# Stored data for newform 220.4.a.c, downloaded from the LMFDB on 06 March 2026.
{"Nk2": 3520, "analytic_conductor": 12.980420201262936, "analytic_rank": 0, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[2, -1], [5, -1], [11, 1]], "atkin_lehner_string": "--+", "char_conductor": 1, "char_degree": 1, "char_is_minimal": true, "char_is_real": true, "char_orbit_index": 1, "char_orbit_label": "a", "char_order": 1, "char_parity": 1, "char_values": [220, 1, [111, 177, 101], [1, 1, 1]], "cm_discs": [], "conrey_index": 1, "dim": 1, "field_disc": 1, "field_disc_factorization": [], "field_poly": [0, 1], "field_poly_is_cyclotomic": false, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 0, "fricke_eigenval": 1, "has_non_self_twist": 0, "hecke_cutters": [[3, [-8, 1]]], "hecke_orbit": 3, "hecke_orbit_code": 9007199321850076, "hecke_ring_generator_nbound": 1, "hecke_ring_index": 1, "hecke_ring_index_factorization": [], "hecke_ring_index_proved": true, "inner_twist_count": 1, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "is_cm": false, "is_largest": false, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": true, "is_self_twist": false, "is_twist_minimal": true, "label": "220.4.a.c", "level": 220, "level_is_powerful": false, "level_is_prime": false, "level_is_prime_power": false, "level_is_prime_square": false, "level_is_square": false, "level_is_squarefree": false, "level_primes": [2, 5, 11], "level_radical": 110, "minimal_twist": "220.4.a.c", "nf_label": "1.1.1.1", "prim_orbit_index": 1, "qexp_display": "q+8q^{3}+5q^{5}+24q^{7}+37q^{9}-11q^{11}+\\cdots", "related_objects": [], "relative_dim": 1, "rm_discs": [], "sato_tate_group": "3.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "220.4.a", "trace_display": [0, 8, 5, 24], "trace_hash": 951962191465627353, "trace_moments": [{"__RealLiteral__": 0, "data": "0.016", "prec": 17}, {"__RealLiteral__": 0, "data": "1.004", "prec": 17}, {"__RealLiteral__": 0, "data": "0.055", "prec": 17}, {"__RealLiteral__": 0, "data": "2.019", "prec": 17}, {"__RealLiteral__": 0, "data": "0.187", "prec": 17}, {"__RealLiteral__": 0, "data": "5.034", "prec": 17}], "trace_zratio": 0, "traces": [0, 1, 0, 8, 0, 5, 0, 24, 0, 37, 0, -11, 0, -22, 0, 40, 0, 22, 0, -28, 0, 192, 0, -44, 0, 25, 0, 80, 0, 110, 0, -40, 0, -88, 0, 120, 0, -362, 0, -176, 0, 210, 0, 260, 0, 185, 0, -460, 0, 233, 0, 176, 0, 662, 0, -55, 0, -224, 