# Stored data for newform 46.4.a.a, downloaded from the LMFDB on 19 April 2024. {"label": "46.4.a.a", "space_label": "46.4.a", "level": 46, "weight": 4, "hecke_orbit": 1, "hecke_orbit_code": 67108910, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 557972260671365688, "analytic_rank": 1, "is_twist_minimal": true, "hecke_cutters": [[3, [1, 1]]], "qexp_display": "q-2q^{2}-q^{3}+4q^{4}-10q^{5}+2q^{6}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 736, "fricke_eigenval": -1, "atkin_lehner_string": "+-", "analytic_conductor": 2.714087860264068, "hecke_ring_index": 1, "level_radical": 46, "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": true, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": 0, "analytic_rank_proved": true, "char_values": [46, 1, [5], [1]], "hecke_ring_generator_nbound": 1, "inner_twist_count": 1, "level_primes": [2, 23], "conrey_indexes": [1], "field_disc": 1, "field_disc_factorization": [], "field_poly": [0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "0.973", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.961", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "4.969", "prec": 17}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "3.2.3.c1", "atkin_lehner_eigenvals": [[2, 1], [23, -1]], "trace_display": [-2, -1, -10, -12], "traces": [0, 1, -2, -1, 4, -10, 2, -12, -8, -26, 20, -42, -4, 7, 24, 10, 16, 20, 52, 106, -40, 12, 84, 23, 8, -25, -14, 53, -48, -227, -20, 67, -32, 42, -40, 120, -104, 74, -212, -7, 80, -497, -24, -88, -168, 260, -46, 215, -16, -199, 50, -20, 28, 314, -106, 420, 96, -106, 454, 176, 40, -298, -134, 312, 64, -70, -84, 266, 80, -23, -240, -981, 208, -411, -148, 25, 424, 504, 14, 806, -160, 649, 994, -952, 48, -200, 176, 227, 336, -1332, -520, -84, 92, -67, -430, -1060, 32, -1328, 398, 1092, -100, 714, 40, -1480, -56, -120, -628, 1670, 212, -640, -840, -74, -192, 540, 212, -230, -908, -182, -352, -240, -80, 433, 596, 497, 268, 1500, -624, 2689, -128, 88, 140, 1227, 168, -1272, -532, -530, -160, 2644, 46, -2051, 480, -215, 1962, -294, -416, 2270, 822, 199, 296, 2294, -50, -1925, -848, -520, -1008, -670, -28, 3008, -1612, -314, 320, -276, -1298, -3655, -1988, -420, 1904, -696, -96, -2148, 400, -2756, -352, 2102, -454, 300, -672, -176, 2664, -2547, 1040, -1862, 168, 298, -184, -740, 134, -840, 860, -636, 2120, -18, -64, -4367, 2656, 70, -796, 1189, -2184, 3562, 200, -266, -1428, 2724, -80, 4970, 2960, -598, 112, -4452, 240, 3324, 1256, 981, -3340, 880, -424, -804, 1280, 411, 1680, 140, 148, -2160, 384, 650, -1080, -656, -424, 2700, 460, -504, 1816, 2723, 364, -2150, 704, -806, 480, 1971, 160, -1042, -866, -2080, -1192, 1990, -994, 742, -536, 952, -3000, 3848, 1248, -966, -5378, 200, 256, -4521, -176, -888, -280, 5902, -2454, -5542, -336, -3140, 2544, 1332, 1064, 4801, 1060, 1400, 320, 84, -5288, 1050, -92, -671, 4102, -1742, -960, -5860, 430, 5346, -3924, 1060, 588, 5964, 832, -4513, -4540, 1328, -1644, -6768, -398, -1760, -592, -2226, -4588, 161, 100, 1056, 3850, -714, 1696, 2980, 1040, 1352, 2016, 1480, 1340, -4733, 56, -880, -6016, -3120, 3224, -166, 628, 9534, -640, -1670, 552, 2120, 2596, -175, 7310, 640, 3976, -2580, 840, 1985, -3808, -1924, 1392, -2660, 192, 1476, 4296, -540, -800, -2814, 5512, 6504, 704, 230, -4204, -2556, 908, -9471, -600, 371, 1344, -6911, 352, 9810, -5328, 240, 5094, 7530, -2080, 4377, 3724, -433, -336, 4110, -596, -12936, 368, 12922, 1480, -3768, -268, 10614, 1680, -1500, -1720, -1589, 1272, -640, -4240, -2689, 36, -1628, 128, -5040, 8734, 2288, -5312, -4744, -140, 460, 1592, -1227, -2378, -8060, 4368, -12969, -7124, 1272, -400, -8630, 532, 469, 2856, -6490, -5448, -3108, 160, 11549, -9940, -2644, -5920, -2112, 1196, 9520, -224, 2051, 8904, -1848, -480, -4884, -6648, -5590, -2512, -500, -1962, 3576, 6680, 294, -1760, -2904, 848, -8398, 1608, -2270, -2560, 2438, -822, 7381, -3360, 5174, -280, -10937, -296, 13320, 4320, -2294, -768, 13470, -1300, 20874, 2160, 1925, 1312, 840, 848, 9096, -5400, 1060, -920, 19641, 1008, 15528, -3632, 670, -5446, -6414, -728, -3192, 4300, -3008, -1408, 3696, 1612, -2650, -960, -8164, -3942, -4416, -320, 518, 2084, 276, 1732, 13280, 4160, 985, 2384, 3655, -3980, -18155, 1988, -4540, -1484, -10920, 1072, 11772, -1904, -4793, 6000, 696, -7696, -1802, -2496, -7140, 1932, 