# Stored data for newform 26.3.f.b, downloaded from the LMFDB on 23 April 2024.
{"label": "26.3.f.b", "space_label": "26.3.f", "level": 26, "weight": 3, "hecke_orbit": 2, "hecke_orbit_code": 4503943275085850, "dim": 8, "is_polredabs": true, "nf_label": "8.0.612074651904.1", "trace_hash": 384485373873534898, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[3, [97344, 3744, 12312, -468, 1209, -24, 39, 0, 1]]], "qexp_display": "q+(-\\beta _{3}-\\beta _{4})q^{2}+(-\\beta _{2}+\\beta _{4}-\\beta _{5}+\\cdots)q^{3}+\\cdots", "char_order": 12, "char_parity": -1, "char_degree": 4, "char_conductor": 13, "char_orbit_label": "f", "char_is_real": false, "Nk2": 234, "analytic_conductor": 0.7084486873367719, "hecke_ring_index": 1, "level_radical": 26, "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": "0.085", "prec": 17}, "analytic_rank_proved": true, "char_values": [26, 12, [15], [11]], "hecke_ring_generator_nbound": 9, "inner_twist_count": 2, "level_primes": [2, 13], "conrey_indexes": [7, 11, 15, 19], "field_disc": 612074651904, "field_disc_factorization": [[2, 8], [3, 6], [1811, 2]], "field_poly": [121801, 0, -25778, 0, 2067, 0, -74, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "7.906", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "219.677", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "10157.633", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "2.2.3.c12", "trace_display": [-4, 0, 6, -2], "traces": [0, 8, -4, 0, 0, 6, 6, -2, -16, -42, -18, -18, 0, 36, 20, 66, 16, -42, 84, 46, 24, -102, -42, -36, -12, 0, 40, 72, -4, -6, -192, 32, 16, 42, -60, -78, -48, -106, 0, 12, -24, 132, 102, -108, 84, 240, 90, 60, 0, 258, 194, 0, 32, -132, -270, -162, -12, -294, -24, 18, -120, 36, -12, -72, 0, -300, 108, -74, 60, 258, 156, -174, 132, 166, -32, 6, -92, 0, 126, -96, 48, -12, -252, -240, -132, -24, 132, 360, -12, 294, 0, 298, -216, 270, -60, 714, 0, -58, -250, 252, 88, -456, 186, 0, -196, -252, -234, -12, 468, -68, -240, -924, -40, 102, -138, -510, 0, -372, 468, -72, 120, 114, -72, -852, 44, 462, 156, 480, -32, 0, 18, 816, 84, -122, 162, 156, 144, 78, 216, 16, -84, 270, 0, -174, -336, -342, -166, 486, 64, 270, -306, -160, 44, 108, -126, 0, 72, -688, 432, 120, -72, 66, 348, 638, 24, -66, 468, 642, 0, 118, -468, -420, -132, -1314, -720, -88, 96, -1134, -210, -888, -480, 0, -492, 456, 180, 612, -96, 546, -156, 816, 252, -192, 48, -188, 0, 954, -32, -126, -252, -612, -176, 1386, 360, 270, 60, 1230, 0, 0, 24, -168, 708, -684, 600, 246, 270, 66, -144, -334, 276, 234, 0, 126, 708, -758, 40, -1986, -204, -198, -156, -692, -168, -1482, 