# Stored data for newform 441.7.d.c, downloaded from the LMFDB on 20 April 2024.
{"label": "441.7.d.c", "space_label": "441.7.d", "level": 441, "weight": 7, "hecke_orbit": 3, "hecke_orbit_code": 9007405530612153, "dim": 8, "is_polredabs": true, "trace_hash": 1185041367203439251, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[2, [4512, -284, -202, 5, 1]]], "qexp_display": "q+(-1+\\beta _{3})q^{2}+(42-4\\beta _{3}-\\beta _{4})q^{4}+\\cdots", "char_order": 2, "char_parity": -1, "char_degree": 1, "char_conductor": 7, "char_orbit_label": "d", "char_is_real": true, "Nk2": 21609, "analytic_conductor": 101.4538508763543, "hecke_ring_index": 9408, "level_radical": 21, "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": false, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.506", "prec": 17}, "analytic_rank_proved": true, "char_values": [441, 2, [344, 199], [2, 1]], "hecke_ring_generator_nbound": 13, "inner_twist_count": 2, "level_primes": [3, 7], "conrey_indexes": [244], "field_disc": 209173825936033529481, "field_disc_factorization": [[3, 4], [3359, 2], [478411, 2]], "field_poly": [21068100, -601290, 985651, 36821, 39800, 473, 212, -1, 1], "hecke_ring_index_factorization": [[2, 6], [3, 1], [7, 2]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "6.906", "prec": 17}, {"__RealLiteral__": 0, "data": "1.126", "prec": 17}, {"__RealLiteral__": 0, "data": "265.182", "prec": 24}, {"__RealLiteral__": 0, "data": "353.985", "prec": 24}, {"__RealLiteral__": 0, "data": "15163.368", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 8, "sato_tate_group": "6.2.3.c2", "trace_display": [-10, 0, 0, 0], "traces": [0, 8, -10, 0, 346, 0, 0, 0, -3326, 0, 0, -628, 0, 0, 0, 0, 25442, 0, 0, 0, 0, 0, 86106, 7856, 0, 34076, 0, 0, 0, 8300, 0, 0, -372414, 0, 0, 0, 0, -129412, 0, 0, 0, 0, 0, 45740, 185058, 0, 223008, 0, 0, 0, -967216, 0, 0, -1081948, 0, 0, 0, 0, -1079598, 0, 0, 0, 0, 0, 2378626, -828408, 0, 2317804, 0, 0, 0, -1442344, 0, 0, -865880, 0, 0, 0, 0, -1222904, 0, 0, 0, 0, 0, -275112, 1632448, 0, 732882, 0, 0, 0, -678720, 0, 0, -1183584, 0, 0, 0, 0, 637492, 0, 0, 0, 0, 0, -4341090, -8128420, 0, -1728652, 0, 0, 0, 6139040, 0, 0, 12865506, 0, 0, 0, 0, 1010092, 0, 0, 0, 0, 0, -3423056, -21475198, 0, -19193592, 0, 0, 0, 2748148, 0, 0, 2015360, 0, 0, 0, 0, -17597568, 0, 0, 0, 0, 0, -10093652, -20758888, 0, 1305740, 0, 0, 0, -138492, 0, 0, -5200202, 0, 0, 0, 0, 9688648, 0, 0, 0, 0, 0, -22491652, -17566068, 0, -27921212, 0, 0, 0, -32608238, 0, 0, -11897296, 0, 0, 0, 0, -24946560, 0, 0, 0, 0, 0, 23622444, -41430232, 0, 22456736, 0, 0, 0, -8590456, 0, 0, -56503748, 0, 0, 0, 0, -24846216, 0, 0, 0, 