# Stored data for newform 189.3.d.c, downloaded from the LMFDB on 25 April 2024. {"label": "189.3.d.c", "space_label": "189.3.d", "level": 189, "weight": 3, "hecke_orbit": 3, "hecke_orbit_code": 9007405463503037, "dim": 2, "is_polredabs": true, "nf_label": "2.0.3.1", "trace_hash": 1571361182070935854, "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\\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": "0.084", "prec": 17}, {"__RealLiteral__": 0, "data": "15.121", "prec": 20}, {"__RealLiteral__": 0, "data": "2.066", "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], [0, -7], [-7, 0], [0, 0], [1, -2], [-17, 0], [0, 0], [-10, 20], [0, -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], [0, 21], [-2, 0], [0, 0], [-13, 26], [33, 0], [0, 0], [18, -36], [-14, 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], [-49, 49], [22, 0], [0, 0], [30, -60], [1, 0], [0, 0], [-17, 34], [0, 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], [-14, 7], [10, 0], [0, 0], [33, -66], [8, 0], [0, 0], [-36, 72], [0, 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], [140, -70], [96, 0], [0, 0], [-22, 44], [-36, 0], [0, 0], [-53, 106], [-49, 49], [0, 0], [-66, 0]]}