# Stored data for newform 210.4.a.a, downloaded from the LMFDB on 25 April 2024.
{"label": "210.4.a.a", "space_label": "210.4.a", "level": 210, "weight": 4, "hecke_orbit": 1, "hecke_orbit_code": 67109074, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 908105232987468570, "analytic_rank": 1, "is_twist_minimal": true, "hecke_cutters": [[11, [-12, 1]], [13, [-2, 1]]], "qexp_display": "q-2q^{2}-3q^{3}+4q^{4}-5q^{5}+6q^{6}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 3360, "fricke_eigenval": -1, "atkin_lehner_string": "+++-", "analytic_conductor": 12.390401101205528, "hecke_ring_index": 1, "level_radical": 210, "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": [210, 1, [71, 127, 31], [1, 1, 1]], "hecke_ring_generator_nbound": 1, "inner_twist_count": 1, "level_primes": [2, 3, 5, 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": "1.004", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "2.051", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "5.255", "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], [3, 1], [5, 1], [7, -1]], "trace_display": [-2, -3, -5, 7], "traces": [0, 1, -2, -3, 4, -5, 6, 7, -8, 9, 10, 12, -12, 2, -14, 15, 16, -18, -18, 56, -20, -21, -24, -156, 24, 25, -4, -27, 28, -186, -30, -52, -32, -36, 36, -35, 36, -178, -112, -6, 40, -138, 42, -412, 48, -45, 312, -456, -48, 49, -50, 54, 8, -198, 54, -60, -56, -168, 372, 348, 60, 110, 104, 63, 64, -10, 72, -196, -72, 468, 70, -936, -72, 542, 356, -75, 224, 84, 12, 992, -80, 81, 276, -276, -84, 90, 824, 558, -96, 630, 90, 14, -624, 156, 912, -280, 96, 110, -98, 108, 100, 570, -108, -304, -16, 105, 396, 216, -108, 614, 120, 534, 112, -498, 336, 780, -744, 18, -696, -126, -120, -1187, -220, 414, -208, -125, -126, -1888, -128, 1236, 20, -2892, -144, 392, 392, 135, 144, 822, -936, -376, -140, 1368, 1872, 24, 144, 930, -1084, -147, -712, 3390, 150, -2968, -448, -162, -168, 260, -24, 1874, -1984, 594, 160, -1092, -162, 452, -552, 180, 552, -1416, 168, -2193, -180, 504, -1648, 426, -1116, 175, 192, -1044, -1260, 2700, -180, -1978, -28, -330, 1248, 890, -312, -216, -1824, -189, 560, -2328, -192, -3166, -220, 30, 196, -414, -216, -1636, -200, 588, -1140, -1302, 216, 690, 608, -1404, 32, 672, -210, -2860, -792, 2808, -432, 2060, 216, -364, -1228, -1626, -240, -36, -1068, -1096, -224, 225, 996, 6276, -672, -754, -1560, -252, 1488, 3870, -36, 2280, 1392, -2976, 252, 744, 240, 5474, 2374, -243, 440, -245, -828, 112, 416, 828, 250, 1980, 252, -1872, 3776, -270, 256, -210, -2472, -1246, -40, -1674, 5784, -1428, 288, 990, -784, -1890, -784, 4122, -270, 5780, -288, -42, -1644, 300, 1872, 4574, 752, -468, 280, 3450, -2736, -700, -3744, 840, -48, -966, -288, -4589, -1860, -330, 2168, 7170, 294, -1740, 1424, -324, -6780, -312, -300, -2884, 5936, -1710, 896, -550, 324, 6644, 336, 912, -520, -5376, 48, 2126, -3748, -315, 3968, 1074, -1188, -2232, -320, -648, 2184, -1008, 324, 50, -904, -1842, 1104, -3192, -360, -2788, -1104, -1602, 2832, 980, -336, -6334, 4386, 1494, 360, -624, -1008, 343, 3296, -2340, -852, -7032, 2232, -1474, -350, -54, -384, 7950, 2088, 4680, 2520, 378, -5400, 6624, 360, -3723, 3956, 3561, 56, -2710, 660, 1784, -2496, -1242, -1780, -1386, 624, -1978, 432, 375, 3648, -372, 378, -10780, -1120, 5664, 4656, -5880, 384, -420, 6332, -3708, 440, 6438, -60, 2808, -392, 8676, 828, -4960, 432, 2954, 3272, -1176, 400, -5574, -1176, -104, 2280, -405, 2604, -2136, -432, -15406, -1380, -2466, -1216, 2436, 2808, 1380, -64, 1128, -1344, 2940, 420, 254, 5720, -4104, 1584, -450, -5616, 770, 864, -72, -4120, -13248, -432, 16598, 728, -2790, 2456, -8736, 3252, -6532, 480, 441, 72, 12216, 2136, -3150, 2192, -10170, 448, 306, -450, -1656, -1992, 8904, -12552, -70, 1344, -6046, 1508, 486, 3120, 7122, 504, -11248, -2976, -780, -7740, -18252, 72, -1372, -4560, -5622, -2784, -4944, 5952, 1400, -504, -1782, -1488, -18168, -480, -356, -10948, 3276, -4748, -550, 486, 19856, -880, -1356, 490, 11220, 1656, 3348, -224, -540, -832, -6552, -1656, -9268, -500, 4248, -3960, 