# Stored data for newform 110.4.g.b, downloaded from the LMFDB on 28 December 2025.
{"Nk2": 1760, "analytic_conductor": 6.490210100631468, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 11, "char_degree": 4, "char_is_minimal": true, "char_is_real": false, "char_orbit_index": 7, "char_orbit_label": "g", "char_order": 5, "char_parity": 1, "char_values": [110, 5, [67, 101], [5, 3]], "cm_discs": [], "conrey_index": 31, "dim": 12, "field_disc": 4908506557596403361328125, "field_disc_factorization": [[5, 9], [1585293461, 2]], "field_poly": [14641, 103818, 529133, 1418439, 2006313, 226101, 95917, 4434, 1903, 56, 18, -3, 1], "field_poly_is_cyclotomic": false, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 0, "has_non_self_twist": 1, "hecke_cutters": [[3, [43151761, -28916738, 26521759, -6331483, 1394337, -255587, 86559, -5934, 2899, -476, 122, -15, 1]]], "hecke_orbit": 2, "hecke_orbit_code": 4504012011339886, "hecke_ring_generator_nbound": 11, "hecke_ring_index": 5, "hecke_ring_index_factorization": [[5, 1]], "hecke_ring_index_proved": true, "inner_twist_count": 2, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 11, 3, 1, 5, 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": true, "label": "110.4.g.b", "level": 110, "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": true, "level_primes": [2, 5, 11], "level_radical": 110, "minimal_twist": "110.4.g.b", "prim_orbit_index": 3, "qexp_display": "q+2\\beta _{4}q^{2}+(2-\\beta _{1}+2\\beta _{4})q^{3}-4\\beta _{7}q^{4}+\\cdots", "related_objects": [], "relative_dim": 3, "rm_discs": [], "sato_tate_group": "3.2.3.c5", "self_twist_discs": [], "self_twist_type": 0, "space_label": "110.4.g", "trace_display": [-6, 15, 15, 15], "trace_hash": 1677622743535382030, "trace_moments": [{"__RealLiteral__": 0, "data": "0.046", "prec": 17}, {"__RealLiteral__": 0, "data": "11.397", "prec": 20}, {"__RealLiteral__": 0, "data": "0.248", "prec": 17}, {"__RealLiteral__": 0, "data": "498.442", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "46792.659", "prec": 30}], "trace_zratio": 0, "traces": [0, 12, -6, 15, -12, 15, -20, 15, -24, 62, -120, 34, -40, -114, 30, -75, -48, -17, -166, -162, 60, 148, -142, -210, -80, -75, 342, -147, 40, -57, -150, 816, 384, -1188, 696, -50, -332, 870, 466, -413, 120, 754, 586, 136, -204, -210, -430, -792, 240, 1008, -150, -504, 684, 359, -1364, -220, -400, -1242, -114, 1252, 200, 1346, -1858, 3469, -192, 570, -2336, 376, -68, -889, -150, 2038, 496, 945, 1740, -250, -568, -754, 1364, -149, 240, -1346, 368, -614, -1468, 785, 22, -4442, 352, -3122, -620, -4694, 1280, 1487, 2326, 810, 480, 1617, 1956, -3855, 1200, -2705, -1008, 470, -912, -1465, 448, 1043, -588, -8730, -340, 7098, 160, -4887, 4086, 1075, 1932, 5062, 2504, -57, 400, -6008, -3448, -190, -3716, 375, -1132, 1511, -384, 