# Stored data for newform 49.4.a.b, downloaded from the LMFDB on 25 April 2024. {"label": "49.4.a.b", "space_label": "49.4.a", "level": 49, "weight": 4, "hecke_orbit": 2, "hecke_orbit_code": 4503599694479409, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 836144790978388819, "analytic_rank": 1, "is_twist_minimal": false, "hecke_cutters": [[2, [1, 1]], [3, [-2, 1]]], "qexp_display": "q-q^{2}+2q^{3}-7q^{4}-2^{4}q^{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": 784, "fricke_eigenval": -1, "atkin_lehner_string": "-", "analytic_conductor": 2.89109359028129, "hecke_ring_index": 1, "level_radical": 7, "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": {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, "analytic_rank_proved": true, "char_values": [49, 1, [3], [1]], "hecke_ring_generator_nbound": 1, "inner_twist_count": 1, "level_primes": [7], "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": "0.998", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.989", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "4.951", "prec": 17}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "3.2.3.c1", "atkin_lehner_eigenvals": [[7, -1]], "trace_display": [-1, 2, -16, 0], "traces": [0, 1, -1, 2, -7, -16, -2, 0, 15, -23, 16, -8, -14, -28, 0, -32, 41, -54, 23, 110, 112, 0, 8, 48, 30, 131, 28, -100, 0, -110, 32, -12, -161, -16, 54, 0, 161, -246, -110, -56, -240, -182, 0, 128, 56, 368, -48, -324, 82, 0, -131, -108, 196, -162, 100, 128, 0, 220, 110, -810, 224, 488, 12, 0, -167, 448, 16, 244, 378, 96, 0, -768, -345, 702, 246, 262, -770, 0, 56, 440, -656, 421, 182, 1302, 0, 864, -128, -220, -120, -730, -368, 0, -336, -24, 324, -1760, -322, -294, 0, 184, -917, 688, 108, -1388, -420, 0, 162, 244, 700, 90, -128, -492, 0, 1318, -220, -768, 770, 644, 810, 0, -480, -1267, -488, -364, 84, -96, 0, -1776, 1455, 256, -448, 1118, 112, 0, -244, 1600, -810, 2274, -96, 210, 0, -648, 768, 224, -943, 1760, -702, 0, 1722, -2010, -262, 1112, 1650, 1242, 0, 192, 392, -124, -440, -324, 2576, 0, -421, 2008, 1274, 256, -1302, -2884, 0, -1413, -864, -2530, -896, -2228, 220, 0, -328, -1620, 730, -820, -2576, -3892, 0, 976, 720, 3936, 24, 432, 2268, 0, 1760, -5048, -334, -2962, 294, 896, 0, 3334, -184, -1860, 1965, 488, -688, 0, 756, 2912, 1388, -1104, -1148, -880, 0, -4268, 1134, -1536, -244, -2048, -1500, 0, -90, 1404, -896, 1512, 492, 5432, 0, -3013, -1318, 2046, -1540, 2980, 768, 0, -1650, 4458, -644, 5184, 5670, 880, 0, 4440, -1312, -3302, 1267, 3542, -3416, 0, 364, -3080, -180, 2604, 96, -1582, 0, -384, 1776, 1728, -119, -2354, -256, 0, -3136, 2530, -1118, -3872, -240, 2592, 0, -1460, -1708, -180, -1600, -2032, -2214, 0, -2274, -1048, -672, -5426, -210, 276, 0, 842, 648, 3782, 5376, -3520, -224, 0, 3703, -1997, -1760, -588, -4914, 4312, 0, 12960, -3690, 800, 2010, -1344, -1834, 0, -1112, 1376, 4510, -7808, -1242, -2674, 0, -2776, -192, 3768, -840, -2438, 124, 0, -3080, -3186, 324, 880, 2672, 488, 0, -5940, -2947, -3668, -2008, 180, -2730, 0, -256, 8672, -9114, 5658, 2884, -3904, 0, 814, 1413, 2636, -6048, 96, 2530, 0, 1920, -1536, 2228, 9344, 1540, 5180, 0, 2800, 1288, -12178, 1620, 12288, 5110, 0, 820, 440, 5520, 5241, 3892, -2534, 0, -11232, -976, 9816, 1968, 4186, -3936, 0, 168, -442, -432, -192, -4860, 3080, 0, -3960, 12320, -3552, 5048, -6708, 2910, 0, 2962, -2944, 2058, -13350, -896, -2592, 0, 2236, -3334, -7040, -1288, 1356, 1860, 0, 5371, 6222, -488, 336, -4816, -6736, 0, 1968, -1620, -5150, -2912, 4548, 9716, 0, 1104, -20832, 4508, 420, 880, -2310, 0, 1262, 4268, 7452, -2430, -7074, 1536, 0, -1708, 448, 2048, -4488, -4100, -17038, 0, 3520, -630, 5280, -1404, -16200, 1920, 0, -1512, -8772, 3444, 11680, -5432, -4020, 0, 2130, 3013, 1456, -9226, 2224, -2046, 0, 3300, 10534, -2980, 5400, 5376, 9268, 0, -9392, -4510, 384, -4458, 10806, -4508, 0, -5184, -248, -12150, -1024, -880, 14410, 0, 3726, -4440, -4940, 5152, 6888, 3302, 0, 8869, 4704, -3542, -5216, 7320, 4016, 0, 4412, 2548, 5940, 3080, -2944, -492, 0, -2604, 19060, 672, -5768, 1582, -12768, 0, -11008, 