0, 0, 4853576, -46973682, 0, 12996726, 0, 0, 0, -63179660, 0, 0, -54734832, 0, 0, 0, 0, -151211436, 0, 0, 0, 0, 0, -29321118, -27438496, 0, 80755728, 0, 0, 0, 4149608, 0, 0, 70774716, 0, 0, 0, 0, 82175076, 0, 0, 0, 0, 0, 30845040, 96538546, 0, 94709378, 0, 0, 0, -56336256, 0, 0, -104178040, 0, 0, 0, 0, 8332592, 0, 0, 0, 0, 0, 164071056, -143098624, 0, -62937668, 0, 0, 0, -76419952, 0, 0, 161900616, 0, 0, 0, 0, 100983896, 0, 0, 0, 0, 0, -99372660, 113144948, 0, -193815996, 0, 0, 0, 218758486, 0, 0, -53306064, 0, 0, 0, 0, 19813542, 0, 0, 0, 0, 0, -94076014, 40293044, 0, -37440228, 0, 0, 0, 132079584, 0, 0, 229327672, 0, 0, 0, 0, 38424980, 0, 0, 0, 0, 0, -169824928, 127932410, 0, -100606644, 0, 0, 0, 320611724, 0, 0, -57970072, 0, 0, 0, 0, 87070290, 0, 0, 0, 0, 0, -42302556, -72380272, 0, -67434004, 0, 0, 0, -138455448, 0, 0, 40314496, 0, 0, 0, 0, -43715516, 0, 0, 0, 0, 0, -152599204, 143153892, 0, -16603656, 0, 0, 0, 34302322, 0, 0, 311442272, 0, 0, 0, 0, 376253916, 0, 0, 0, 0, 0, 640855580, 261023312, 0, 56287788, 0, 0, 0, -207289472, 0, 0, -451703364, 0, 0, 0, 0, 69448092, 0, 0, 0, 0, 0, 92061868, 450954712, 0, 570620430, 0, 0, 0, 1599222, 0, 0, 47243216, 0, 0, 0, 0, 269082568, 0, 0, 0, 0, 0, 17255088, 751663556, 0, 21623112, 0, 0, 0, -74410600, 0, 0, 358717788, 0, 0, 0, 0, -165307192, 0, 0, 0, 0, 0, 170869828, 661456738, 0, 713674476, 0, 0, 0, 645938352, 0, 0, -118970672, 0, 0, 0, 0, 201675792, 0, 0, 0, 0, 0, -73572712, 36056964, 0, -215856232, 0, 0, 0, -157727068, 0, 0, -746988156, 0, 0, 0, 0, -480112372, 0, 0, 0, 0, 0, 604488336, -222129472, 0, 406579694, 0, 0, 0, -368996990, 0, 0, -87222120, 0, 0, 0, 0, -94618896, 0, 0, 0, 0, 0, 492344652, 316906008, 0, -569862152, 0, 0, 0, -1525687752, 0, 0, 286107560, 0, 0, 0, 0, -434780972, 0, 0, 0, 0, 0, -546704048, -1334395104, 0, -491906316, 0, 0, 0, 942117604, 0, 0, 28109012, 0, 0, 0, 0, 967584792, 0, 0, 0, 0, 0, -1649640744, -717956944, 0, -357062372, 0, 0, 0, 147597152, 0, 0, -9673378, 0, 0, 0, 0, -826666284, 0, 0, 0, 0, 0, -58095324, -1171068750, 0, -387396268, 0, 0, 0, 1413321780, 0, 0, 248513552, 0, 0, 0, 0, 594406126, 0, 0, 0, 0, 0, -1257041976, 792919560, 0, -961439432, 0, 0, 0, -916953208, 0, 0, 327427326, 0, 0, 0, 0, 416976488, 0, 0, 0, 0, 0, -1608331076, -882307414, 0, -72435450, 0, 0, 0, 1182743522, 0, 0, 595162160, 0, 0, 0, 0, -423493848, 0, 0, 0, 0, 0, 1194125936, -2387693980, 0, 712549740, 0, 0, 0, -25069048, 0, 0, 1971672580, 0, 0, 0, 0, -1522729296, 0, 0, 0, 0, 0, 957642440, -2156865110, 0, -2697947774, 0, 0, 0, 339335436, 0, 0, -586056076, 0, 0, 0, 0, -2453176468, 0, 0, 0, 0, 0, 3438082668, -299736480, 0, -948794544, 