11477, 1140, -1780, 4228, -9766, -2988, -2440, -1256, 3259, 5742, 5882, -300, 2006, -10164, -3259, 672, -2415, 1890, 17347, -1460, 4819, 750, 7407, 1864, 5386, -6198, -1130, -1652, -2699, 1142, 3345, 480, 10308, -2692, -4827, -7504, -3560, 3312, -4144, -2936, 1713, 170, 10082, -316, -6551, 7706, -1250, 704, -15108, -5594, -9703, 1660, 1976, 9572, -953, 2560, 1825, -12036, -7012, -2968, 7719, 1620, 541, -640, 9729, -1656, -360, 4032, 5854, -360, 2976, -600, -5326, 1600, -6366, 4284, -3770, 940, 12648, -1824, -8078, -1480, -10865, 896, 649, -924, -55, 3904, 1616, 8300, -13464, 1420, -7124, -8584, 9200, 480, 1550, 16446, 262, 8172, 1167, 2100, -26846, -6816, -1053, 10124, 3960, -1552, -10439, 5926, 8434, 800, 5666, 6464, -15584, 5384, 7485, -9820, 12750, 6528, 6717, 750, 3627, -23224, -29068, -11968, -5355, -768, 5260, -18726, 4939, -3420, -5743, 10540, 40866, 4696, 5830, -20192, -24322, 5224, -5160, 1470, 5329, -2512, 8817, -34712, 1100, -15856, -6710, 11764, -7418, -400, 10086, -6148, -5431, 8152, 8010, -8528, -24300, 1984, 9952, 570, 4225, -620, 23127, 34694, 1940, -8080, 5267, -4112, 29887, 1500, -10874, 3934, 991, -2592, 2420, 1432, 49036, 12424, -6524, -8160, 26298, 576, -2111, 11872, -17345, 2284, 8087, -15660, -17588, -3840, 15136, 20616, -24330, 6656, -2850, 12776, -53425, 1472, -13922, 11880, -10366, -2456, 23254, -16118, 7470, 4688, 5541, 3426, 3339, -6960, -2019, 36784, -3059, -632, 4445, 4788, -37566, -6528, 18861, 500, 44460, 1088, -53496, 3264, -2515, 17432, 5051, 31004, 2196, 3320, -11507, 11972, 19320, -736, 775, -1906, 29097, -3440, -24751, -8700, -25850, 5948, 152, -4124, 1250, 9304, 3350, -47972, 19217, -4660, 7329, 1082, -25143, -1280, -4405, -4412, -14058, -3312, -21104, 4130, -23734, -11976, -6789, -14762, 4220, 23380, 11596, -32018, -90081, -1200, -25260, 9918, 7582, 3200, -8320, -12132, 40256, -9072, 66246, -7540, -13678, 5840, -3749, -20404, 1070, -3648, 53522, 22124, 33540, -5860, 1885, -3830, -19619, 2872, -3925, 1298, -20999, -4648, -1183, -1360, 20959, 7808, -19086, -13108, -19265, 860, -27612, -7328, -16400, 2040, 100744, -19808, 28139, 2972, 13985, 16500, -25391, 960, -31917, 2100, -3032, -26688, 39178, 524, 23470, -9936, -31503, -4436, 56800, 4300, 12822, -22412, 23032, 7728, -7610, -10546, 9054, -17032, -32543, 7920, -16371, -13824, 25596, 74412, 5825, 11852, 24069, -31202, -41639, -2400, -56694, -24628, 115554, 20108, 7890, -2128, 3331, -3872, -13401, -10080, -23453, -19640, -44315, -74000, 7975, 3616, -27368, 13434, 29925, 1500, -51266, -9226, -60442, -4528, -19050, 36734, 82134, 6044, -34399, 5040, -12802, -1536, 92266, 10520, -7300, -16912, 4948, 56368, 22130, -6840, -50516, -2406, -34731, -17520, -9175, -10588, 33316, 11392, 73982, -3590, -56442, 59916, -41518, 24846, -5215, 10448, 2352, 43940, 55630, 13640, 29242, 