18576, -504, -2850, 3744, 6579, -7552, -11190, 540, 3794, -512, -1512, 420, 1520, 4944, -5472, 2492, -1278, 80, -306, 3348, 17444, -11568, -525, 2856, 936, -576, 12169, -1980, 3132, 1568, -276, 3780, -1080, 1568, -8100, -8244, 588, 540, -538, -11560, 5934, 576, -3070, 84, 19820, 3288, 990, -600, -10416, -3744, 6944, -9148, -2670, -1504, -16686, 936, -824, -560, 648, -6900, -16788, 5472, 2490, 1400, 567, 7488, 15906, -1680, 17084, 96, 6984, 1932, -3900, 576, 25382, 9178, 9498, 3720, -1932, 660, -2376, -4336, -90, -14340, 13764, -588, -2912, 3480, 1242, -2848, -13266, 648, 630, 13560, 4908, 624, 9600, 600, -19582, 5768, -1764, -11872, 5935, 3420, 3944, -1792, 3906, 1100, -912, -648, 20846, -13288, -2070, -672, 15342, -1824, -5128, 1040, 4212, 10752, 4410, -96, 625, -4252, -2016, 7496, 3204, 630, 31016, -7936, 8580, -2148, 9440, 2376, 98, 4464, -8424, 640, 15474, 1296, 24644, -4368, -6180, 2016, -16632, -648, 4176, -100, 1092, 1808, -10542, 3684, 14460, -2208, 4878, 6384, 15276, 720, 1478, 5576, 108, 2208, -1960, 3204, 29016, -5664, 3288, -1960, 1320, 672, -19366, 12668, -675, -8772, -21390, -2988, 770, -720, -18828, 1248, -21672, 2016, -4110, -686, 2262, -6592, -396, 4680, -5992, 1704, 756, 14064, 1880, -4464, 2484, 2948, -11610, 700, 17766, 108, -9968, 768, -6840, -15900, 3990, -4176, -24514, -9360, 8928, -5040, 8112, -756, -120, 10800, -2232, -13248, -13176, -720, -2128, 7446, -16422, -7912, -4650, -7122, 20792, -112, 729, 5420, 7416, -1320, -21742, -3568, 735, 4992, -2352, 2484, 39044, 3560, -336, 2772, -31116, -1248, -16950, 3956, -2484, -864, 1512, -750, -29320, -7296, -5940, 744, 14840, -756, -2266, 21560, 5616, 2240, -29946, -11328, 4298, -9312, 810, 11760, 696, -768, -23110, 840, 630, -12664, -31950, 7416, -1300, -880, 3738, -12876, -7728, 120, -11232, -5616, 5022, 784, -9370, -17352, 6284, -1656, 4284, 9920, -3486, -864, 220, -5908, -2970, -6544, 5946, 2352, 8208, -800, 5670, 11148, 6504, 2352, 5460, 208, -12366, -4560, 27090, 810, -20104, -5208, -17340, 4272, -2260, 864, -23072, 30812, 126, 2760, 7302, 4932, -24136, 2432, -900, -4872, 22680, -5616, -20338, -2760, -13722, 128, -882, -2256, 7080, 2688, 1404, -5880, 6600, -840, 10207, -508, -10350, -11440, 10965, 8208, -8309, -3168, 2100, 900, 27768, 11232, -40174, -1540, -2520, -1728, -20778, 144, 7400, 8240, 2898, 26496, 684, 864, -2130, -33196, 13767, -1456, 11904, 5580, -392, -4912, 990, 17472, -875, -6504, -9754, 13064, -21510, -960, 14310, -882, -14092, -144, 5220, -24432, 45600, -4272, -13216, 6300, 972, -4384, -25536, 20340, -13500, -896, 936, -612, 9672, 900, 3564, 3312, 8652, 3984, 9890, -17808, 8012, 25104, 5130, 140, 2136, -2688, -3312, 12092, 1650, -3016, -20244, -972, -15280, -6240, -19932, -14244, -1872, -1008, -4450, 22496, -2736, 5952, 20910, 1560, 2744, 15480, 16128, 36504, 1080, -144, -38122, 2744, -6378, 9120, 42810, 11244, 21528, 5568, 945, 9888, 39864, -11904, 1084, -2800, -3222, 1008, -23850, 3564, 11640, 2976, 6696, 36336, 5754, 960, -27087, 712, 1944, 21896, 15830, -6552, -12832, 9496, 3024, 1100, -15804, -972, -2632, -39712, -150, 1760, -33114, 2712, 7560, -980, 5526, -22440, -58632, -3312, 2070, -6696, 9576, 448, 64272, 1080, 55784, 1664, 8364, 13104, 8180, 3312, -23326, 18536, 4806, 1000], "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": "210.4.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], [-3], [4], [-5], [6], [7], [-8], [9], [10], [12], [-12], [2], [-14], [15], [16], [-18], [-18], [56], [-20], [-21], [-24], [-156], [24], [25], [-4], [-27], [28], [-186], [-30], [-52], [-32], [-36], [36], [-35], [36], [-178], [-112], [-6], [40], [-138], [42], [-412], [48], [-45], [312], [-456], [-48], [49], [-50], [54], [8], [-198], [54], [-60], [-56], [-168], [372], [348], [60], [110], [104], [63], [64], [-10], [72], [-196], [-72], [468], [70], [-936], [-72], [542], [356], [-75], [224], [84], [12], [992], [-80], [81], [276], [-276], [-84], [90], [824], [558], [-96], [630], [90], [14], [-624], [156], [912], [-280], [96], [110], [-98], [108], [100]]}