# Stored data for newform 21.5.f.b, downloaded from the LMFDB on 19 April 2024.
{"label": "21.5.f.b", "space_label": "21.5.f", "level": 21, "weight": 5, "hecke_orbit": 2, "hecke_orbit_code": 4503943308640277, "dim": 2, "is_polredabs": true, "nf_label": "2.0.3.1", "trace_hash": 1333098095116841253, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[2, [25, -5, 1]]], "qexp_display": "q+5\\zeta_{6}q^{2}+(3+3\\zeta_{6})q^{3}+(-9+9\\zeta_{6})q^{4}+\\cdots", "char_order": 6, "char_parity": -1, "char_degree": 2, "char_conductor": 7, "char_orbit_label": "f", "char_is_real": false, "Nk2": 525, "analytic_conductor": 2.170769224760731, "hecke_ring_index": 1, "level_radical": 21, "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": "0.166", "prec": 17}, "analytic_rank_proved": true, "char_values": [21, 6, [8, 10], [6, 1]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 2, "level_primes": [3, 7], "conrey_indexes": [10, 19], "field_disc": -3, "field_disc_factorization": [[-1, 1], [3, 1]], "field_poly": [1, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.977", "prec": 17}, {"__RealLiteral__": 0, "data": "0.030", "prec": 17}, {"__RealLiteral__": 0, "data": "11.716", "prec": 20}, {"__RealLiteral__": 0, "data": "0.996", "prec": 17}, {"__RealLiteral__": 0, "data": "96.501", "prec": 20}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "4.2.3.c6", "trace_display": [5, 9, -3, -91], "traces": [0, 2, 5, 9, -9, -3, 0, -91, 70, 27, -15, 149, -81, 0, -70, -18, 319, -462, -135, -618, 0, -315, 1490, 560, 315, -622, 360, 0, 693, 470, -45, -2229, -1035, 1341, 0, 168, -486, -1970, -3090, 216, -105, 0, 945, 5596, 1341, -81, -2800, 7152, 0, 3479, -6220, -1386, 648, -901, -1215, 0, -3185, -3708, 1175, 2391, 81, -6180, 0, -378, -142, 72, 6705, 4156, 4158, 0, 525, 968, 945, -1644, 9850, -5598, 0, -11473, 2160, -4325, -957, -729, -24390, 0, 4536, 924, 13990, 2115, 5215, 3426, 0, -1512, -10080, -6687, 35760, 618, -9315, 0, -5635, 8046, -5598, -7500, 6930, 25032, 0, 819, -9010, -4465, -2187, -3320, -2235, 0, -4466, -19468, -9270, -1680, -2115, 1944, 0, 16170, -630, -7560, -30900, -14634, 20061, 0, 10395, -58298, 16205, 25182, -360, 47733, 0, 34608, 41560, -243, -16170, -17824, -25200, 0, -567, 42912, 2420, -10728, -8613, -705, 0, 7056, 35460, -9214, -27990, -11975, -21630, 0, -67795, 4458, 1944, -3444, 21625, -8109, 0, -7840, -7290, 20800, -43902, -1341, 11295, 0, -11025, 53666, 2310, -16686, -25182, -4188, 0, 47894, 95062, 7173, 17130, -19378, 729, 0, -20160, -37080, 19600, 5910, 33435, -68838, 0, 5103, 6180, 28760, -639, 44089, -47205, 0, -41454, -92956, 20115, -67956, -21770, 37404, 0, -21385, 24948, -4878, 125160, -15120, 22968, 0, 630, -55376, -8109, 4356, 22325, -8394, 0, 78015, -33200, -4932, -4023, -11088, 88650, 0, 79695, -33588, -48670, 128283, 16686, 41394, 0, -75096, 16450, -96382, 9720, -7152, -21519, 0, -48510, -88552, -2871, -98637, 37800, -6561, 0, -8085, -146340, 14832, -78015, 6777, 18705, 0, 22113, 166880, -145745, 4158, -82161, 50838, 0, 27580, -1296, 6345, 