48, 0, 414, -456, 36, 1392, -102, 696, 504, 1094, -272, -1044, 72, -240, 0, 446, -128, 1194, -462, -492, -312, 366, -562, -720, -64, -696, -462, 0, 24, 264, -420, 324, -276, 1254, 478, -876, 28, -294, -216, -514, 0, -798, -456, 336, -216, -480, -32, -624, 240, -162, 0, 2280, 348, 0, -162, 1692, 264, -532, 1158, 1158, -496, 240, 12, 258, 360, 984, 0, 624, 1200, -630, 160, 1608, -88, 402, -78, -376, -252, -1164, -804, 0, -588, 48, 1058, -204, -768, -1350, -1152, -288, 48, 270, -210, -1236, 0, -1054, -404, -522, -24, 462, 132, -578, -708, 1422, 282, -2238, 264, 0, 202, -960, -48, -18, 276, 42, 84, -1110, 288, 1188, -228, 346, 0, 1056, -336, 138, 1134, 966, 420, -672, 1134, 24, -204, 162, 930, 0, 868, -300, -1122, -832, -144, -2334, 606, -1980, 888, -186, 750, 1164, 0, -348, -1644, 218, -252, 2226, 384, -330, -48, 1392, 608, 2808, 116, 0, -288, 48, -500, -48, -102, -1464, 216, 1822, -1084, 1620, -600, -450, 0, -548, 384, 612, -270, 864, -120, -860, -522, 2778, 480, 1254, 492, 0, 56, -2052, -1110, 156, -1164, 250, -1530, -192, 264, 702, -2742, -228, 0, -2658, 1536, -1218, 144, 576, 668, -1626, -344, -1446, 564, 84, 480, 0, -774, -120, -1848, -1188, 1026, -3450, 64, 702, -180, -780, 924, -618, 0, 786, 1176, 236, 692, 1080, 336, 2766, 1950, 1040, 24, 2028, -636, 0, 108, -1568, 12, -1476, -540, -1254, 936, -8, -492, 1266, 1212, 1746, 0, 770, -3080, 2952, 272, -420, 2088, 1118, -144, -330, -726, -1824, 1704, 0, -8, 984, 88, 1170, -2112, 944, -588, -2706, 180, 216, 600, -1524, 0, -2580, 328, -516, 720, -234, 128, -528, 588, 288, -960, -306, -778, 0, 684, 3360, 1074, 368, 24, 1650, -486, 426, -216, -850, 210, -2904, 0, 3048, 2700, -870, -28, 462, 588, -1098, 372, 274, -542, -1920, -288, 0, 1926, -536, 156, -498, -906, 1722, -732, -2376, -2184, -3126, -1812, 564, 0, -1920, -624, 1056, 162, -2448, 0, 48, -1682, -4326, 324, 678, 84, 0, -828, -108, -1230, 522, -192, 386, 452, 3444, 948, -714, -2106, 1164, 0, 3474, 480, 2658, -12, 174, -516, 5040, -296, -294, -246, 762, -540, 0, -30, 840, -612, -966, 1026, 2340, 1132, 1014, -540, 356, 456, 762, 0, 1200, -120, 3590, 376, -1278, 504, -114, 1080, 184, -240, -3258, 1632, 0, 480, 1132, 1344, 2034, -1428, -132, 264, -26, 192, -2250, 534, -5202, 0, 668, -804, -1932, -48, -3498, -540, -98, 276, -900, -690, 1884, -696, 0, 1322, -1356, 1276, -390, -120, -1080, 480, 1464, -300, -996, 1620, -130, 0, -1308, 960, -3186, -1422, -1452, -564, -2898, 912, -1098, -408, -3090, -602, 0, 816, 1176, 930, 1340, 564, 4338, 672, 2190, -1128, 54, 1794, 4542, 0, -3960, -1176, 254, -288, 648, -2376, 3330, -492, -2604, 458, 4572, 176, 