# Stored data for newform 26.3.f.a, downloaded from the LMFDB on 19 April 2024.
{"label": "26.3.f.a", "space_label": "26.3.f", "level": 26, "weight": 3, "hecke_orbit": 1, "hecke_orbit_code": 343647715354, "dim": 4, "is_polredabs": true, "nf_label": "4.0.144.1", "trace_hash": 2279656532603477658, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[3, [9, 0, 3, 0, 1]]], "qexp_display": "q+(\\zeta_{12}+\\zeta_{12}^{2}-\\zeta_{12}^{3})q^{2}+(-\\zeta_{12}+\\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": true, "field_poly_root_of_unity": 12, "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": 3, "inner_twist_count": 2, "level_primes": [2, 13], "conrey_indexes": [7, 11, 15, 19], "field_disc": 144, "field_disc_factorization": [[2, 4], [3, 2]], "field_poly": [1, 0, -1, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.001", "prec": 17}, {"__RealLiteral__": 0, "data": "4.038", "prec": 17}, {"__RealLiteral__": 0, "data": "0.680", "prec": 17}, {"__RealLiteral__": 0, "data": "45.637", "prec": 20}, {"__RealLiteral__": 0, "data": "23.513", "prec": 20}, {"__RealLiteral__": 0, "data": "811.687", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "2.2.3.c12", "trace_display": [2, 0, 0, -22], "traces": [0, 4, 2, 0, 0, 0, -6, -22, 8, 12, -12, -6, 0, -12, -4, 6, 8, 78, 24, -58, -12, 42, 18, 12, 12, 0, -14, 0, -44, -54, 0, -128, -8, -30, -24, 42, 0, 40, 0, -12, 0, 0, 42, 120, 36, 36, 54, 132, 0, 42, 38, 0, 40, -168, -90, 6, -84, -102, -42, 6, 24, 78, -60, -120, 0, -120, -12, 86, -24, -126, 84, 42, 24, -136, -38, 114, 116, 0, 90, 192, -24, -18, -78, 192, -36, -42, -156, -96, 12, -60, 0, 38, 168, 222, 132, -42, 0, 280, 92, -108, -76, -78, -114, 0, -40, -12, 48, -156, -180, 8, 48, 36, -8, -354, 42, -114, 0, 180, -132, -180, 24, -54, 156, -156, -188, 0, -12, -504, 16, 0, -36, 264, -60, 350, 198, 180, 180, 384, -24, -28, 12, 198, 0, 318, 96, 258, -136, -150, -76, 120, 114, -320, -28, 468, -162, 0, 144, -224, 312, -132, -48, -126, 18, -494, 156, 54, -276, 102, 0, -220, -312, -264, -156, -498, -192, -380, 48, -78, 198, 276, -72, 0, -324, -72, 108, 42, 384, -30, -132, 360, 204, 408, 48, 200, 0, -42, 200, -600, -108, 612, -152, 138, -246, 726, 156, -234, 72, 0, -168, 24, -132, 324, 264, 150, 162, 114, 0, 274, 732, -42, 0, -822, -84, -310, -8, 0, -708, -534, -60, 224, -24, 90, 84, 0, -24, 0, 12, -216, 174, 192, -24, -356, 316, 0, 72, -108, 0, 730, -512, -150, 0, 180, -24, 78, -454, -72, -32, -570, -354, 0, 36, -648, 516, -264, -108, -264, -446, -336, -52, 162, 0, 1090, 0, -222, 900, 228, -24, 342, -56, -204, 96, -480, 0, -468, -84, 0, 306, 468, 48, 508, 324, 414, -188, 756, -84, -78, 84, -360, 0, 624, 0, 378, -320, 504, -56, 198, 396, 232, -60, 36, 324, 0, 12, 192, -256, -252, 432, 324, 384, -804, 0, 6, -894, -1284, 