0, 0, 0, 0, 52, -102, 0, -64, 0, 0, -49, -44, 0, 0, -2, 0, 0, -49, 0, -4, 0, 0, 0, 0, 0, 26, -60, 0, -68, 0, 0, -21, -20, 0, 0, -16, 0, 0, -119, 0, -92, 0, 0, 0, 0, 0, -108, -52, 0, 238, 0, 0, 210, -192, 0, 0, 72, 0, 0, 49, 0, -132, 0, 0, 0, 0, 0, 2, 214, 0, -176, 0, 0, -35, 400, 0, 0, -12, 0, 0, 378, 0, 336, 0, 0, 0, 0, 0, 286, 238, 0, 60, 0, 0, -252, 68, 0, 0, -20, 0, 0, -63, 0, 20, 0, 0, 0, 0, 0, -48, -158, 0, -146, 0, 0, 119, -78, 0, 0, 92, 0, 0, -224, 0, -452, 0, 0, 0, 0, 0, -262, 108, 0, -156, 0, 0, -154, 170, 0, 0, 238, 0, 0, -210, 0, 448, 0, 0, 0, 0, 0, -72, -380, 0, 622, 0, 0, 147, -614, 0, 0, 308, 0, 0, -14, 0, 48, 0, 0, 0, 0, 0, -392, 6, 0, -214, 0, 0, 273, 176, 0, 0, -1080, 0, 0, 231, 0, -400, 0, 0, 0, 0, 0, 28, -356, 0, 132, 0, 0, -378, -176, 0, 0, -336, 0, 0, -147, 0, 720, 0, 0, 0, 0, 0, 1088, -286, 0, -342, 0, 0, -56, 180, 0, 0, 232, 0, 0, 252, 0, 204, 0, 0, 0, 0, 0, 20, 748, 0, -272, 0, 0, 147, -740, 0, 0, 60, 0, 0, -168, 0, -1366, 0, 0, 0, 0, 0, -312, 112, 0, 158, 0, 0, -182, 146, 0, 0, 240, 0, 0, 357, 0, 78, 0, 0, 0, 0, 0, 276, 454, 0, 68, 0, 0, 224, 1296, 0, 0, 452, 0, 0, -462, 0, 796, 0, 0, 0, 0, 0, -1220, 262, 0, 324, 0, 0, 686, 364, 0, 0, 1030, 0, 0, 154, 0, -1122, 0, 0, 0, 0, 0, -238, -452, 0, -142, 0, 0, -630, 198, 0, 0, 320, 0, 0, 7, 0, 436, 0, 0, 0, 0, 0, 592, -216, 0, 380, 0, 0, 357, -622, 0, 0, -914, 0, 0, -343, 0, 614, 0, 0, 0, 0, 0, 220, -896, 0, -780, 0, 0, 14, 272, 0, 0, -48, 0, 0, 1092, 0, -354, 0, 0, 0, 0, 0, 1096, 392, 0, -14, 0, 0, -840, -642, 0, 0, -716, 0, 0, -273, 0, 528, 0, 0, 0, 0, 0, 1080, 1300, 0, 180, 0, 0, -91, -632, 0, 0, -1200, 0, 0, 210, 0, -38, 0, 0, 0, 0, 0, -1670, 20, 0, 356, 0, 0, 238, -132, 0, 0, 884, 0, 0, -1134, 0, 176, 0, 0, 0, 0, 0, -1008, -318, 0, 196, 0, 0, 147, -566, 0, 0, -720, 0, 0, 70, 0, 604, 0, 0, 0, 0, 0, -426, -1088, 0, -858, 0, 0, -693, -610, 0, 0, -24, 0, 0, 56, 0, -420, 0, 0, 0, 0, 0, -232, -1404, 0, 990, 0, 0, 756, 480, 0, 0, -476, 0, 0, -833, 0, -1568, 0, 0, 0, 0, 0, 52, 60, 0, -748, 0, 0, 322, 272, 0, 0, 1258, 0, 0, 105, 0, 740, 0, 0, 0, 0, 0, -140, 232, 0, 1180, 0, 0, 168, 1408, 0, 0, 1366, 0, 0, 1239, 0, -34, 0, 0, 0, 0, 0, 936, 312, 0, 80, 0, 0, 378, 474, 0, 0, -212, 0, 0, 182, 0, 438, 0, 0, 0, 0, 0, -240, 1320, 0, -1604, 0, 0, -833, 208, 0, 0, 234, 0, 0, -630, 0, 818, 0, 0, 0, 0, 0, 1534, -644, 0, -454, 0, 0, -1470, -68, 0, 0, 520, 0, 0, 672, 0, -1296, 0, 0, 0, 0, 0, 1356, 2146, 0, -42, 0, 0, 462, 1006, 0, 0, -796, 0, 0, -252, 0, 128, 0, 0, 0, 0, 0, 610, 1220, 0, 786, 0, 0, 1113, -756, 0, 0, -308, 