0, -68, 0, 606, 0, 888, 0, -110, 0, -312, 0, -352, 0, 360, 0, -1042, 0, 200, 0, -264, 0, -552, 0, -359, 0, 268, 0, 110, 0, 880, 0, -966, 0, -528, 0, -320, 0, -140, 0, -1334, 0, -407, 0, -1362, 0, 1564, 0, 960, 0, -1108, 0, -1482, 0, -2896, 0, -1030, 0, -220, 0, -814, 0, 528, 0, 121, 0, 1680, 0, 125, 0, 1928, 0, 2080, 0, -996, 0, -672, 0, 400, 0, 578, 0, -1484, 0, -3680, 0, 242, 0, 550, 0, 1864, 0, 3214, 0, 1960, 0, 814, 0, -200, 0, -2810, 0, 5296, 0, -1056, 0, 1688, 0, -440, 0, 3616, 0, -1713, 0, -1036, 0, 3714, 0, 600, 0, -544, 0, 444, 0, -4658, 0, 4848, 0, -1810, 0, -242, 0, 1920, 0, -216, 0, 470, 0, -880, 0, 2362, 0, -1728, 0, -2496, 0, 2640, 0, 1050, 0, -1628, 0, 308, 0, 1740, 0, 2880, 0, 1300, 0, -960, 0, -8336, 0, -484, 0, -964, 0, 925, 0, 1932, 0, 4718, 0, -2112, 0, 198, 0, -2300, 0, -4416, 0, -4136, 0, -3222, 0, -5032, 0, 1165, 0, 616, 0, 2144, 0, 6916, 0, 484, 0, 880, 0, 5714, 0, -8688, 0, 4070, 0, 4464, 0, 3310, 0, -7728, 0, 4886, 0, 5040, 0, -4224, 0, -275, 0, 3970, 0, -1480, 0, 2882, 0, 2308, 0, -1120, 0, 5040, 0, -4429, 0, -10672, 0, 8610, 0, -340, 0, -880, 0, 968, 0, 6240, 0, -10896, 0, 3030, 0, -5532, 0, 12512, 0, -1688, 0, -678, 0, 4440, 0, -10794, 0, -1210, 0, -8864, 0, -616, 0, -550, 0, -11856, 0, -11040, 0, 9228, 0, -13394, 0, -1560, 0, -7946, 0, -8240, 0, 440, 0, -2640, 0, -1760, 0, -4676, 0, 606, 0, -1760, 0, -238, 0, 1800, 0, 4224, 0, 9856, 0, -6075, 0, 968, 0, -5210, 0, 772, 0, 7770, 0, 15888, 0, -7990, 0, 1000, 0, -2420, 0, -3444, 0, 15424, 0, 1764, 0, -1320, 0, 9620, 0, 7262, 0, -968, 0, -7968, 0, -2760, 0, 1702, 0, -5376, 0, 1698, 0, 880, 0, -1795, 0, 3982, 0, 5258, 0, 4624, 0, -1632, 0, 1340, 0, -11872, 0, -4772, 0, 12830, 0, -17020, 0, 550, 0, 14544, 0, 1936, 0, -10872, 0, 14282, 0, 4400, 0, 1232, 0, -3928, 0, 8621, 0, 8192, 0, -4830, 0, 25712, 0, -3518, 0, -2310, 0, 15680, 0, -2640, 0, -4346, 0, 1760, 0, 1062, 0, 5084, 0, -1600, 0, 18456, 0, -7488, 0, -22480, 0, -2860, 0, -700, 0, 24494, 0, -6648, 0, 7964, 0, -8448, 0, -6670, 0, -1492, 0, 13504, 0, 20364, 0, 2420, 0, -2035, 0, 8640, 0, 1444, 0, 28928, 0, 600, 0, -6810, 0, -13704, 0, -3274, 0, -25008, 0, -2240, 0, 7820, 0, 5060, 0, 29712, 0, -11702, 0, -17316, 0, 4800, 0, -880, 0, -10231, 0, -2516, 0, -4620, 0, -5540, 0, 3552, 0, -2563, 0, -19066, 0, -37264, 0, -7410, 0, 20396, 0, 22422, 0, -3080, 0, -13248, 0, -14480, 0, -21166, 0, -5720, 0, -1936, 0, 17572, 0, -5150, 0, -8616, 