# Stored data for newform 1764.4.k.j, downloaded from the LMFDB on 25 April 2024.
{"label": "1764.4.k.j", "space_label": "1764.4.k", "level": 1764, "weight": 4, "hecke_orbit": 10, "hecke_orbit_code": 40533083908212452, "dim": 2, "is_polredabs": true, "nf_label": "2.0.3.1", "trace_hash": 1681468570803992406, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[5, [16, -4, 1]], [11, [400, 20, 1]], [13, [4, 1]]], "qexp_display": "q+4\\zeta_{6}q^{5}+(-20+20\\zeta_{6})q^{11}-4q^{13}+\\cdots", "char_order": 3, "char_parity": 1, "char_degree": 2, "char_conductor": 7, "char_orbit_label": "k", "char_is_real": false, "Nk2": 28224, "analytic_conductor": 104.07936925012645, "hecke_ring_index": 1, "level_radical": 42, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 6, "field_poly_is_real_cyclotomic": false, "hecke_ring_index_proved": true, "self_twist_type": 0, "is_self_dual": false, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.003", "prec": 17}, "analytic_rank_proved": true, "char_values": [1764, 3, [883, 785, 1081], [3, 3, 2]], "hecke_ring_generator_nbound": 25, "inner_twist_count": 2, "level_primes": [2, 3, 7], "conrey_indexes": [361, 1549], "field_disc": -3, "field_disc_factorization": [[-1, 1], [3, 1]], "field_poly": [1, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.006", "prec": 17}, {"__RealLiteral__": 0, "data": "1.942", "prec": 17}, {"__RealLiteral__": 0, "data": "0.150", "prec": 17}, {"__RealLiteral__": 0, "data": "11.295", "prec": 20}, {"__RealLiteral__": 0, "data": "2.005", "prec": 17}, {"__RealLiteral__": 0, "data": "102.567", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "3.2.3.c3", "trace_display": [0, 0, 4, 0], "traces": [0, 2, 0, 0, 0, 4, 0, 0, 0, 0, 0, -20, 0, -8, 0, 0, 0, 24, 0, -44, 0, 0, 0, 72, 0, 109, 0, 0, 0, 76, 0, -184, 0, 0, 0, 0, 0, 30, 0, 0, 0, 432, 0, -328, 0, 0, 0, 520, 0, 0, 0, 0, 0, -146, 0, -160, 0, 0, 0, 460, 0, -628, 0, 0, 0, -16, 0, -556, 0, 0, 0, -1184, 0, -1024, 0, 0, 0, 0, 0, 104, 0, 0, 0, 648, 0, 192, 0, 0, 0, 896, 0, 0, 0, 0, 0, 176, 0, -1840, 0, 0, 0, 1108, 0, -1448, 0, 0, 0, 1316, 0, 86, 0, 0, 0, -3556, 0, -288, 0, 0, 0, 0, 0, 931, 0, 0, 0, 1872, 0, -1856, 0, 0, 0, 1404, 0, 0, 0, 0, 0, -1370, 0, 1032, 0, 0, 0, 80, 0, 152, 0, 0, 0, 1390, 0, -136, 0, 0, 0, -1472, 0, 148, 0, 0, 0, 0, 