# Stored data for newform 126.3.n.a, downloaded from the LMFDB on 19 April 2024.
{"label": "126.3.n.a", "space_label": "126.3.n", "level": 126, "weight": 3, "hecke_orbit": 1, "hecke_orbit_code": 893403529342, "dim": 4, "is_polredabs": true, "nf_label": "4.0.576.2", "trace_hash": 1849258133067888395, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[5, [144, -144, 36, 12, 1]]], "qexp_display": "q+\\beta _{1}q^{2}+2\\beta _{2}q^{4}+(-2+2\\beta _{1}+2\\beta _{2}+\\cdots)q^{5}+\\cdots", "char_order": 6, "char_parity": -1, "char_degree": 2, "char_conductor": 7, "char_orbit_label": "n", "char_is_real": false, "Nk2": 1134, "analytic_conductor": 3.4332513309397408, "hecke_ring_index": 1, "level_radical": 42, "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": "0.170", "prec": 17}, "analytic_rank_proved": true, "char_values": [126, 6, [29, 73], [6, 5]], "hecke_ring_generator_nbound": 7, "inner_twist_count": 2, "level_primes": [2, 3, 7], "conrey_indexes": [19, 73], "field_disc": 576, "field_disc_factorization": [[2, 6], [3, 2]], "field_poly": [4, 0, 2, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.028", "prec": 17}, {"__RealLiteral__": 0, "data": "3.829", "prec": 17}, {"__RealLiteral__": 0, "data": "0.087", "prec": 17}, {"__RealLiteral__": 0, "data": "48.918", "prec": 20}, {"__RealLiteral__": 0, "data": "6.208", "prec": 17}, {"__RealLiteral__": 0, "data": "926.147", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "2.2.3.c6", "trace_display": [0, 0, -12, -10], "traces": [0, 4, 0, 0, -4, -12, 0, -10, 0, 0, -24, 12, 0, 0, -24, 0, -8, 48, 0, -42, 0, 0, 0, -24, 0, 22, -96, 0, 40, 0, 0, 102, 0, 0, 0, 108, 0, 22, -24, 0, 48, 0, 0, 28, 24, 0, -72, 132, 0, -2, 192, 0, 12, -120, 0, 0, 48, 0, -96, 24, 0, -72, 0, 0, 32, -180, 0, 110, -96, 0, 96, -312, 0, -66, 48, 0, 0, -120, 0, -10, 48, 0, 48, 0, 0, -288, 24, 0, 0, 72, 0, -222, 96, 0, -24, 132, 0, 0, 0, 0, 44, -36, 0, 42, 0, 0, 144, 288, 0, -290, -144, 0, -40, -168, 0, -288, 0, 0, 0, -96, 0, 170, -96, 0, -204, 0, 0, 500, 0, 0, 168, 108, 0, 258, 336, 0, -48, 168, 0, 0, -24, 0, 168, -36, 0, 576, 0, 0, -88, 264, 0, 340, 48, 0, -144, -120, 0, 648, -264, 0, 0, -552, 0, -100, -312, 0, -456, 0, 0, -872, -240, 0, -28, 648, 0, -220, -96, 0, 0, 84, 0, 0, 456, 0, -144, 156, 0, 288, 0, 0, 432, 252, 0, -218, 48, 0, -4, 288, 0, -216, -192, 0, 0, 576, 0, -216, -456, 0, -24, 0, 0, -296, -240, 0, -72, -228, 0, 288, -192, 0, -144, -144, 0, 0, 0, 0, 168, 180, 0, 222, 0, 0, 384, -492, 0, -216, -48, 0, -72, -1128, 0, -576, 0, 0, 0, -960, 0, -150, 144, 0, -240, 0, 0, -288, 120, 0, -32, -36, 0, 398, 720, 0, -144, 192, 0, 0, 336, 0, 