0, -14230, 0, -15316, 0, -1728, 0, -1100, 0, 22794, 0, 3760, 0, 6432, 0, -7282, 0, -4070, 0, -12144, 0, 1120, 0, 18896, 0, -698, 0, 2640, 0, -13824, 0, 6600, 0, -2254, 0, -11544, 0, 605, 0, 17848, 0, 21120, 0, 10120, 0, 2266, 0, 8400, 0, -19374, 0, -3692, 0, -3520, 0, -23184, 0, 625, 0, 2464, 0, -7964, 0, -2808, 0, 13920, 0, 9640, 0, -5126, 0, 13320, 0, 7074, 0, 16696, 0, 10400, 0, 4756, 0, 748, 0, -7680, 0, 7614, 0, -4980, 0, -38554, 0, 27772, 0, -17938, 0, -3872, 0, -3360, 0, -4840, 0, -7712, 0, -6666, 0, -42, 0, 2000, 0, 6226, 0, -32016, 0, 15456, 0, -23176, 0, 2890, 0, 37744, 0, -14564, 0, 13004, 0, -9768, 0, -7420, 0, 4620, 0, 1584, 0, 21758, 0, 10136, 0, -18400, 0, -32688, 0, -18578, 0, -20424, 0, 1760, 0, 1210, 0, -33088, 0, 5760, 0, 37536, 0, -25776, 0, 2750, 0, 15764, 0, -30563, 0, 5720, 0, 18898, 0, 9320, 0, 3432, 0, -26916, 0, 4928, 0, 2176, 0, 16070, 0, 9916, 0, -26592, 0, 12800, 0, 55328, 0, 9800, 0, 36926, 0, 3872, 0, -34374, 0, -35568, 0, 4070, 0, 1496, 0, -7094, 0, 45712, 0, -2234, 0, -1000, 0, -69504, 0, -5880, 0, -3960, 0, 8800, 0, -14050, 0, -12956, 0, 35712, 0, -24720, 0, -13332, 0, 26480, 0, -6042, 0, -10120, 0, -35742, 0, 11462, 0, -5280, 0, 39088, 0, -13566, 0, 28348, 0, 40320, 0, 8440, 0, -7280, 0, -19536, 0, -26810, 0, 37596, 0, -2200, 0, -852, 0, 28294, 0, 31760, 0, 5126, 0, 18080, 0, -3200, 0, -10176, 0, -12289, 0, 23056, 0, -8565, 0, 2904, 0, 18464, 0, 15928, 0, 20954, 0, -5180, 0, -36402, 0, -6140, 0, 40320, 0, 17524, 0, 18570, 0, -35432, 0, 6072, 0, 6864, 0, -49358, 0, 3000, 0, 9266, 0, 68880, 0, 4978, 0, 42328, 0, -2720, 0, -20480, 0, 46272, 0, 3949, 0, 12880, 0, 2220, 0, 7744, 0, -4400, 0, 14564, 0, 49920, 0, -23290, 0, 27232, 0, -50394, 0, 17992, 0, -2948, 0, 24240, 0, -23904, 0, 1064, 0, -44256, 0, -7920, 0, -9050, 0, 57868, 0, 32882, 0, -6524, 0, -13504, 0, -1210, 0, 9414, 0, -5424, 0, 11270, 0, -9240, 0, 9600, 0, -5576, 0, 22924, 0, -86352, 0, 13526, 0, -1080, 0, -9680, 0, 13872, 0, -28191, 0, -40996, 0, 2350, 0, 14128, 0, -4928, 0, -3540, 0, -35616, 0, -4400, 0, 11050, 0, 10626, 0, -54834, 0, -19460, 0, 11810, 0, -88320, 0, -11440, 0, -30776, 0, 73824, 0, -8640, 0, 31370, 0, -28960, 0], "weight": 4, "weight_parity": 1, "id": null, "artin_degree": null, "artin_field": null, "artin_field_label": null, "artin_image": null, "embedded_related_objects": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp": [[0], 