# Stored data for newform 49.4.c.b, downloaded from the LMFDB on 14 October 2024.
{"Nk2": 784, "analytic_conductor": 2.89109359028129, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 7, "char_degree": 2, "char_is_minimal": false, "char_is_real": false, "char_orbit_index": 3, "char_orbit_label": "c", "char_order": 3, "char_parity": 1, "char_values": [49, 3, [3], [2]], "cm_discs": [], "conrey_index": 18, "dim": 2, "field_disc": -3, "field_disc_factorization": [[-1, 1], [3, 1]], "field_poly": [1, -1, 1], "field_poly_is_cyclotomic": true, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 6, "has_non_self_twist": 1, "hecke_cutters": [[2, [1, -1, 1]], [3, [4, 2, 1]]], "hecke_orbit": 2, "hecke_orbit_code": 4503737133432881, "hecke_ring_generator_nbound": 2, "hecke_ring_index": 1, "hecke_ring_index_factorization": [], "hecke_ring_index_proved": true, "inner_twist_count": 2, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 7, 3, 1, 3, 0]], "is_cm": false, "is_largest": false, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": false, "is_self_twist": false, "is_twist_minimal": false, "label": "49.4.c.b", "level": 49, "level_is_powerful": true, "level_is_prime": false, "level_is_prime_power": true, "level_is_prime_square": true, "level_is_square": true, "level_is_squarefree": false, "level_primes": [7], "level_radical": 7, "minimal_twist": "7.4.a.a", "nf_label": "2.0.3.1", "prim_orbit_index": 3, "qexp_display": "q+\\zeta_{6}q^{2}+(-2+2\\zeta_{6})q^{3}+(7-7\\zeta_{6})q^{4}+\\cdots", "related_objects": [], "relative_dim": 1, "rm_discs": [], "sato_tate_group": "3.2.3.c3", "self_twist_discs": [], "self_twist_type": 0, "space_label": "49.4.c", "trace_display": [1, -2, 16, 0], "trace_hash": 621626901603175734, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "2.026", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "12.260", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "111.782", "prec": 24}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, "traces": [0, 2, 1, -2, 7, 16, -4, 0, 30, 23, -16, 8, 14, -56, 0, -64, -41, 54, -23, -110, 224, 0, 16, -48, -30, -131, -28, -200, 0, -220, -32, 12, 161, 16, 108, 0, 322, 246, 110, 56, 240, -364, 0, 256, -56, -368, 48, 324, 164, 0, -262, 108, -196, 162, -100, 256, 0, 440, -110, 810, -224, -488, 24, 0, -334, -448, -16, -244, -378, 192, 0, -1536, 345, -702, -246, -262, -1540, 0, 112, -440, 656, -421, -182, 2604, 0, 1728, 128, 220, 120, 730, -736, 0, -672, 24, -324, 1760, 322, -588, 0, 368, 917, -688, -108, 1388, -840, 0, 324, -244, -700, -90, 128, -984, 0, 2636, 220, 768, -770, -644, 1620, 0, -960, 1267, 488, 364, -84, -192, 0, -3552, -1455, -256, 448, -1118, 224, 0, -488, -1600, 810, -2274, 96, 420, 0, -1296, -768, -224, 943, -1760, -1404, 0, 3444, 2010, 262, -1112, -1650, 2484, 0, 384, -392, 124, 440, 324, 5152, 0, -842, -2008, -1274, -256, 1302, -5768, 0, -2826, 864, 2530, 896, 2228, 440, 0, -656, 1620, -730, 820, 2576, -7784, 0, 1952, -720, -3936, -24, -432, 4536, 0, 3520, 5048, 334, 2962, -294, 1792, 0, 6668, 184, 1860, -1965, -488, -1376, 0, 1512, -2912, -1388, 1104, 1148, -1760, 0, -8536, -1134, 1536, 