220, 780, 0, -360, 0, 0, 96, -132, 0, 410, -120, 0, -336, 384, 0, 114, 312, 0, 0, 876, 0, -146, 576, 0, 132, 0, 0, 576, 96, 0, -144, -1800, 0, -214, 672, 0, 168, 336, 0, 0, 120, 0, -264, -348, 0, -930, 0, 0, 40, -120, 0, 0, -96, 0, 720, -768, 0, 2238, -96, 0, 0, -612, 0, 370, 120, 0, 744, 0, 0, 1156, 192, 0, 288, 612, 0, -940, -96, 0, 216, -288, 0, 0, -744, 0, 0, 300, 0, -72, 0, 0, -720, 312, 0, -380, -528, 0, 768, 2184, 0, -1266, -96, 0, 0, 1200, 0, 650, 144, 0, 48, 0, 0, -836, 264, 0, -168, 624, 0, 72, -672, 0, 144, -1212, 0, 0, -480, 0, -552, -1524, 0, -654, 0, 0, -176, -840, 0, 678, 72, 0, -480, 264, 0, -1374, 528, 0, 0, 672, 0, -792, 384, 0, -144, 0, 0, -340, -144, 0, -144, 1104, 0, 552, -1152, 0, -312, 108, 0, 0, -768, 0, -580, 72, 0, 360, 0, 0, -1488, -288, 0, -144, 0, 0, -80, -1464, 0, 936, 168, 0, 0, 108, 0, 454, -144, 0, 576, 0, 0, 932, 0, 0, 24, 468, 0, -1100, -960, 0, 336, 84, 0, 0, 576, 0, 240, -1128, 0, 1218, 0, 0, -680, 240, 0, -14, 192, 0, -456, 336, 0, -576, 648, 0, 0, -228, 0, 658, -816, 0, 888, 0, 0, 2448, 432, 0, -500, -348, 0, 1920, 0, 0, 72, 828, 0, 0, -480, 0, 336, 1968, 0, -1410, 0, 0, 1056, 672, 0, -526, 1008, 0, -324, 1080, 0, -2160, -336, 0, 0, 12, 0, -238, 96, 0, 96, 0, 0, 104, 336, 0, 576, 576, 0, -1634, -384, 0, -804, -1356, 0, 0, -384, 0, 648, -468, 0, -504, 0, 0, -672, 756, 0, -250, 72, 0, 384, 2928, 0, 1794, -384, 0, 0, -1212, 0, 720, 960, 0, 1344, 0, 0, -1140, 240, 0, 88, -2652, 0, 2160, -1056, 0, 1368, 1272, 0, 0, -48, 0, 680, -1020, 0, 330, 0, 0, 960, -324, 0, 1124, 2808, 0, 0, -1176, 0, 1122, 120, 0, 0, -360, 0, -746, 672, 0, -1296, 0, 0, -2392, -528, 0, 96, -2220, 0, -1914, -1152, 0, -192, 0, 0, 0, 624, 0, -360, -3780, 0, 144, 0, 0, 400, 1116, 0, 72, 624, 0, -1056, 384, 0, 426, -216, 0, 0, -1320, 0, -1728, 168, 0, -2328, 0, 0, 916, -432, 0, 872, -2232, 0, -264, 960, 0, -432, 888, 0, 0, 1224, 0, -56, 2088, 0, -114, 0, 0, -1008, -1044, 0, -1152, 1392, 0, -932, 1392, 0, -174, 96, 0, 0, 2304, 0, -1460, 864, 0, 0, 0, 0, -2160, 168, 0, 384, 228, 0, 702, 672, 0, 708, -2304, 0, 0, -1008, 0, 1224, 480, 0, 2154, 0, 0, 576, -660, 0, -538, -312, 0, 1080, 456, 0, -2448, -1008, 0, 0, 1008, 0, 970, -528, 0, -288, 0, 0, 2104, -1176, 0, -432, 624, 0, 2900, -1008, 0, -1560, 1368, 0, 0, 1008, 0, -436, 1740, 0, -606, 0, 0, 240, -996, 0, -936, -1440, 0, 16, -2592, 0, -2304, -288, 0, 0, -588, 0, -696, -1296, 0, 432, 0, 0, 2016, -384, 0, -408, -396, 0, 576, -3408, 0, 1152, -204, 0, 0, 0, 0, -288, 24, 0, -438, 0, 0, 864, -420, 0, 1004, 912, 0, -936, 3192, 0, 2586, 672, 0, 0, 432, 0, 1656, -504, 0, 1968, 0, 0, 1244, -336, 0, 296, 1464, 0, 850, 