0, -4038, -2308, 192, -1668, 984, -2262, 948, -1714, 2196, 1656, -1596, 918, 0, 1422, -984, -5190, -24, -1284, 408, 84, -74, 1014, 420, 738, -2616, 0, -556, 648, -402, -624, 1788, -490, -1414, 840, 432, 1470, 2394, 3046, 0, 3882, 2256, -1314, -888, 3678, 372, -636, -204, 3474, 1416, -1620, 312, 0, -702, 1728, 1632, 3702, 1374, -642, -1680, 738, 3456, 658, 1452, -624, 0, 678, 0, 338, -1392, -5316, -1216, -2610, -3636, -1552, 292, 1416, -558, 0, -2832, -552, 234, 1140, 1032, 1398, 2316, -610, -708, 1302, -2424, -240, 0, -1494, -2740, 1044, 1084, -1662, -3240, -714, 424, 3888, 12, -1182, -2772, 0, 1796, -5808, 720, -1338, 18, -1340, 624, -1662, -756, 126, -624, 2490, 0, -2016, -2832, -1950, -2778, 3516, -960, -2544, -2382, 1680, 1632, 888, 2028, 0, 496, -1224, 654, 2202, 2388, -1116, 1242, 1842, 504, 1468, 894, -1302, 0, -420, 1776, 982, -264, 6198, -1404, -2076, 2988, -130, 1266, -3744, -540, 0, 2412, 2400, 132, -3516, 1662, 2544, -792, -4182, 2008, 1680, -1476, 312, 0, -2494, 272, -4050, 1446, -1416, -1128, -6004, -42, -1854, 648, -1524, 2334, 0, -960, 6756, 420, -300, 2988, -826, -1500, -864, -980, 186, 2526, 4194, 0, 3990, 2220, -690, 180, 2580, 1560, 2346, -1128, 750, -1236, 1308, 396, 0, -2772, -624, -312, 522, -180, 1932, -760, 1620, 1596, 960, 1704, -6582, 0, -2526, -1872, 3124, -1040, 3348, -48, -468, -2028, 2548, -1464, 2412, -396, 0, 1392, -1140, 586, 1320, 432, 3624, -3144, -1308, -936, 318, -126, -882, 0, 2404, 260, -2718, 492, 1218, -2532, 3246, -516, -2766, -1002, -5160, -1008, 0, -4194, -4968, 2188, -1674, -3522, -4832, 44, 24, 480, -5448, -1800, 2870, 0, -1998, 288, 48, 330, -2964, 1452, 942, 1650, -1560, -36, -4416, -1308, 0, 1804, 564, -960, 1108, -48, 294, -942, -762, 552, -40, -84, 3126, 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, 13, 6, -1, 12, 0]], "char_orbit_index": 6, "prim_orbit_index": 6, "minimal_twist": "26.3.f.b", "char_is_minimal": true, "conrey_index": 7, "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, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -1, -1, 0, 0, 0], [0, 0, -1, 0, 1, -1, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0], [2, 0, 1, -1, 1, 0, 1, -1], [0, -1, 0, 0, -1, 0, -1, 1], [-1, 1, 1, 1, 0, -1, 0, 1], [-2, 0, 0, 0, 2, -2, 0, 0], [-11, 0, 0, 11, -4, 2, -1, -1], [-3, 2, 1, 2, -2, 1, 0, -1], [0, -1, -1, -6, 6, -1, -1, 1], [2, 0, 0, -2, 0, 0, 2, 0], [3, 0, 1, 1, 6, -9, -1, 2], [3, -1, -1, 1, 0, -1, 1, -2], [17, -2, -1, -15, -15, 15, 2, -1], [0, 0, 0, 4, 0, 0, 0, 0], [-4, -1, -2, -4, 1, 7, -1, 1], [12, 1, -1, -5, 13, -8, -1, 2], [3, 3, 1, 9, -10, 9, 2, -3], [2, 0, -2, 