244, 2048, -3000, 0, -180, -1404, 896, -1512, -492, 10864, 0, -6026, 1318, -2046, 1540, -2980, 1536, 0, -3300, -4458, 644, -5184, -5670, 1760, 0, 8880, 1312, 3302, -1267, -3542, -6832, 0, 728, 3080, 180, -2604, -96, -3164, 0, -768, -1776, -1728, 119, 2354, -512, 0, -6272, -2530, 1118, 3872, 240, 5184, 0, -2920, 1708, 180, 1600, 2032, -4428, 0, -4548, 1048, 672, 5426, 210, 552, 0, 1684, -648, -3782, -5376, 3520, -448, 0, 7406, 1997, 1760, 588, 4914, 8624, 0, 25920, 3690, -800, -2010, 1344, -3668, 0, -2224, -1376, -4510, 7808, 1242, -5348, 0, -5552, 192, -3768, 840, 2438, 248, 0, -6160, 3186, -324, -880, -2672, 976, 0, -11880, 2947, 3668, 2008, -180, -5460, 0, -512, -8672, 9114, -5658, -2884, -7808, 0, 1628, -1413, -2636, 6048, -96, 5060, 0, 3840, 1536, -2228, -9344, -1540, 10360, 0, 5600, -1288, 12178, -1620, -12288, 10220, 0, 1640, -440, -5520, -5241, -3892, -5068, 0, -22464, 976, -9816, -1968, -4186, -7872, 0, 336, 442, 432, 192, 4860, 6160, 0, -7920, -12320, 3552, -5048, 6708, 5820, 0, 5924, 2944, -2058, 13350, 896, -5184, 0, 4472, 3334, 7040, 1288, -1356, 3720, 0, 10742, -6222, 488, -336, 4816, -13472, 0, 3936, 1620, 5150, 2912, -4548, 19432, 0, 2208, 20832, -4508, -420, -880, -4620, 0, 2524, -4268, -7452, 2430, 7074, 3072, 0, -3416, -448, -2048, 4488, 4100, -34076, 0, 7040, 630, -5280, 1404, 16200, 3840, 0, -3024, 8772, -3444, -11680, 5432, -8040, 0, 4260, -3013, -1456, 9226, -2224, -4092, 0, 6600, -10534, 2980, -5400, -5376, 18536, 0, -18784, 4510, -384, 4458, -10806, -9016, 0, -10368, 248, 12150, 1024, 880, 28820, 0, 7452, 4440, 4940, -5152, -6888, 6604, 0, 17738, -4704, 3542, 5216, -7320, 8032, 0, 8824, -2548, -5940, -3080, 2944, -984, 0, -5208, -19060, -672, 5768, -1582, -25536, 0, -22016, -384, 2826, -12432, -5500, -3456, 0, -23042, 11000, -2354, -22208, 1792, 5184, 0, -8912, -6720, -7338, 2530, -17582, -15652, 0, 7744, -648, 656, 9863, 2592, 37260, 0, 10192, -1460, 3904, -3660, 1640, 360, 0, -22400, 1618, -2032, 7784, -8694, -2880, 0, 32288, 15918, 11224, -1048, 12100, 2880, 0, 10852, -7872, 1470, -4654, 276, -7168, 0, 1728, 842, 10078, -4536, 21088, -7564, 0, -23040, 5930, -3520, 19048, 1568, -20192, 0, 12576, -3841, -14366, -1997, 5924, -24640, 0, 1176, -1296, -10530, 10304, 4312, 7252, 0, -2640, 12960, -6668, 10086, -1062, -1600, 0, 28140, 3720, -1344, 10200, -3930, 50316, 0, -11224, 7784, -20272, 1376, 25664, -35420, 0, 15616, -9072, 8694, -19018, -2674, 11648, 0, 34668, -2776, 18730, 1344, 4800, -7536, 0, -4592, 14839, -2438, 1760, -868, 26568, 0, -13856, -6600, 8536, -3186, -28416, 4536, 0, -1760, -17664, 23280, -16302, 488, -9436, 0, -8192, -5940, -21436, -6315, -6480, 7336, 0, -28112, -4458, 180, 17888, 7462, -32292, 0, -53280, 1792, 7432, 8672, -3024, 39060, 0, -11316, 5280, -20188, -10864, -3904, -7808, 0, 116, 814, 13100, -9891, -21516, -5272, 0, 25920, -4092, 96, -18108, -17710, -72768, 0, 11920, -5248, -4536, -1536, -10078, 31192, 0, -18688, 3360, 3300, -9828, 5180, 17832, 0, 37524, 2800, 27060, -1336, -10368, 24356, 0, 22680, -6810, 12288, 10120, 10950, -1152, 0, -7168, -5740, -8880, 440, 4860, 30176, 0, -10482, 6604, -27244, 