238665, 89078, 46935, 0, 108150, 20556, 37404, 123387, 1215, -73329, 0, -16632, -178240, 92678, -45360, 46516, -242370, 0, 5880, 100568, 107280, -64086, -4356, 5562, 0, 102438, -55890, -12373, -3525, -28323, 14796, 0, -85995, -4782, -68950, 36207, 46070, 40320, 0, -254618, -119750, -22500, -197142, 6180, 62370, 0, -18774, 150192, 11145, 91086, 7560, -160809, 0, 2835, 77850, 61583, -40545, 35015, 213, 0, 215600, 190344, -6561, 44784, -104000, -29880, 0, -400512, -13410, 91480, 20331, 53190, 367920, 0, 60291, 19990, 134165, -87606, -4158, -332121, 0, -98098, 195860, -5040, -20940, -62458, -19035, 0, 283010, 11664, 154215, -143796, -35865, -1452, 0, 19404, -193780, -164044, -2835, -3013, 64530, 0, -22680, 3288, -92700, -7431, -178640, -131706, 0, 69377, 120366, -78626, -344190, 11223, 250320, 0, 68040, 112468, 5562, -262341, -143800, 379914, 0, 9387, 440890, 75546, -84969, 4262, -3240, 0, 121765, 286398, -232390, 12975, -36207, 253236, 0, 168714, -396836, 90812, 187020, -53496, 67500, 0, -16450, -587060, -48510, 78501, 24390, -160416, 0, -83685, -151200, 2259, 74520, -145422, -460410, 0, -6237, 8512, -138440, 193104, -31535, 287364, 0, 346080, 80370, -32184, -41970, 147662, -77517, 0, -234045, -4230, -29880, -346080, 24660, -177765, 0, -30429, -110880, 293981, 159570, -3426, 425025, 0, 6461, 42440, -83970, 726822, 87606, -107775, 0, -1008, -129780, 176467, 206970, 37422, 15120, 0, -234675, 284572, 74965, 20061, 481910, -676380, 0, -320012, -71520, -10332, 83685, 416902, 194625, 0, -232848, -48654, -221380, -262542, 9315, -141840, 0, 105840, 136080, -9441, -32805, -206027, -216300, 0, -11760, -954226, -131706, -108570, -74160, -12069, 0, -44044, 67770, -164810, 33669, 220752, -647055, 0, -13230, 15000, 417200, 241497, 262341, 817071, 0, 57540, -303050, -50058, 254190, -25032, -226638, 0, -758450, -25128, 2520, 726162, -31725, -518748, 0, 313488, 890780, 343266, 427779, -33759, 13515, 0, -116802, 234144, 51390, 13395, 145460, -174402, 0, 686294, 4374, -305090, -366645, 38718, 478170, 0, -98280, -521948, -160416, -166860, -463390, -145230, 0, 60550, 465160, 17730, -436266, -251263, 300915, 0, 33495, -413028, 251420, -358221, -193104, 29202, 0, 56133, 33880, -510862, 27810, -374600, 96552, 0, 1365840, -696640, -1917, -678831, 61865, 396801, 0, -47439, -283230, 134249, -57540, -1944, -580185, 0, -218295, 918348, -11955, -418302, 628430, 1109400, 0, -42042, 165852, -203868, 201600, -461284, -195930, 0, -195860, 224424, -107775, 22680, 112500, 681915, 0, -74025, 61800, -171648, 112266, -404900, 660420, 0, -401555, 517904, 375480, -220488, -20061, -136080, 0, -191856, 137808, -385009, -804045, -276246, 30996, 0, -8505, -422042, -151375, -249192, -307915, 87447, 0, 137592, 350150, 13068, -48615, 161168, 200925, 0, 458640, -50364, 475860, 552444, -25515, 356259, 0, 93618, -374400, 466049, -149400, -47733, -1556082, 0, -1251600, 206516, -12069, 346530, -457400, -99792, 0, -47586, 531900, 131600, 662256, 255015, -62340, 0, 521640, 321946, 49975, -151146, -241497, -372711, 