0, 0, -686, 0, 260, 0, 0, 0, 0, 0, -1030, 480, 0, 864, 0, 0, 462, -938, 0, 0, 442, 0, 0, 1491, 0, 160, 0, 0, 0, 0, 0, -1020, -714, 0, 452, 0, 0, 84, 142, 0, 0, 88, 0, 0, 1470, 0, -198, 0, 0, 0, 0, 0, -2112, -1156, 0, -1460, 0, 0, -7, -1868, 0, 0, -436, 0, 0, -749, 0, -1526, 0, 0, 0, 0, 0, -1364, -592, 0, 504, 0, 0, 616, 1140, 0, 0, -3120, 0, 0, -357, 0, -1866, 0, 0, 0, 0, 0, 914, -576, 0, -340, 0, 0, -245, 696, 0, 0, 1842, 0, 0, -1400, 0, 2400, 0, 0, 0, 0, 0, 2376, -1452, 0, 896, 0, 0, 672, 780, 0, 0, 1276, 0, 0, 42, 0, -272, 0, 0, 0, 0, 0, -144, -524, 0, -1538, 0, 0, -1092, -884, 0, 0, 354, 0, 0, -2646, 0, 300, 0, 0, 0, 0, 0, -1674, -1096, 0, 1176, 0, 0, -1176, -10, 0, 0, 512, 0, 0, 840, 0, 1498, 0, 0, 0, 0, 0, 716, -2432, 0, 258, 0, 0, -819, -1564, 0, 0, -1232, 0, 0, 987, 0, 508, 0, 0, 0, 0, 0, 160, 3240, 0, -1300, 0, 0, -1001, -180, 0, 0, -1584, 0, 0, -833, 0, 632, 0, 0, 0, 0, 0, 2800, -216, 0, -416, 0, 0, -210, -3308, 0, 0, 38, 0, 0, 147, 0, 106, 0, 0, 0, 0, 0, 352, 1670, 0, -132, 0, 0, 1764, 1068, 0, 0, -1836, 0, 0, -238, 0, -396, 0, 0, 0, 0, 0, -884, -770, 0, 1980, 0, 0, 2646, 2488, 0, 0, 528, 0, 0, 70, 0, 908, 0, 0, 0, 0, 0, -1070, 2352, 0, 318, 0, 0, -1680, -196, 0, 0, 1900, 0, 0, 441, 0, 566, 0, 0, 0, 0, 0, -2160, 1664, 0, 2302, 0, 0, -70, 882, 0, 0, -604, 0, 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": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 7, 2, -1, 2, 0]], "char_orbit_index": 4, "prim_orbit_index": 2, "minimal_twist": "189.3.d.a", "char_is_minimal": true, "conrey_index": 55, "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], [-1, 0], [0, 0], [-3, 0], [1, -2], [0, 0], [-7, 7], [7, 0], [0, 0], [-1, 2], [17, 0], [0, 0], [10, -20], [7, -7], [0, 0], [5, 0], [18, -36], [0, 0], [-12, 24], [-3, 6], [0, 0], [-17, 0], [32, 0], [0, 0], [22, 0], [-10, 20], [0, 0], [21, -21], [2, 0], [0, 0], [13, -26], [-33, 0], [0, 0], [-18, 36], [7, 7], [0, 0], [8, 0], [12, -24], [0, 0], [7, -14], [-8, 16], [0, 0], [26, 0], [-51, 0], [0, 0], [-32, 0], [-22, 44], [0, 0], [0, -49], [-22, 0], [0, 0], [-30, 60], [-1, 0], [0, 0], [17, -34], [-49, 49], [0, 0], [-2, 0], [52, -104], [0, 0], [-40, 80], [-13, 26], [0, 0], [13, 0], [-30, 0], [0, 0], [-34, 0], [-54, 108], [0, 0], [-7, -7], [-10, 0], [0, 0], [-33, 66], [-8, 0], [0, 0], [36, -72], [-119, 119], [0, 0], [-46, 0], [5, -10], [0, 0], [8, -16], [59, -118], [0, 0], [-54, 0], [-26, 0], [0, 0], [119, 0], [-30, 60], [0, 0], [70, 70], [-96, 0], [0, 0], [22, -44], [36, 0], [0, 0], [53, -106], [0, 49], [0, 0], [-66, 0]]}