0, 0, 0, -3017475868, 0, 0, -3519055150, 0, 0, 0, 0, 2013884624, 0, 0, 0, 0, 0, -3150558048, 1175804988, 0, 4074569304, 0, 0, 0, 357240962, 0, 0, -367612840, 0, 0, 0, 0, -242770752, 0, 0, 0, 0, 0, 1618044288, -518312696, 0, 2267579668, 0, 0, 0, -2086387720, 0, 0, 1820110048, 0, 0, 0, 0, -1897664368, 0, 0, 0, 0, 0, 1524708536, 477981592, 0, 608785812, 0, 0, 0, 14289312, 0, 0, -3308833200, 0, 0, 0, 0, -259429562, 0, 0, 0, 0, 0, -484580028, 1018053000, 0, -135079680, 0, 0, 0, -2960569584, 0, 0, -891139284, 0, 0, 0, 0, -676397808, 0, 0, 0, 0, 0, -796001760, -2196082308, 0, 1494410232, 0, 0, 0, 1608725676, 0, 0, 307121960, 0, 0, 0, 0, -1662016788, 0, 0, 0, 0, 0, -677499732, -4013130868, 0, -485585456, 0, 0, 0, 2307303908, 0, 0, -41937222, 0, 0, 0, 0, 608551392, 0, 0, 0, 0, 0, 663453100, 5706863500, 0, 3122349760, 0, 0, 0, -2019767282, 0, 0, -1360122080, 0, 0, 0, 0, -376524522, 0, 0, 0, 0, 0, 5184044100, 1722275168, 0, -2404701408, 0, 0, 0, -997481948, 0, 0, -343804048, 0, 0, 0, 0, 5099691832, 0, 0, 0, 0, 0, -4211894644, -422862336, 0, -5094493950, 0, 0, 0, 154646868, 0, 0, 1931002728, 0, 0, 0, 0, -1465115376, 0, 0, 0, 0, 0, -6148368852, -3775416624, 0, 2135417204, 0, 0, 0, 3769318784, 0, 0, 1353420526, 0, 0, 0, 0, 365006492, 0, 0, 0, 0, 0, 745260692, 4326803464, 0, -11542905246, 0, 0, 0, -604461036, 0, 0, -3666635112, 0, 0, 0, 0, 2362998816, 0, 0, 0, 0, 0, 672159108, 290160224, 0, 4692864420, 0, 0, 0, -955215976, 0, 0, 8614400760, 0, 0, 0, 0, 4829832608, 0, 0, 0, 0, 0, -6087588872, 8381013840, 0, -156420474, 0, 0, 0, 10656371530, 0, 0, -740078992, 0, 0, 0, 0, -2286757830, 0, 0, 0, 0, 0, 8407259640, -1342806944, 0, 380864024, 0, 0, 0, 3784383840, 0, 0, 9973682776, 0, 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, 2, -1, 2, 0]], "char_orbit_index": 4, "prim_orbit_index": 2, "minimal_twist": "21.7.f.a", "char_is_minimal": true, "conrey_index": 244, "id": null, "nf_label": 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, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [42, 0, 0, -4, -1, 0, 0, 0], [0, 25, -3, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-404, 0, 0, 50, 5, 0, 0, -4], [0, 0, 0, 0, 0, 0, 0, 0], [0, 290, -32, 0, 0, 9, 5, 0], [-55, 0, 0, 103, -11, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 264, 3, 0, 0, 19, 20, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [3020, 0, 0, -646, -35, 0, 0, 20], [0, -442, -82, 0, 0, 6, 24, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -1550, 85, 0, 0, 37, -44, 0], [0, 1440, -366, 0, 0, 27, 15, 0], [0, 0, 0, 0, 0, 0, 0, 0], [10798, 0, 0, 308, -81, 0, 0, -44], [1088, 0, 0, 280, 16, 0, 0, 64], [0, 0, 0, 0, 