384, -2826, 12432, 5500, -1728, 0, -11521, -11000, 2354, 22208, -1792, 2592, 0, -4456, 6720, 7338, -2530, 17582, -7826, 0, 3872, 648, -656, -9863, -2592, 18630, 0, 5096, 1460, -3904, 3660, -1640, 180, 0, -11200, -1618, 2032, -7784, 8694, -1440, 0, 16144, -15918, -11224, 1048, -12100, 1440, 0, 5426, 7872, -1470, 4654, -276, -3584, 0, 864, -842, -10078, 4536, -21088, -3782, 0, -11520, -5930, 3520, -19048, -1568, -10096, 0, 6288, 3841, 14366, 1997, -5924, -12320, 0, 588, 1296, 10530, -10304, -4312, 3626, 0, -1320, -12960, 6668, -10086, 1062, -800, 0, 14070, -3720, 1344, -10200, 3930, 25158, 0, -5612, -7784, 20272, -1376, -25664, -17710, 0, 7808, 9072, -8694, 19018, 2674, 5824, 0, 17334, 2776, -18730, -1344, -4800, -3768, 0, -2296, -14839, 2438, -1760, 868, 13284, 0, -6928, 6600, -8536, 3186, 28416, 2268, 0, -880, 17664, -23280, 16302, -488, -4718, 0, -4096, 5940, 21436, 6315, 6480, 3668, 0, -14056, 4458, -180, -17888, -7462, -16146, 0, -26640, -1792, -7432, -8672, 3024, 19530, 0, -5658, -5280, 20188, 10864, 3904, -3904, 0, 58, -814, -13100, 9891, 21516, -2636, 0, 12960, 4092, -96, 18108, 17710, -36384, 0, 5960, 5248, 4536, 1536, 10078, 15596, 0, -9344, -3360, -3300, 9828, -5180, 8916, 0, 18762, -2800, -27060, 1336, 10368, 12178, 0, 11340, 6810, -12288, -10120, -10950, -576, 0, -3584, 5740, 8880, -440, -4860, 15088, 0, -5241, -6604, 27244, -14410, 2534, 13636, 0, -4283, 11232, -6912, -6832, -2088, -9816, 0, -7728, -1952, -4186, -5160, -27552, -6160, 0, -28152, -360, 32160, 442, -29946, -3024, 0, 192, -16808, -13284, -3164, -3080, -17792, 0, 21674, 3960, -768, -26400, -7422, 3552, 0, 35336, -19872, 6708, 22680, -238, -13790, 0, -4708, 20734, 6232, 2944, -1572, -4410, 0, 13350, -20020, -6272, 6144, 2592, 11000, 0, 1984, -2236, 1766, -23338, -7744, 7040, 0, 2760, -13664, -1356, 5184, 13020, -1204, 0, 17496, -21091, 16790, -6222, -5616, -3416, 0, -336, -360, 10320, -7050, 6736, -23282, 0, -4064, -1968, -32128, -4428, 14080, 5150, 0, -20384, 10142, -4548, -9192, -20820, -2096, 0, -46716, 7728, -11240, 20832, -10852, 4676, 0, -420, 46144, 6160, 1200, 2310, -700, 0, -12289, -1262, 1684, 29876, 22608, -7452, 0, -6642, 7564, 7074, -11808, 10752, 37492, 0, 40480, 3660, -28894, -448, 2770, 14336, 0, 4488, 17688, 16100, 35648, 17038, -3994, 0, -3520, -3520, -6832, 1350, 6762, -5280, 0, -9828, -33566, 16200, 8624, 5248, 16758, 0, 11468, -10584, 25920, 8772, 50356, -7380, 0, -11680, -3368, -38024, -35640, 4020, 13120, 0, -2688, -2130, 1320, 21091, 8748, -1456, 0, 19770, 62272, -2224, -8716, -14322, -15824, 0, 7632, 9020, -10416, -10534, -15616, -20860, 0, -5400, -23080, -11520, -5348, -9268, 21504, 0, -32226, 9392, 31924, 17710, -45110, -384, 0, -31206, 7536, -10806, -6912, 9660, -16674, 0, -4876, -36288, -43832, 248, -8736, -33210, 0, 1024, -736, -6160, -19656, -14410, -6372, 0, 38138, -3726, 80768, -31080, 1760, 4940, 0, 5344, -29647, -6888, -5612, 23114, 47392, 0, 26224, -19005, -11880, -4704, -18762, -24794, 0, 5216, -7336, 20008, 38394, -4016, 5840, 0, -2070, -4412, -5388, -5460, -53344, -5940, 0, 21560, 6144, 2944, 25472, 1932, 17344, 0, 29760, -18228, 17096, -19060, 24600, -1440], "weight_parity": 1, "has_non_self_twist": 0, "level_is_prime": false, "level_is_prime_power": true, "level_is_square": true, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "7.4.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], [-1], [2], [-7], [-16], [-2], [0], [15], [-23], [16], [-8], [-14], [-28], [0], [-32], [41], [-54], [23], [110], [112], [0], [8], [48], [30], [131], [28], [-100], [0], [-110], [32], [-12], [-161], [-16], [54], [0], [161], [-246], [-110], [-56], [-240], [-182], [0], [128], [56], [368], [-48], [-324], [82], [0], [-131], [-108], [196], [-162], [100], [128], [0], [220], [110], [-810], [224], [488], [12], [0], [-167], [448], [16], [244], [378], [96], [0], [-768], [-345], [702], [246], [262], [-770], [0], [56], [440], [-656], [421], [182], [1302], [0], [864], [-128], [-220], [-120], [-730], [-368], [0], [-336], [-24], [324], [-1760], [-322], [-294], [0], [184], [-917]]}