1, 0, 8, 0, 5, 0, 24, 0, 37, 0, -11, 0, -22, 0, 40, 0, 22, 0, -28, 0, 192, 0, -44, 0, 25, 0, 80, 0, 110, 0, -40, 0, -88, 0, 120, 0, -362, 0, -176, 0, 210, 0, 260, 0, 185, 0, -460, 0, 233, 0, 176, 0, 662, 0, -55, 0, -224, 0, -68, 0, 606, 0, 888, 0, -110, 0, -312, 0, -352, 0, 360, 0, -1042, 0, 200, 0, -264, 0, -552, 0, -359, 0, 268, 0, 110, 0, 880, 0, -966, 0, -528, 0, -320, 0, -140, 0, -1334, 0, -407, 0, -1362, 0, 1564, 0, 960, 0, -1108, 0, -1482, 0, -2896, 0, -1030, 0, -220, 0, -814, 0, 528, 0, 121, 0, 1680, 0, 125, 0, 1928, 0, 2080, 0, -996, 0, -672, 0, 400, 0, 578, 0, -1484, 0, -3680, 0, 242, 0, 550, 0, 1864, 0, 3214, 0, 1960, 0, 814, 0, -200, 0, -2810, 0, 5296, 0, -1056, 0, 1688, 0, -440, 0, 3616, 0, -1713, 0, -1036, 0, 3714, 0, 600, 0, -544, 0, 444, 0, -4658, 0, 4848, 0, -1810, 0, -242, 0, 1920, 0, -216, 0, 470, 0, -880, 0, 2362, 0, -1728, 0, -2496, 0, 2640, 0, 1050, 0, -1628, 0, 308, 0, 1740, 0, 2880, 0, 1300, 0, -960, 0, -8336, 0, -484, 0, -964, 0, 925, 0, 1932, 0, 4718, 0, -2112, 0, 198, 0, -2300, 0, -4416, 0, -4136, 0, -3222, 0, -5032, 0, 1165, 0, 616, 0, 2144, 0, 6916, 0, 484, 0, 880, 0, 5714, 0, -8688, 0, 4070, 0, 4464, 0, 3310, 0, -7728, 0, 4886, 0, 5040, 0, -4224, 0, -275, 0, 3970, 0, -1480, 0, 2882, 0, 2308, 0, -1120, 0, 5040, 0, -4429, 0, -10672, 0, 8610, 0, -340, 0, -880, 0, 968, 0, 6240, 0, -10896, 0, 3030, 0, -5532, 0, 12512, 0, -1688, 0, -678, 0, 4440, 0, -10794, 0, -1210, 0, -8864, 0, -616, 0, -550, 0, -11856, 0, -11040, 0, 9228, 0, -13394, 0, -1560, 0, -7946, 0, -8240, 0, 440, 0, -2640, 0, -1760, 0, -4676, 0, 606, 0, -1760, 0, -238, 0, 1800, 0, 4224, 0, 9856, 0, -6075, 0, 968, 0, -5210, 0, 772, 0, 7770, 0, 15888, 0, -7990, 0, 1000, 0, -2420, 0, -3444, 0, 15424, 0, 1764, 0, -1320, 0, 9620, 0, 7262, 0, -968, 0, -7968, 0, -2760, 0, 1702, 0, -5376, 0, 1698, 0, 880, 0, -1795, 0, 3982, 0, 5258, 0, 4624, 0, -1632, 0, 1340, 0, -11872, 0, -4772, 0, 12830, 0, -17020, 0, 550, 0, 14544, 0, 1936, 0, -10872, 0, 14282, 0, 4400, 0, 1232, 0, -3928, 0, 8621, 0, 8192, 0, -4830, 0, 25712, 0, -3518, 0, -2310, 0, 15680, 0, -2640, 0, -4346, 0, 1760, 0, 1062, 0, 5084, 0, -1600, 0, 18456, 0, -7488, 0, -22480, 0, -2860, 0, -700, 0, 24494, 0, -6648, 0, 7964, 0, -8448, 0, -6670, 0, -1492, 0, 13504, 0, 20364, 0, 2420, 0, -2035, 0, 8640, 0, 1444, 0, 28928, 0, 600, 0, -6810, 0, -13704, 0, -3274, 0, -25008, 0, -2240, 0, 7820, 0, 5060, 0, 29712, 0, -11702, 