10658, 2172, -544, -20750, 26834, -78624, 13036, -97198, 2200, -2404, 22968, 51003, 3180, 21460, -15932, -45423, -14836, -62063, 4000, 33841, 39572, 18152, -12296, 24435, 29948, -73479, 4024, 92865, 12420, 32758, 30944, 86242, 25850, 8000, -5312, 43487, -11396, -82570, 1140, -23844, -18220, -5587, -12640, 21290, 46254, -27782, -39732, -19410, -12520, -42528, -5840, 83118, -166, 29060, 19276, 35801, -27406, 58169, -2000, 4717, -21748, -31012, -74992, 17815, -34188, -62029, -5184, -24141, -13460, -35889, -13636, -75946, -4988, -51000, -1072, -1936, -49758, 31380, 18580, -70942, -14334, 12259, 1152, -1875, 45388, 139292, -25896, 72948, -34690, 75372, -1192, 2746, -26996, -7405, 13380, 9128, 28484, 60660, 1920, -2902, -29618, 34194, -50648, -57385, -48660, -44602, -5088, -34542, -5700, -39663, 25552, -47874, 37040, -26350, 12064, -27032, 12356, -51652, 23360, -17268, -34742, 10767, -1712, 50480, -9342, -4782, -32236, 17996, -3760, 124841, 4736, 36099, 11082, 12200, -2968, -9264, -51622, 76275, 680, 9660, -35408, -133914, 40328, -27095, 29072, -37458, 176, -58723, 8890, 31639, 33256, -133187, 66248, 19915, -13056, 4496, -30468, -80777, 1500, 132056, 33900, 48294, -4544, -10680, 1768, 46178, 23688, 46259, -20380, -14111, 34864, -81193, 46192, -24830, -46392, -59351, 4392, 36024, -4960, 42718, -35604, -151108, 7904, -21300, -30480, -94352, 38288, -48061, -9450, -2399, 2328, 54076, 58194, 49665, -6720, 19970, 16728, 28359, -17400, -126370, 13530, 105548, 12176, 18955, -58926, 190122, 52212, 3358, 2500, 130146, -12672, -61387, 7300, -37035, -95944, 3534, 150764, -81532, 5680, 25429, 14658, -22485, 25824, -3580, 66464, 4010, -2560, -184452, 7540, -98682, 38916, 58513, -29046, 20400, 12936, 114377, -42208, 38036, -13640, 11574, 37672, -120584, -23952, 13495, 13532, 53622, 17816, 164197, 1490, 141862, -1720, -87358, 25012, -2850, 58084, -54147, 39448, -32462, -2400, 28317, 55240, 12997, 2936, 63310, 15164, -78180, -21640, -42498, 13460, -149040, -25464, 1500, -62178, 15610, 17136, -52235, -95288, 48927, -3680, 52105, -27356, 11046, -30880, 14675, -148908, -61091, -40808, -23256, 6140, 100858, 10944, -23356, -16446, -122030, -44592, 10100, -33520, 34463, 14680, -114342, 6060, 226702, -7660, 3710, 40672, -84255, -18656, -13390, -7850, -44792, 25336, 181641, -70428, 96390, -3696, -48618, 7974, 92536, -220, 30741, -332, 24964, -4704, 32755, -38172, 150706, 39504, 15924, 44420, -83849, 1720, -75928, 9316, -1250, 41584, 76384, 57010, -115732, -3520, -77902, 25708, 127543, 53864, -8160, -12882, 4685, 5944, 52547, 31220, 65307, -139600, 38045, -50782, 48515, 1280, 193274, 91696, 83540, 6200, -22464, -141254, -10588, 65784, 24845, -43964, -61660, -46492, -82067, 46940, 76904, -25632, -117174, -23276, -2910, -8872, -141042, -105030, 97632, -12800, 116519, 12854, -18408, 