0, 4, 0, -2, 0], [-3, 1, 0, -19, 3, -22, 0, -1], [-10, -1, 0, 10, -1, 0, 1, 1], [-6, -2, -1, 2, -13, -1, 0, 2], [-2, 0, 2, 2, -2, 2, 0, -2], [-14, 0, 0, 25, 11, -11, -3, 0], [6, -1, -1, 2, -12, 0, 3, -2], [8, 3, 3, -2, 18, 21, -2, 4], [0, 2, 2, -4, -4, 2, -2, 2], [1, 0, 5, -1, -4, 3, 2, -1], [-16, 2, 4, -16, -2, 16, 0, 0], [3, -3, -3, -1, 6, -5, -3, 0], [4, 0, 0, -4, 0, -4, 0, 0], [1, -5, -1, 15, 12, -15, 4, -5], [-11, -2, 0, 6, 11, -5, 0, 2], [-18, 1, 0, 18, -7, 4, 3, 3], [-8, -4, -2, 4, -20, -2, 0, 0], [-12, 6, 1, 4, -4, 18, 6, -1], [7, 1, -1, -19, 6, -5, -5, 0], [10, 2, -5, -16, 29, -43, -2, -6], [-4, -2, -2, -2, -2, -4, -2, 4], [17, 8, 2, -10, -10, 25, -8, 2], [-1, 0, -1, 25, -19, 39, -2, 1], [-6, 1, 2, -6, -1, -16, 6, -6], [12, 0, 2, 0, 10, -10, 2, -2], [28, -8, -7, -1, -28, -1, -1, 8], [18, -1, 2, -10, 5, 10, 3, -1], [11, -1, 1, -9, -12, 3, -1, 2], [0, 4, 0, 0, 4, 0, 0, 0], [43, -4, -2, -21, -1, -2, 0, -1], [25, 0, -3, -3, 3, -25, 0, 3], [-10, -3, 3, 26, 6, -9, 6, 0], [12, 2, 4, -18, -6, 12, -2, 0], [-14, -2, -2, 5, 26, 24, 5, -10], [-37, -4, -5, 13, 13, -41, 4, -5], [-5, 0, -3, -43, -5, 13, -10, 5], [0, -2, -4, 0, 2, 4, 2, -2], [-31, 7, 0, -15, -31, 46, 0, 7], [-1, 6, 2, 3, 2, 3, 4, -6], [-21, 7, 1, 37, 22, -37, -6, 7], [-30, 2, -2, 34, 32, 2, 2, -4], [7, -2, 0, -7, 6, -4, -4, -4], [-2, 0, 0, -2, -8, 0, 0, 6], [-30, -10, 4, 34, -34, 20, -10, -4], [0, 0, 0, 0, -8, 8, 0, 0], [-27, -4, 9, -16, -7, 6, 8, 6], [13, 9, 9, -1, -16, -7, -1, 2], [-8, -11, 1, 8, 8, -19, 11, 1], [2, 0, 2, 16, 6, -14, 4, -2], [14, 2, 4, 14, -2, -26, -15, 15], [24, -4, 2, -4, 22, -18, 2, -6], [-31, 5, 11, 15, 10, 15, -6, -5], [26, 2, 4, -18, 6, 18, 2, 2], [36, -2, -3, -27, -33, 6, 3, -1], [-11, -4, 0, 11, 30, -17, -6, -6], [1, 28, 14, 5, 68, 14, 0, -11], [-20, -2, -6, 12, -12, 18, -2, 6], [2, 7, -7, 0, -28, 35, 4, 0], [-8, -1, -4, 28, -53, 36, -13, 13], [-12, -16, -16, 0, -24, -40, 0, 0], [8, -4, 0, 0, 0, 4, 4, 0], [12, 0, -12, 3, 36, -60, 24, -12], [-23, -8, -16, -23, 8, -7, -4, 4], [-47, -3, 5, 43, -52, 9, 5, -8], [6, -2, -2, -46, 40, -46, 0, 2], [11, 2, -11, -42, -18, 42, -13, 2], [5, 7, 5, 19, -10, 29, -5, -2], [92, -3, 0, -92, -19, 8, 4, 4], [-2, 4, 2, 2, -22, 2, 0, -2], [66, -1, -7, -63, 63, -67, -1, 7], [36, -7, 7, -63, -29, 22, 9, 0], [31, -1, -7, 17, 38, 39, 6, 3], [-26, 4, 4, 2, -8, -4, 2, -4], [7, 2, -3, 53, 53, 9, -2, -3], [2, 0, 0, -14, -8, 16, 4, -2], [66, -1, -2, 66, 1, -32, 13, -13], [-4, -4, -4, 4, 0, -4, -4, 0], [-22, -3, 7, 18, -6, 18, -10, 3], [-19, 3, 4, -25, -45, 25, 1, 3], [10, 2, 4, 38, -14, 52, -4, 2], [22, -6, 0, -22, -50, 22, 0, 0]]}