0, 1212, 0, 0, 0, -3952, 0, -4362, 0, 0, 0, -2692, 0, 0, 0, 0, 0, -2580, 0, -4072, 0, 0, 0, -120, 0, 480, 0, 0, 0, 3960, 0, -2, 0, 0, 0, -7548, 0, 3560, 0, 0, 0, 0, 0, 864, 0, 0, 0, 1760, 0, -5384, 0, 0, 0, -656, 0, 0, 0, 0, 0, -96, 0, 9056, 0, 0, 0, -3652, 0, 4804, 0, 0, 0, 2758, 0, -2080, 0, 0, 0, -13056, 0, 56, 0, 0, 0, 0, 0, 176, 0, 0, 0, -9800, 0, -2880, 0, 0, 0, -6784, 0, 0, 0, 0, 0, -4544, 0, -1168, 0, 0, 0, -4052, 0, 2752, 0, 0, 0, 2180, 0, -4366, 0, 0, 0, -15468, 0, 4052, 0, 0, 0, 0, 0, 4337, 0, 0, 0, 6840, 0, 3680, 0, 0, 0, -288, 0, 0, 0, 0, 0, 2512, 0, 14648, 0, 0, 0, -4192, 0, 6840, 0, 0, 0, 6630, 0, -760, 0, 0, 0, -2112, 0, -436, 0, 0, 0, 0, 0, 6868, 0, 0, 0, -4448, 0, -14756, 0, 0, 0, -3680, 0, 0, 0, 0, 0, -2676, 0, -10248, 0, 0, 0, 4560, 0, -2368, 0, 0, 0, 3656, 0, 4923, 0, 0, 0, -8192, 0, 1616, 0, 0, 0, 0, 0, -2734, 0, 0, 0, -304, 0, -2760, 0, 0, 0, 6888, 0, 0, 0, 0, 0, -2046, 0, 3456, 0, 0, 0, -416, 0, -3116, 0, 0, 0, 2958, 0, 736, 0, 0, 0, -1200, 0, -7944, 0, 0, 0, 0, 0, 1296, 0, 0, 0, -8168, 0, -12612, 0, 0, 0, -2616, 0, 0, 0, 0, 0, -11824, 0, -9008, 0, 0, 0, 3168, 0, -13056, 0, 0, 0, 132, 0, -3584, 0, 0, 0, -9732, 0, -4320, 0, 0, 0, 0, 0, -10106, 0, 0, 0, 36072, 0, 10576, 0, 0, 0, 15164, 0, 0, 0, 0, 0, 3280, 0, -9592, 0, 0, 0, 7896, 0, -120, 0, 0, 0, -3680, 0, -2920, 0, 0, 0, 15864, 0, 912, 0, 0, 0, 0, 0, 2004, 0, 0, 0, -8992, 0, 8864, 0, 0, 0, 12620, 0, 0, 0, 0, 0, 5792, 0, -20800, 0, 0, 0, 18008, 0, -13292, 0, 0, 0, 4416, 0, 6983, 0, 0, 0, -1728, 0, -5264, 0, 0, 0, 0, 0, 8570, 0, 0, 0, 688, 0, -3832, 0, 0, 0, -1672, 0, 0, 0, 0, 0, 19926, 0, 1312, 0, 0, 0, 4244, 0, -7112, 0, 0, 0, -22794, 0, -14028, 0, 0, 0, 15696, 0, -8368, 0, 0, 0, 0, 0, -2920, 0, 0, 0, -104, 0, 16192, 0, 0, 0, 5808, 0, 0, 0, 0, 0, -10464, 0, 2368, 0, 0, 0, -3724, 0, -13152, 0, 0, 0, -2080, 0, 18334, 0, 0, 0, 16244, 0, -5980, 0, 0, 0, 0, 0, -9881, 0, 0, 0, 1440, 0, 25056, 0, 0, 0, -3712, 0, 0, 0, 0, 0, 20798, 0, -3864, 0, 0, 0, -8424, 0, 9200, 0, 0, 0, -17750, 0, -5616, 0, 0, 0, 55160, 0, 9292, 0, 0, 0, 0, 0, 2736, 0, 0, 0, 25120, 0, 22972, 0, 0, 0, 7116, 0, 0, 0, 0, 0, -7612, 0, -10960, 0, 0, 0, 584, 0, 21572, 0, 0, 0, 2064, 0, 5184, 0, 0, 0, 3404, 0, 1320, 0, 0, 0, 0, 0, -6370, 0, 0, 0, -26496, 0, 640, 0, 0, 0, -8808, 0, 0, 0, 0, 0, 4142, 0, 35536, 