960, 0, 2568, 1128, 0, 0, 576, 0, -144, 4368, 0, -432, 0, 0, -2544, 1380, 0, -1728, -2160, 0, 732, -120, 0, 3702, 192, 0, 0, 1560, 0, -652, 1440, 0, 288, 0, 0, 748, -288, 0, -72, -2100, 0, -1970, -576, 0, -1584, -876, 0, 0, -192, 0, -984, 1728, 0, -2448, 0, 0, -672, -348, 0, 226, -360, 0, -1680, 1920, 0, -360, 288, 0, 0, -252, 0, 1474, 288, 0, -3552, 0, 0, -1820, 1800, 0, -384, 2796, 0, -960, 1968, 0, 648, -864, 0, 0, -2160, 0, -432, -3936, 0, 2736, 0, 0, 288, 324, 0, 3774, -2280, 0, 768, -2112, 0, -2520, 1128, 0, 0, -1680, 0, 244, -1200, 0, 1152, 0, 0, -1372, 0, 0, -384, -1968, 0, 1770, 3216, 0, 288, -1140, 0, 0, 984, 0, 912, -4296, 0, 2448, 0, 0, 600, 264, 0, 562, -288, 0, 2712, -480, 0, 798, -120, 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, 4, -1, 6, 0]], "char_orbit_index": 14, "prim_orbit_index": 4, "minimal_twist": "42.3.g.a", "char_is_minimal": true, "conrey_index": 19, "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, 0, 0], [1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 0, 0], [0, 0, 2, 0], [-2, 2, 2, 4], [0, 0, 0, 0], [-5, 2, -5, 4], [0, 0, 0, 2], [0, 0, 0, 0], [-8, -2, -4, 2], [0, 0, -6, 0], [0, 0, 0, 0], [-1, 16, -2, 8], [-8, -5, -4, -5], [0, 0, 0, 0], [-4, 0, -4, 0], [16, 2, 8, -2], [0, 0, 0, 0], [-7, 2, 7, 4], [-4, -8, -8, -4], [0, 0, 0, 0], [0, 0, 0, -6], [-12, 18, -12, 0], [0, 0, 0, 0], [0, -24, -11, -24], [-16, -1, 16, -2], [0, 0, 0, 0], [10, -8, 0, -4], [0, 0, 0, 24], [0, 0, 0, 0], [34, -6, 17, 6], [0, -4, 0, -4], [0, 0, 0, 0], [4, 16, 8, 8], [20, -2, -14, -22], [0, 0, 0, 0], [11, -12, 11, 0], [-8, -7, -4, 7], [0, 0, 0, 0], [8, -4, -8, -8], [26, -8, 52, -4], [0, 0, 0, 0], [7, 0, 0, -6], [12, 0, 12, 0], [0, 0, 0, 0], [0, -12, 36, -12], [22, 2, -22, 4], [0, 0, 0, 0], [0, 20, 1, -20], [48, 0, 0, -11], [0, 0, 0, 0], [4, -16, 2, 16], [0, -18, 60, -18], [0, 0, 0, 0], [12, 24, 24, 12], [8, 10, -8, 0], [0, 0, 0, 0], [-48, 0, -48, 0], [8, -14, 4, 14], [0, 0, 0, 0], [-12, 8, 12, 16], [-12, 34, -24, 17], [0, 0, 0, 0], [8, 0, 0, 0], [-90, -42, -90, 0], [0, 0, 0, 0], [0, -42, -55, -42], [-16, 4, 16, 8], [0, 0, 0, 0], [44, 20, 40, -14], [-78, 0, 0, -42], [0, 0, 0, 0], [-22, -40, -11, 40], [0, 11, -24, 11], [0, 0, 0, 0], [-14, -8, -28, -4], [-30, 24, 0, 12], [0, 0, 0, 0], [-5, 66, -5, 0], [16, 8, 8, -8], [0, 0, 0, 0], [8, 26, -8, 52], [-10, 76, -20, 38], [0, 0, 0, 0], [-72, 0, 0, 60], [12, 7, 12, 0], [0, 0, 0, 0], [0, 12, 0, 12], [12, 0, -12, 0], [0, 0, 0, 0], [-101, -34, -91, -80], [24, 0, 0, 36], [0, 0, 0, 0], [-8, 22, -4, -22], [0, -54, -66, -54], [0, 0, 0, 0], [-12, -8, -24, -4], [40, 0, 80, 1], [0, 0, 0, 0], [22, 48, 22, 0]]}