0, -152, -812, -378, 156, -1386, 108, -598, -84, 228, -114, 78, 72, 0, -14, 0, -84, 606, -612, -246, 396, 162, -288, -732, -324, -4, 0, -720, 144, 492, -78, -198, 396, 888, 114, -720, 0, 714, 276, 0, -196, 648, -270, -176, 48, 468, -156, 396, 120, -546, 666, 264, 0, 942, 1260, 706, 204, -150, 816, 858, 48, -384, -46, 720, -560, 0, 120, -192, 184, -384, -1434, -432, 72, -148, -484, -96, 0, 996, 0, -472, -672, 54, 726, -132, 312, 152, -156, -318, -24, 654, -180, 0, -40, -36, -426, -684, -252, -1264, 426, 396, -336, 228, 198, -672, 0, 6, -480, -798, 0, -882, 548, -126, 740, 90, -324, -1488, -96, 0, -192, 312, 72, 78, -666, 318, -160, 612, 456, 312, 0, -762, 0, 666, -408, 1048, 224, 540, -48, 156, 282, 256, 216, -180, 1068, 0, 336, -1360, -396, 144, 156, -582, -72, 836, -1068, -504, -1044, -486, 0, -644, 652, 636, 316, 438, 0, 1330, 228, 582, -84, 588, 312, 0, 1168, 72, -376, -558, -576, 496, -528, 126, 828, 420, -504, 426, 0, 1080, 200, -240, -72, 1590, -64, -1080, -294, 120, 240, 198, 506, 0, -192, -432, -900, 172, 768, -798, -18, -2322, -24, -152, 504, 432, 0, -468, -156, 462, -52, 486, 324, -18, 180, -244, -338, 900, -360, 0, -870, 896, 768, -468, 114, -1254, -228, -1920, -456, -114, 36, -1392, 0, -1860, 336, -288, -480, -780, 0, -1062, -446, 18, -132, -666, 348, 0, 84, 564, -546, 798, 0, 1312, -1444, -108, 384, 870, -438, 780, 0, -540, 756, -306, -84, 3054, -156, -1068, 8, 1656, -90, 1602, -240, 0, 1014, 576, 228, -318, 1518, -156, 884, -420, 156, 1636, 408, 474, 0, -660, -288, -428, 232, -234, -120, 624, -24, 2096, 120, -1890, -696, 0, 144, -844, 384, 438, -288, 774, 216, 2018, 384, 750, 648, -654, 0, 826, -1164, 648, 0, 1614, 12, -1342, -1020, -468, 1410, -3180, -36, 0, -1330, -2748, -988, -222, -24, -768, -312, -1380, -132, -672, 36, 1132, 0, -120, 768, -954, 228, -2340, -228, -402, -120, -738, -168, 846, -692, 0, -1104, 2160, 1062, -1376, 144, -1086, -144, 918, 168, -318, 966, 174, 0, 1560, 504, 154, -288, 1152, -1464, -102, -516, -1482, 530, 1260, 760, 0, -450, -980, 96, 396, 318, 714, 276, -128, -300, 576, 156, 390, 0, -18, -648, 234, -720, -2856, 0, -300, 520, 1038, -600, 1824, 528, 0, 716, 1404, 732, 2028, -468, 1804, 1526, 276, 336, -18, -468, -598, 0, 522, -1680, -1470, 120, -234, -1092, 1404, 636, 114, -528, 744, 264, 0, 1710, -1128, 720, -774, 1386, -234, -288, 2172, 1008, -2566, -564, 684, 0, -942, 0, -2696, -384, -828, -92, 720, 252, -2432, 292, 384, -1896, 0, -120, 744, 1470, 1440, 168, 288, -12, 958, 468, -282, -576, 3540, 0, 1386, -436, 144, -484, -2382, -192, 2970, -152, -1188, -894, -1662, -276, 0, -1972, -264, -492, -306, 108, -868, 504, -414, 300, 582, -144, -3702, 0, -336, 312, 60, -318, -744, -48, -456, 414, -768, 504, -1674, -852, 0, -64, 492, 66, 90, -876, 900, 702, 