14410, -2534, 27272, 0, -8566, -11232, 6912, 6832, 2088, -19632, 0, -15456, 1952, 4186, 5160, 27552, -12320, 0, -56304, 360, -32160, -442, 29946, -6048, 0, 384, 16808, 13284, 3164, 3080, -35584, 0, 43348, -3960, 768, 26400, 7422, 7104, 0, 70672, 19872, -6708, -22680, 238, -27580, 0, -9416, -20734, -6232, -2944, 1572, -8820, 0, 26700, 20020, 6272, -6144, -2592, 22000, 0, 3968, 2236, -1766, 23338, 7744, 14080, 0, 5520, 13664, 1356, -5184, -13020, -2408, 0, 34992, 21091, -16790, 6222, 5616, -6832, 0, -672, 360, -10320, 7050, -6736, -46564, 0, -8128, 1968, 32128, 4428, -14080, 10300, 0, -40768, -10142, 4548, 9192, 20820, -4192, 0, -93432, -7728, 11240, -20832, 10852, 9352, 0, -840, -46144, -6160, -1200, -2310, -1400, 0, -24578, 1262, -1684, -29876, -22608, -14904, 0, -13284, -7564, -7074, 11808, -10752, 74984, 0, 80960, -3660, 28894, 448, -2770, 28672, 0, 8976, -17688, -16100, -35648, -17038, -7988, 0, -7040, 3520, 6832, -1350, -6762, -10560, 0, -19656, 33566, -16200, -8624, -5248, 33516, 0, 22936, 10584, -25920, -8772, -50356, -14760, 0, -23360, 3368, 38024, 35640, -4020, 26240, 0, -5376, 2130, -1320, -21091, -8748, -2912, 0, 39540, -62272, 2224, 8716, 14322, -31648, 0, 15264, -9020, 10416, 10534, 15616, -41720, 0, -10800, 23080, 11520, 5348, 9268, 43008, 0, -64452, -9392, -31924, -17710, 45110, -768, 0, -62412, -7536, 10806, 6912, -9660, -33348, 0, -9752, 36288, 43832, -248, 8736, -66420, 0, 2048, 736, 6160, 19656, 14410, -12744, 0, 76276, 3726, -80768, 31080, -1760, 9880, 0, 10688, 29647, 6888, 5612, -23114, 94784, 0, 52448, 19005, 11880, 4704, 18762, -49588, 0, 10432, 7336, -20008, -38394, 4016, 11680, 0, -4140, 4412, 5388, 5460, 53344, -11880, 0, 43120, -6144, -2944, -25472, -1932, 34688, 0, 59520, 18228, -17096, 19060, -24600, -2880], "weight": 4, "weight_parity": 1, "id": null, "artin_degree": null, "artin_field": null, "artin_field_label": null, "artin_image": null, "atkin_lehner_eigenvals": null, "atkin_lehner_string": null, "embedded_related_objects": null, "fricke_eigenval": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp": [[0, 0], [1, 0], [0, 1], [-2, 2], [7, -7], [0, 16], [-2, 0], [0, 0], [15, 0], [0, 23], [-16, 16], [8, -8], [0, 14], [-28, 0], [0, 0], [-32, 0], [0, -41], [54, -54], [-23, 23], [0, -110], [112, 0], [0, 0], [8, 0], [0, -48], [-30, 30], [-131, 131], [0, -28], [-100, 0], [0, 0], [-110, 0], [0, -32], [12, -12], [161, -161], [0, 16], [54, 0], [0, 0], [161, 0], [0, 246], [110, -110], [56, -56], [0, 240], [-182, 0], [0, 0], [128, 0], [0, -56], [-368, 368], [48, -48], [0, 324], [82, 0], [0, 0], [-131, 0], [0, 108], [-196, 196], [162, -162], [0, -100], [128, 0], [0, 0], [220, 0], [0, -110], [810, -810], [-224, 224], [0, -488], [12, 0], [0, 0], [-167, 0], [0, -448], [-16, 16], [-244, 244], [0, -378], [96, 0], [0, 0], [-768, 0], [0, 345], [-702, 702], [-246, 246], [0, -262], [-770, 0], [0, 0], [56, 0], [0, -440], [656, -656], [-421, 421], [0, -182], [1302, 0], [0, 0], [864, 0], [0, 128], [220, -220], [120, -120], [0, 730], [-368, 0], [0, 0], [-336, 0], [0, 24], [-324, 324], [1760, -1760], [0, 322], [-294, 0], [0, 0], [184, 0], [0, 917]]}