0, 0, 0, -3936, 0, 5564, 0, 0, 0, -11120, 0, 17564, 0, 0, 0, 76560, 0, -5560, 0, 0, 0, 0, 0, -36192, 0, 0, 0, -1088, 0, -28, 0, 0, 0, -26504, 0, 0, 0, 0, 0, -1840, 0, 80368, 0, 0, 0, -35340, 0, 20056, 0, 0, 0, -9504, 0, 11840, 0, 0, 0, 1184, 0, 14852, 0, 0, 0, 0, 0, 2512, 0, 0, 0, -39576, 0, 24960, 0, 0, 0, -20480, 0, 0, 0, 0, 0, 16986, 0, -53192, 0, 0, 0, -4848, 0, 7216, 0, 0, 0, -34898, 0, -12928, 0, 0, 0, 86328, 0, 41228, 0, 0, 0, 0, 0, -7904, 0, 0, 0, 2736, 0, -45890, 0, 0, 0, -8724, 0, 0, 0, 0, 0, -2160, 0, 10552, 0, 0, 0, 840, 0, 26028, 0, 0, 0, -29448, 0, 10768, 0, 0, 0, -4160, 0, 2224, 0, 0, 0, 0, 0, -25866, 0, 0, 0, -18944, 0, 98744, 0, 0, 0, -11160, 0, 0, 0, 0, 0, 22880, 0, -20640, 0, 0, 0, -6992, 0, 3504, 0, 0, 0, -8144, 0, -22708, 0, 0, 0, 32384, 0, -6480, 0, 0, 0, 0, 0, 46320, 0, 0, 0, 4736, 0, 6540, 0, 0, 0, -2280, 0, 0, 0, 0, 0, -1920, 0, 98112, 0, 0, 0, -24876, 0, 15552, 0, 0, 0, 23428, 0, 4096, 0, 0, 0, 13356, 0, -15840, 0, 0, 0, 0, 0, -4065, 0, 0, 0, -16, 0, 31088, 0, 0, 0, -31124, 0, 0, 0, 0, 0, 50062, 0, -35840, 0, 0, 0, 328, 0, -15096, 0, 0, 0, -11808, 0, 20872, 0, 0, 0, 28480, 0, 46924, 0, 0, 0, 0, 0, -11040, 0, 0, 0, 12848, 0, 27044, 0, 0, 0, 33612, 0, 0, 0, 0, 0, -22812, 0, -75528, 0, 0, 0, 23544, 0, -416, 0, 0, 0, -19680, 0, 1242, 0, 0, 0, -30144, 0, 4424, 0, 0, 0, 0, 0, 3520, 0, 0, 0, -95392, 0, 26440, 0, 0, 0, -10768, 0, 0, 0, 0, 0, 27618, 0, -8480, 0, 0, 0, 18400, 0, -53380, 0, 0, 0, 1140, 0, -17876, 0, 0, 0, -2592, 0, -37440, 0, 0, 0, 0, 0, -16944, 0, 0, 0, 69560, 0, -65340, 0, 0, 0, 48144, 0, 0, 0, 0, 0, -47888, 0, -768, 0, 0, 0, -17524, 0, 22160, 0, 0, 0, 18112, 0, 45754, 0, 0, 0, -40480, 0, -9516, 0, 0, 0, 0, 0, -42118, 0, 0, 0, 57920, 0, -29216, 0, 0, 0, 13344, 0, 0, 0, 0, 0, -19216, 0, -11040, 0, 0, 0, 71336, 0, -20720, 0, 0, 0, -3584, 0, -27632, 0, 0, 0, 45272, 0, -11032, 0, 0, 0, 0, 0, 56212, 0, 0, 0, 113360, 0, -52640, 0, 0, 0, 37212, 0, 0, 0, 0, 0, -37684, 0, 16416, 0, 0, 0, 46864, 0, -26112, 0, 0, 0, 1720, 0, -47182, 0, 0, 0, 448, 0, -14208, 0, 0, 0, 0, 0, -7066, 0, 0, 0, -161984, 0, -21024, 0, 0, 0, -768, 0, 0, 0, 0, 0, 44950, 0, -117872, 0, 0, 0, -704, 0, -65444, 0, 0, 0, 24576, 0, 35560, 0, 0, 0, -12464, 0, -67040, 0, 0, 0, 0, 0, -19600, 0, 0, 0, 26856, 0, 7360, 0, 0, 0, -5760, 0, 0, 0, 0, 