1578, -24, -1312, -204, -210, 0, 816, 1584, -1522, -336, -66, 456, -684, 348, -632, -330, -252, -324, 0, -396, 696, 228, 780, -462, 2616, -360, 930, -680, -936, 2748, 576, 0, 586, 32, 804, 90, 264, -648, -1784, -1470, -1134, -24, -834, -48, 0, 816, -396, 1548, 576, 228, 3478, 516, -108, 92, -462, 234, 762, 0, 1014, -372, 6090, 456, -4068, 624, 1902, -708, -48, 564, 4320, 1068, 0, 36, 3984, -120, -726, 1806, 468, 100, -2988, -2340, 264, -504, 138, 0, -1290, 768, 38, 256, -360, 432, -2520, -564, -364, -840, -2628, -876, 0, 600, 1176, -506, -288, -792, -1572, 192, 156, -264, -90, 846, -3378, 0, 1328, -532, -810, -1068, 978, -1008, 1506, -852, 1026, 210, -4884, 48, 0, -318, -1872, -712, 354, 378, 1616, -424, -1536, -828, -1320, -1728, 334, 0, 342, 624, -612, 582, -648, -168, -2172, 1974, -744, -156, -702, 606, 0, -388, -2796, 360, -244, -240, -1098, -210, 114, 552, 1726, 108, 1170, 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.a", "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], [1, 0, 0, 0], [0, 1, 1, -1], [0, -1, 0, -1], [0, 2, 0, 0], [-1, -2, 2, 1], [-1, 1, -1, -2], [-4, -4, -3, 7], [2, 0, 0, 2], [6, 0, -6, 0], [-4, 0, 2, 0], [1, 4, -5, -5], [2, 0, -4, 0], [-9, 8, 12, -2], [-1, -14, 0, 7], [0, 3, 3, -3], [0, 0, 4, 0], [13, -6, 13, 0], [6, 0, 0, -6], [-12, 12, -5, -17], [-2, -2, -2, 4], [10, 1, 1, 10], [9, 1, -9, -2], [4, 21, -2, -21], [4, -2, -2, -2], [0, 0, 0, 19], [-4, 5, 1, 15], [0, -30, 0, 15], [-14, -8, 6, -6], [0, -16, -27, -16], [0, 6, 0, 0], [-37, -10, 10, 37], [-4, 4, 4, 0], [-6, -6, -3, 9], [-19, 26, 26, -19], [21, 1, -21, -2], [0, 12, 0, -12], [7, -13, 6, 6], [17, 0, -34, 7], [4, 21, -14, -15], [0, -8, 0, 4], [-13, 13, 26, -26], [0, 1, 21, 1], [20, -39, 20, 0], [10, 2, -2, -10], [6, -6, 6, 12], [23, 23, -19, -4], [33, 0, 0, 33], [0, 4, 0, -8], [14, 25, -7, -25], [0, -19, 19, 19], [-6, 0, 12, -39], [4, -18, 12, 24], [-42, 44, 0, -22], [-30, -15, 15, -15], [0, 9, 3, 9], [-14, -2, -14, 0], [-22, 7, -7, 22], [11, -11, -43, -32], [-10, -10, 23, -13], [6, 0, 0, 6], [39, 6, -39, -12], [-20, -64, 10, 64], [-42, 18, 24, 24], [0, 0, 0, 8], [-25, 2, -10, -7], [-3, -18, 0, 9], [33, 10, -23, 23], [0, 26, -12, 26], [-21, -6, -21, 0], [22, 2, -2, -22], [-4, 4, 29, 25], [12, 12, -12, 0], [-7, -54, -54, -7], [-19, 7, 19, -14], [38, 0, -19, 0], [34, -24, -10, -10], [-32, 0, 64, 15], [35, 5, -25, 2], [48, 72, 0, -36], [-8, -4, 4, -4], [0, 0, -9, 0], [-13, 39, -13, 0], [25, -46, 46, -25], [-20, 20, 22, 2], [-33, -33, 45, -12], [-59, 40, 40, -59], [-48, -27, 48, 54], [4, 18, -2, -18], [13, 43, -56, -56], [-12, 0, 24, 0], [22, -86, -25, -37], [42, 8, 0, -4], [64, 47, -17, 17], [0, 0, 66, 0], [-7, 51, -7, 0], [4, 8, -8, -4], [71, -71, -2, 69], [32, 32, -18, -14], [-24, -6, -6, -24], [-38, 0, 38, 0]]}