17836, -25250, 32654, -29887, -1824, 66797, -14870, -127887, -21092, 96944, -88592, -32465, -12864, 21965, -65086, 189710, -23260, 95275, 90688, -142580, -6208, -162670, -196168, -116752, -41756, -93183, -8100, -172595, -456, 156979, 48138, -32280, 57336, -49913, 26732, -93849, -4800, 9035, 69412, 91996, 37924, 43130, -80252, -87950, 10496, 9060, -16170, -120083, 35424, 20051, -80298, 1800, -7744, -35061, 332428, -44853, -19560, -127565, -46906, -67232, -1520, 36905, 25180, 16456, 51000, -347828, 38550, -65186, 26112, -77335, 70594, 80045, -16472, 78371, 59850, 236569, -12000], "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, "nf_label": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [2, -1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0], [5, 0, 0, 0, 5, 0, -5, -5, 0, 0, 0, 0], [0, 2, -2, -2, 4, 0, 0, -4, 0, 0, 0, 0], [0, -2, 0, 1, 0, 0, 1, 4, 1, 0, 0, -1], [0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0], [11, -1, -1, -3, 10, -1, 0, -11, 1, -1, -2, 1], [-10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [8, -1, -4, -1, 10, -4, -3, -9, -2, 2, 2, -1], [0, 0, 0, 0, 0, -4, -8, -8, 0, 0, 0, 0], [-20, 0, -3, -1, -17, 0, 0, 18, 0, -2, 0, -2], [2, 0, 0, -2, 2, 2, 10, 0, 0, 2, -2, 0], [0, 0, -5, 0, 10, -5, -10, -10, 0, 0, 0, 0], [-16, 0, 0, 0, -16, 0, 16, 16, 0, 0, 0, 0], [-23, -8, -2, 2, -29, -6, 23, 32, -3, 2, 1, -4], [0, 6, -4, -4, 20, -4, -22, -18, -2, 0, 0, 2], [-31, 1, -5, 12, -26, -2, 22, 5, -10, 4, 6, -5], [0, 0, 0, 0, -20, 0, 0, 0, 0, 0, 0, 0], [-7, -9, 2, 0, 4, 16, 54, 47, 3, 3, -4, -4], [-6, 8, -8, 0, 10, -6, -14, -16, 4, -2, 0, 0], [-4, 9, -13, 0, 4, 12, -29, -33, 0, 0, -4, -4], [-16, 0, 0, 8, -16, 0, 0, 16, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, -25, 0, 0, 0, 0, 0], [0, 6, -6, -2, -36, 2, 40, 38, -4, 8, 4, -4], [43, -18, 11, 1, 80, -17, -43, -80, 0, -5, -10, 10], [20, -4, 4, -4, 16, -8, -20, -20, 4, -4, -4, 8], [0, -13, -10, 18, 38, -8, -41, 59, -5, 2, 1, 3], [-20, 10, 0, 0, -20, 0, 0, 0, 0, 0, 0, 0], [118, 2, 5, -7, 77, 2, 0, -118, -2, 2, 4, -2], [32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -5, 6, -2, 123, -15, -157, -122, 2, -7, 2, 4], [46, 14, -16, 0, -2, 0, 20, 18, 4, 4, 2, 2], [5, -5, 0, -5, 25, -5, 0, -5, 5, -5, -10, 5], [-44, 4, 0, 8, -44, -8, 0, 0, 0, -4, 4, 0], [0, 21, 8, -33, -82, 2, 88, 109, 12, -6, -3, -6], [44, 10, 2, 6, -14, 16, -44, 6, 8, 2, 12, -4], [-89, 17, 16, 26, -55, 43, 89, 63, -8, 5, 2, -10], [0, 0, 0, 0, 0, 0, 0, 40, 0, 0, 0, 0], [44, -25, 4, -1, 40, -7, 131, -4, 8, -12, 4, 4], [108, -6, 2, -38, 80, -6, 0, -100, 6, 2, -12, 14], [27, -44, 54, 0, -11, 26, 8, 18, 1, 1, 11, 11], [-28, -4, 20, 12, -36, 4, 4, 8, -4, 4, -4, -4], [0, 15, -10, 0, 0, -10, -55, -50, -5, -5, 0, 0], [-58, 0, 26, -24, -74, 0, 0, 66, 0, 8, 0, 8], [-125, -5, 5, -17, -130, 7, 127, -5, 10, -11, 1, 