2148, 10756, -831, -400, 4932, -512, 5618, 9042, 14800, 352, -9030, 1776, -2102, 560, -16924, -11804, -8064, 4908, -300, 11084, 1340, 672, 529, 6280, -4576, -5088, -3479, -2664, -16700, -2128, 2547, -9602, 8358, -2120, -16459, -2800, 1862, -640, 6400, -168, 601, 10576, 7748, -2100, -24062, 184, -9672, 1342, 740, -8204, -14260, 3484, -616, 1920, 840, 11720, 19788, -860, -5400, -10692, -7788, 7848, 22714, -2120, -12956, -1176, 18, -11928, -575, -1664, -7791, 9026, 4367, 9080, 11424, -2656, -13188, 3288, 1820, 13536, -9801, 796, 7102, 3520, -1189, 1184, 10270, 4452, 2400, 9176, -3562, -322, 8520, -200, 5061, -2112, -6916, -7700, -4330, 1428, -1380, -3392, -2724, -5960, 1505, -2080, -1484, -2704, -4970, -4032, 15570, -2960, -9688, -2680, 1219, 9466, 15984, -112, -11875, 1760, 4452, 12032, 1480, 6240, 180, -6448, -3324, 332, -26890, -1256, -1393, -19068, 25506, 1280, 16860, 3340, 21886, -1104, -880, -4240, 8871, -5192, -7392, 350, 804, -14620, 6767, -1280, -12270, -7952, 10686, 5160, 23360, -1680, 20790, -3970, -140, 7616, 12720, 3848, -5221, -2784, 2160, 5320, 12516, -384, 20187, -2952, -1325, -8592, -30046, 1080, 15936, 1600, 656, 5628, 9125, -11024, -26440, -13008, -2700, -1408, 2198, -460, -31276, 8408, -13104, 5112, 20510, -1816, -9940, 18942, -2723, 1200, 5172, -742, 7844, -2688, 2150, 13822, -8568, -704, -27896, -19620, -20956, 10656, 1541, -480, 2940, -10188, -1971, -15060, -5688, 4160, 17760, -8754, 1042, -7448, 5675, 866, 13374, 672, -15443, -8220, -1760, 1192, -2916, 25872, -1990, -736, -11172, -25844, -11, -2960, -742, 7536, -13152, 536, -22940, -21228, 24752, -3360, -20040, 3000, 20104, 3440, -3848, 3178, 19250, -2544, -7058, 1280, 966, 8480, 3285, 5378, 7680, -72, 5200, 3256, 1232, -256, -10474, 10080, 4521, -17468, -39428, -4576, -1675, 10624, 888, 9488, -52682, 280, 41202, -920, -12031, -3184, -30080, 2454, 34036, 4756, 5542, 16120, -6480, -8736, -2086, 25938, 3140, 14248, -15346, -2544, 4300, 800, 34632, 17260, 17262, -1064, 2760, -938, -4801, -5712, 9490, 12980, 37439, 10896, -1400, 6216, 36550, -320, -9328, -23098, 2184, 19880, -614, 5288, -30053, 11840, -1050, 4224, -8784, -2392, -18374, -19040, 671, 448, -3980, -4102, 6960, -17808, 3551, 3696, -13016, 960, 27140, 9768, 5860, 13296, 21480, 11180, -5196, 5024, -5346, 1000, 1702, 3924, -28994, -7152, 27560, -13360, 7323, -588, -25449, 3520, -5964, 5808, 33017, -1696, -21020, 16796, 4513, -3216, -33852, 4540, 1862, 5120, 34528, -4876, -18000, 1644, 10126, -14762, 6768, 6720, -14380, -10348, -28556, 560, 1760, 21874, -37761, 592, -32268, -26640, -27258, -8640, 22790, 4588, 25470, 1536, -161, -26940, -15209, 2600, 6280, -41748, -1056, -4320, 18620, -3850, 40014, -2624, -18564, -1680, -49010, -1696, 39984, -18192, -2980, 10800, -14724, -2120, -21632, 1840, -1352, -39282, -6867, -2016, -1850, -31056, 38480, 7264, 39487, -1340, -21094, 10892, 4733, 12828, 8400, 1456, 29882, 6384, 880, -8600, -31256, 6016, -11431, 2816, 6360, -7392, 41999, -3224, -2877, 5300, 166, 1920, 3134, 16328, 180, 7884, -9534, 8832, -31728, 640, -25302, -1036, -43420, -4168, 43670, -552, -39371, -3464, -2120, -26560, -5130, -8320, 24612, -1970, 175, -4768, -11006, -7310, 55944, 7960, 16640, 36310, 45546, -3976, -11890, 9080, 2580, 2968, -2024, 21840, 55312, -2144, -1985, -23544, -35620, 3808, 55694, 9586, 3922, -12000], "weight_parity": 1, "has_non_self_twist": 0, "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]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "46.4.a.a", "char_is_minimal": true, "conrey_index": 1, "id": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0], [1], [-2], [-1], [4], [-10], [2], [-12], [-8], [-26], [20], [-42], [-4], [7], [24], [10], [16], [20], [52], [106], [-40], [12], [84], [23], [8], [-25], [-14], [53], [-48], [-227], [-20], [67], [-32], [42], [-40], [120], [-104], [74], [-212], [-7], [80], [-497], [-24], [-88], [-168], [260], [-46], [215], [-16], [-199], [50], [-20], [28], [314], [-106], [420], [96], [-106], [454], [176], [40], [-298], [-134], [312], [64], [-70], [-84], [266], [80], [-23], [-240], [-981], [208], [-411], [-148], [25], [424], [504], [14], [806], [-160], [649], [994], [-952], [48], [-200], [176], [227], [336], [-1332], [-520], [-84], [92], [-67], [-430], [-1060], [32], [-1328], [398], [1092], [-100]]}