0, 0, 0, 0], [4030, 0, 0, -1107, 103, 0, 0, 43], [0, -699, -1457, 0, 0, 131, -105, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [605, 0, 0, -1247, -193, 0, 0, -145], [0, 0, 0, 0, 0, 0, 0, 0], [0, 7331, 530, 0, 0, -18, -44, 0], [-45324, 0, 0, 4098, 581, 0, 0, 116], [0, 0, 0, 0, 0, 0, 0, 0], [0, 8908, -464, 0, 0, 142, -74, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-16510, 0, 0, -1255, 147, 0, 0, -113], [0, -7111, 2639, 0, 0, 93, 297, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 18340, 614, 0, 0, -33, -5, 0], [0, 7782, 1052, 0, 0, 652, 432, 0], [0, 0, 0, 0, 0, 0, 0, 0], [6182, 0, 0, 1901, 399, 0, 0, -221], [24840, 0, 0, 7614, -7, 0, 0, -388], [0, 0, 0, 0, 0, 0, 0, 0], [28024, 0, 0, 56, 408, 0, 0, 64], [0, -39992, -82, 0, 0, -1042, 96, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-119905, 0, 0, 1687, 1477, 0, 0, 412], [0, 0, 0, 0, 0, 0, 0, 0], [0, 137418, 7402, 0, 0, 922, 1174, 0], [-137125, 0, 0, -6857, 353, 0, 0, -511], [0, 0, 0, 0, 0, 0, 0, 0], [0, 43985, -7433, 0, 0, 1251, 920, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-131828, 0, 0, 14186, -155, 0, 0, -772], [0, -15871, 571, 0, 0, 2323, 756, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 38980, -15208, 0, 0, -1304, 720, 0], [0, -62717, -6697, 0, 0, -682, -258, 0], [0, 0, 0, 0, 0, 0, 0, 0], [285124, 0, 0, -49742, -1163, 0, 0, 1044], [-109080, 0, 0, -24294, 2086, 0, 0, 46], [0, 0, 0, 0, 0, 0, 0, 0], [291068, 0, 0, 6357, 1103, 0, 0, -1045], [0, 68544, -1284, 0, 0, 858, -270, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-186172, 0, 0, -22382, -2650, 0, 0, 758], [0, 0, 0, 0, 0, 0, 0, 0], [0, 35228, -14317, 0, 0, -373, -1924, 0], [-113705, 0, 0, -22921, -135, 0, 0, 588], [0, 0, 0, 0, 0, 0, 0, 0], [0, -172566, -20802, 0, 0, -4152, -1716, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-152983, 0, 0, -7998, 2018, 0, 0, 2750], [0, -174940, 3990, 0, 0, -2545, -1605, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -120834, -40378, 0, 0, 3292, -2772, 0], [0, 95781, 15973, 0, 0, 197, 1092, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-39210, 0, 0, -21786, 3154, 0, 0, -326], [197143, 0, 0, -26113, -4731, 0, 0, 1596], [0, 0, 0, 0, 0, 0, 0, 0], [85844, 0, 0, -21950, -6691, 0, 0, 2788], [0, 81874, 3154, 0, 0, -918, -192, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-89712, 0, 0, -13776, -784, 0, 0, -2464], [0, 0, 0, 0, 0, 0, 0, 0], [0, 48026, 52686, 0, 0, -6074, -2674, 0], [-143310, 0, 0, 27108, -5972, 0, 0, -1292], [0, 0, 0, 0, 0, 0, 0, 0], [0, -114285, -33555, 0, 0, -4027, 4, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [45510, 0, 0, -137794, -5224, 0, 0, 3156]]}