5], [0, 0, 16, 0, -32, 16, 32, 32, 0, 0, 0, 0], [-17, 14, 40, 42, -195, 56, 17, 198, -3, 1, -1, -2], [-50, 0, 0, 0, -50, 0, 50, 50, 0, 0, 0, 0], [0, -6, 54, 1, 88, 50, -87, 57, 5, -4, -2, -1], [80, -16, 8, 4, 72, -20, -4, -8, 16, -8, -8, 8], [10, 7, -2, -26, -83, 7, 0, -18, -7, -1, 14, -15], [-86, 44, -24, 0, -10, 12, -94, -74, -10, -10, 10, 10], [-5, -15, 0, 30, -10, -20, -40, -25, 0, 10, 5, 0], [-40, 16, -8, 0, 0, 0, -8, 0, -8, -8, 0, 0], [-247, 20, 57, 44, -280, 20, 0, 237, -20, 10, 40, -30], [-82, 58, 2, -36, -84, 32, 184, -2, 4, -10, 6, 2], [0, 19, -61, 5, -95, -49, 83, 196, -24, 12, 6, 12], [0, -20, 20, 20, -40, 0, 0, 40, 0, 0, 0, 0], [218, 11, 30, -24, 51, -13, -218, -90, 39, -27, -15, 54], [0, -18, -18, 14, 240, -18, -236, -158, 4, 0, 0, -4], [310, -36, 11, -77, 299, 55, 378, -11, 22, -1, -21, 11], [0, 0, 0, 0, 64, 0, 0, 0, 0, 0, 0, 0], [-5, 5, -15, 0, 10, -5, 100, 90, 0, 0, -10, -10], [-314, 16, -28, 24, -296, 10, 66, 56, -14, 6, 10, -18], [120, 42, -28, 0, -21, 12, -192, -178, 7, 7, 21, 21], [40, -8, 40, -8, 128, -8, 0, -44, 8, -12, -16, 4], [-253, 25, -13, 6, -240, 20, 474, 13, -26, 37, -11, -13], [0, 20, 0, -10, 0, 0, -10, -40, -10, 0, 0, 10], [472, -51, 35, 51, 364, 0, -472, -359, -5, 8, 11, -16], [0, 0, 8, 24, -72, 24, 0, 80, -8, 8, 8, -16], [0, 30, -58, -43, -51, -66, 56, 126, 13, -8, -4, -5], [176, -82, -6, 66, 182, -54, 78, 6, -12, 24, -12, -6], [-50, 0, 0, 25, -50, 0, 0, 50, 0, 0, 0, 0], [-88, -52, 28, 0, 20, 8, 124, 100, 4, 4, -20, -20], [192, -57, -44, -40, 313, -78, -426, -238, 26, -13, -51, 23], [178, -80, 76, 0, -6, 42, -48, -52, 10, 10, 6, 6], [-63, -16, -19, 107, -126, -16, 0, 86, 16, 7, -32, 39], [0, 0, 0, 0, 0, 0, 80, 0, 0, 0, 0, 0], [0, 40, -64, -70, 223, -118, -247, -112, 30, -54, -27, 24], [262, 58, -68, -36, 382, 22, -262, -358, -24, 16, 8, -32], [-177, 8, -48, 30, -102, 38, 177, 131, -29, 39, 49, -78], [0, 20, -48, -24, 188, -80, -216, -164, 4, -32, -16, 28], [50, -45, -5, 45, 55, -35, 115, 5, -10, 15, -5, -5], [16, -2, -106, -54, 90, -2, 0, -38, 2, -24, -4, -20], [-577, 49, -36, 0, 5, 12, 361, 374, -18, -18, -5, -5], [8, -40, 24, 32, -64, 16, 8, 80, 8, 0, 0, 16], [-45, 37, -60, 0, 28, -49, -478, -501, -5, -5, -28, -28], [-110, 10, 10, 30, -100, 10, 0, 110, -10, 10, 20, -10], [-670, 134, -11, -28, -659, 50, 339, 11, -22, 3, 19, -11], [0, -52, -32, 36, -132, -64, 116, 132, 16, -32, -16, 16], [541, -61, -52, -58, 549, -119, -541, -565, 16, -3, 10, 6], [254, 12, -48, -24, 28, -12, -254, -6, -22, 12, 2, -24], [0, -40, -15, 60, -125, 35, 155, 35, -20, 50, 25, -30], [64, -32, 0, 0, 64, 0, 0, 0, 0, 0, 0, 0], [186, -3, 21, -6, -64, -3, 0, -156, 3, 27, -6, 33], [34, -108, 110, 0, -4, 82, 360, 362, 2, 2, 4, 4], [-289, 50, -35, 69, -108, -63, -448, 21, -56, -7, 19, -6], [100, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]}