0, -39744, 0, 48928, 0, 0, 0, -55932, 0, -46120, 0, 0, 0, 65508, 0, 27136, 0, 0, 0, -77236, 0, -53300, 0, 0, 0, 0, 0, 65586, 0, 0, 0, 181464, 0, -83632, 0, 0, 0, 84876, 0, 0, 0, 0, 0, -4432, 0, -36352, 0, 0, 0, -13376, 0, 39112, 0, 0, 0, 15914, 0, -71320, 0, 0, 0, -90480, 0, 30176, 0, 0, 0, 0, 0, 5792, 0, 0, 0, 4992, 0, -32416, 0, 0, 0, 26048, 0, 0, 0, 0, 0, -11008, 0, 66240, 0, 0, 0, 58200, 0, 19760, 0, 0, 0, 6336, 0, 49753, 0, 0, 0, -202292, 0, -18720, 0, 0, 0, 0, 0, -43330, 0, 0, 0, -34928, 0, 90112, 0, 0, 0, -5264, 0, 0, 0, 0, 0, 18560, 0, 28800, 0, 0, 0, 45216, 0, -30936, 0, 0, 0, -7614, 0, 7776, 0, 0, 0, 32416, 0, -344, 0, 0, 0, 0, 0, 99712, 0, 0, 0, -69912, 0, -45980, 0, 0, 0, -23552, 0, 0, 0, 0, 0, -47056, 0, -56160, 0, 0, 0, -17348, 0, 13680, 0, 0, 0, 71292, 0, -90378, 0, 0, 0, -191360, 0, 33884, 0, 0, 0, 0, 0, 13680, 0, 0, 0, 14224, 0, -51472, 0, 0, 0, -50140, 0, 0, 0, 0, 0, 17050, 0, 74424, 0, 0, 0, -25184, 0, 9416, 0, 0, 0, 52718, 0, 1152, 0, 0, 0, -75496, 0, 4576, 0, 0, 0, 0, 0, -27400, 0, 0, 0, 38560, 0, 43008, 0, 0, 0, 6480, 0, 0, 0, 0, 0, -4348, 0, -136904, 0, 0, 0, -10320, 0, 88436, 0, 0, 0, 29296, 0, -5548, 0, 0, 0, -80064, 0, 27856, 0, 0, 0, 0, 0, 89482, 0, 0, 0, -118464, 0, -33536, 0, 0, 0, -2472, 0, 0, 0, 0, 0, -27360, 0, 96128, 0, 0, 0, -53748, 0, -3724, 0, 0, 0, -14256, 0, -53740, 0, 0, 0, -11920, 0, -26520, 0, 0, 0, 0, 0, -4920, 0, 0, 0, -6080, 0, -184692, 0, 0, 0, -110768, 0, 0, 0, 0, 0, -54192, 0, 151040, 0, 0, 0, -81612, 0, -4224, 0, 0, 0, 98044, 0, 89038, 0, 0, 0, -7488, 0, 71756, 0, 0, 0, 0, 0, -42624, 0, 0, 0, 9240, 0, -55600, 0, 0, 0, -26864, 0, 0, 0, 0, 0, -22080, 0, 7424, 0, 0, 0, -27472, 0, 32536, 0, 0, 0, -2720, 0, -89504, 0, 0, 0, -106312, 0, 120556, 0, 0, 0, 0, 0, 60604, 0, 0, 0, -147456, 0, -44530, 0, 0, 0, -29512, 0, 0, 0, 0, 0, 39424, 0, -125880, 0, 0, 0, 36168, 0, -6740, 0, 0, 0, -5616, 0, 14720, 0, 0, 0, -30444, 0, 17480, 0, 0, 0, 0, 0, -26592, 0, 0, 0, 102720, 0, -142424, 0, 0, 0, 2960, 0, 0, 0, 0, 0, -101566, 0, -21408, 0, 0, 0, -15600, 0, 142500, 0, 0, 0, -20496, 0, 96428, 0, 0, 0, -69504, 0, -368, 0, 0, 0, 0, 0, -143584, 0, 0, 0, -70848, 0, 36480, 0, 0, 0, -23864, 0, 0, 0, 0, 0, -64528, 0, 218560, 0, 0, 0, 5480, 0, 5392, 0, 0, 0, 51580, 0, -52678, 0, 0, 0, -48480, 0, -14624, 0, 0, 0, 0, 0, 117350, 