0, -17316, 0, 4800, 0, -880, 0, -10231, 0, -2516, 0, -4620, 0, -5540, 0, 3552, 0, -2563, 0, -19066, 0, -37264, 0, -7410, 0, 20396, 0, 22422, 0, -3080, 0, -13248, 0, -14480, 0, -21166, 0, -5720, 0, -1936, 0, 17572, 0, -5150, 0, -8616, 0, -14230, 0, -15316, 0, -1728, 0, -1100, 0, 22794, 0, 3760, 0, 6432, 0, -7282, 0, -4070, 0, -12144, 0, 1120, 0, 18896, 0, -698, 0, 2640, 0, -13824, 0, 6600, 0, -2254, 0, -11544, 0, 605, 0, 17848, 0, 21120, 0, 10120, 0, 2266, 0, 8400, 0, -19374, 0, -3692, 0, -3520, 0, -23184, 0, 625, 0, 2464, 0, -7964, 0, -2808, 0, 13920, 0, 9640, 0, -5126, 0, 13320, 0, 7074, 0, 16696, 0, 10400, 0, 4756, 0, 748, 0, -7680, 0, 7614, 0, -4980, 0, -38554, 0, 27772, 0, -17938, 0, -3872, 0, -3360, 0, -4840, 0, -7712, 0, -6666, 0, -42, 0, 2000, 0, 6226, 0, -32016, 0, 15456, 0, -23176, 0, 2890, 0, 37744, 0, -14564, 0, 13004, 0, -9768, 0, -7420, 0, 4620, 0, 1584, 0, 21758, 0, 10136, 0, -18400, 0, -32688, 0, -18578, 0, -20424, 0, 1760, 0, 1210, 0, -33088, 0, 5760, 0, 37536, 0, -25776, 0, 2750, 0, 15764, 0, -30563, 0, 5720, 0, 18898, 0, 9320, 0, 3432, 0, -26916, 0, 4928, 0, 2176, 0, 16070, 0, 9916, 0, -26592, 0, 12800, 0, 55328, 0, 9800, 0, 36926, 0, 3872, 0, -34374, 0, -35568, 0, 4070, 0, 1496, 0, -7094, 0, 45712, 0, -2234, 0, -1000, 0, -69504, 0, -5880, 0, -3960, 0, 8800, 0, -14050, 0, -12956, 0, 35712, 0, -24720, 0, -13332, 0, 26480, 0, -6042, 0, -10120, 0, -35742, 0, 11462, 0, -5280, 0, 39088, 0, -13566, 0, 28348, 0, 40320, 0, 8440, 0, -7280, 0, -19536, 0, -26810, 0, 37596, 0, -2200, 0, -852, 0, 28294, 0, 31760, 0, 5126, 0, 18080, 0, -3200, 0, -10176, 0, -12289, 0, 23056, 0, -8565, 0, 2904, 0, 18464, 0, 15928, 0, 20954, 0, -5180, 0, -36402, 0, -6140, 0, 40320, 0, 17524, 0, 18570, 0, -35432, 0, 6072, 0, 6864, 0, -49358, 0, 3000, 0, 9266, 0, 68880, 0, 4978, 0, 42328, 0, -2720, 0, -20480, 0, 46272, 0, 3949, 0, 12880, 0, 2220, 0, 7744, 0, -4400, 0, 14564, 0, 49920, 0, -23290, 0, 27232, 0, -50394, 0, 17992, 0, -2948, 0, 24240, 0, -23904, 0, 1064, 0, -44256, 0, -7920, 0, -9050, 0, 57868, 0, 32882, 0, -6524, 0, -13504, 0, -1210, 0, 9414, 0, -5424, 0, 11270, 0, -9240, 0, 9600, 0, -5576, 0, 22924, 0, -86352, 0, 13526, 0, -1080, 0, -9680, 0, 13872, 0, -28191, 0, -40996, 0, 2350, 0, 14128, 0, -4928, 0, -3540, 0, -35616, 0, -4400, 0, 11050, 0, 10626, 0, -54834, 0, -19460, 0, 11810, 0, -88320, 0, -11440, 0, -30776, 0, 73824, 0, -8640, 0, 31370, 0, -28960, 0]}