0, 0, 0, 39384, 0, -4128, 0, 0, 0, -108372, 0, 0, 0, 0, 0, -7488, 0, 63168, 0, 0, 0, -53488, 0, 111616, 0, 0, 0, 84640, 0, -30080, 0, 0, 0, 12928, 0, 39520, 0, 0, 0, 0, 0, 40480, 0, 0, 0, -307792, 0, -105222, 0, 0, 0, -2064, 0, 0, 0, 0, 0, 43620, 0, -309176, 0, 0, 0, 10936, 0, -153244, 0, 0, 0, -44784, 0, 69838, 0, 0, 0, 4836, 0, 79640, 0, 0, 0, 0, 0, -608, 0, 0, 0, 64416, 0, 231104, 0, 0, 0, -5520, 0, 0, 0, 0, 0, 81558, 0, 107680, 0, 0, 0, -74708, 0, 23328, 0, 0, 0, 85014, 0, -27552, 0, 0, 0, -97504, 0, -42672, 0, 0, 0, 0, 0, 112320, 0, 0, 0, 156136, 0, 87660, 0, 0, 0, -5560, 0, 0, 0, 0, 0, -21128, 0, -16368, 0, 0, 0, 43820, 0, -9664, 0, 0, 0, 6912, 0, -63712, 0, 0, 0, -8760, 0, 544, 0, 0, 0, 0, 0, -51600, 0, 0, 0, 39016, 0, 22672, 0, 0, 0, 163572, 0, 0, 0, 0, 0, 12464, 0, 164936, 0, 0, 0, 40720, 0, 4952, 0, 0, 0, -83574, 0, 60056, 0], "weight_parity": 1, "has_non_self_twist": 1, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": true, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 7, 3, 1, 3, 0]], "char_orbit_index": 11, "prim_orbit_index": 3, "minimal_twist": "588.4.a.b", "char_is_minimal": false, "conrey_index": 361, "id": null, "fricke_eigenval": null, "atkin_lehner_string": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "atkin_lehner_eigenvals": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0, 0], [1, 0], [0, 0], [0, 0], [0, 0], [0, 4], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [-20, 20], [0, 0], [-4, 0], [0, 0], [0, 0], [0, 0], [24, -24], [0, 0], [0, -44], [0, 0], [0, 0], [0, 0], [0, 72], [0, 0], [109, -109], [0, 0], [0, 0], [0, 0], [38, 0], [0, 0], [-184, 184], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 30], [0, 0], [0, 0], [0, 0], [216, 0], [0, 0], [-164, 0], [0, 0], [0, 0], [0, 0], [0, 520], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [-146, 146], [0, 0], [-80, 0], [0, 0], [0, 0], [0, 0], [460, -460], [0, 0], [0, -628], [0, 0], [0, 0], [0, 0], [0, -16], [0, 0], [-556, 556], [0, 0], [0, 0], [0, 0], [-592, 0], [0, 0], [-1024, 1024], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 104], [0, 0], [0, 0], [0, 0], [324, 0], [0, 0], [96, 0], [0, 0], [0, 0], [0, 0], [0, 896], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [176, -176], [0, 0], [-920, 0], [0, 0], [0, 0], [0, 0]]}