0, 198261, 32340, 384849, -1660605, 145997, 150174, 0, 680855, 248364, 892562, 64872, 25200, 1075386, 0, -366093, -624580, -48474, 74025, 751212, -2021040, 0, 78372, 1252706, 29160, 1217460, -10579, -64368, 0, 262500, -129114, -310298, -7260, 116775, 119910, 0, -533610, 21456, -174402, -398484, 820220, -1015230, 0, -1401792, -30130, -295911, 116154, -146170, 340200, 0, -52920, -39366, 8220, -1292676, 166860, -191238, 0, -31311, -1159200, -619244, -658530, -107162, -53190, 0, 409955, 181160, -234045, 27642, 393130, 60993, 0, 62510, 112230, 124279, 2281488, -388233, 84600, 0, 76545, -295808, 281170, 750960, 21630, -690636, 0, 255640, -517680, 12474, 1899570, 57384, -739449, 0, 125160, 305028, 396801, 67524, -377730, 1386438, 0, -372330, 42620, -1004868, -5832, 72116, 1293600, 0, -359513, 6888, 715995, -786552, 418302, 801702, 0, 885794, 281610, 148320, 1266180, 8109, 611604, 0, 129780, -2202816, -643770, 92502, -454060, -244956, 0, 58800, -534960, 370161, -262500, -305272, 10935, 0, 162855, -439974, -1467650, -62400, 442134, -1729164, 0, -108864, 87804, -919921, -802080, 214018, 876120, 0, 251055, 259682, -136080, -1056750, -11295, 418644, 0, -362208, -1454220, 73584, -828738, 180549, 1289700, 0, 28665, -1304112, 21280, 452556, 249192, -80499, 0, 105840, -574838, -192258, 1436820, 1103200, -39204, 0, 1081500, 33372, -156275, 1987908, 160920, -459834, 0, 1126818, 1476620, 1056662, -251505, 4188, -509220, 0, -1123416, -1288850, -10575, -299232, -116200, -254907, 0, -78561, 88776, 523456, -888825, -348111, -142593, 0, -621810, 1744276, -99792, -21519, -1469905, 734424, 0, 2652559, -34260, 108621, 765045, -1473312, 414630, 0, -226870, 241920, 106100, -523815, 151146, 416262, 0, -881370, -681380, 12906, -538875, 1557292, -1154547, 0, 27720, 983144, -591426, -336591, -882335, 55620, 0, -2673048, 374220, 1033030, -58800, 396252, -1923120, 0, 253449, 2450680, 711430, 675864, -243225, -1107246, 0, -1665510, 1734876, 273258, -3381900, 68838, 68040, 0, -1890980, -964854, -64368, 859641, 51660, -2731680, 0, 3402, 4169020, 1190822, 350325, -39456, 1921980, 0, 565950, 511340, -121635, -86280, 398484, 315135, 0, 1372448, 1278, 732626, -709200, 120555, 887733, 0, 1411200, 834130, -264600, 856548, 47205, 287061, 0, 1017954, -2060270, 134352, -1971420, 352370, -936000, 0, 51597, -179280, -2385565, -961518, -512190, 139434, 0, -1952496, -266976, 1566880, -60345, -837791, 2307015, 0, -33880, 135912, 60993, -1753980, 824050, 478710, 0], "weight_parity": -1, "has_non_self_twist": 1, "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], [1, 1, 7, 4, -1, 6, 0]], "char_orbit_index": 6, "prim_orbit_index": 4, "minimal_twist": "21.5.f.b", "char_is_minimal": true, "conrey_index": 10, "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, 5], [3, 3], [-9, 9], [-2, 1], [-15, 30], [-35, -21], [35, 0], [0, 27], [-5, -5], [149, -149], [-54, 27], [24, -48], [105, -280], [-9, 0], [0, 319], [-154, -154], [-135, 135], [-412, 206], [9, -18], [-42, -231], [745, 0], [0, 560], [105, 105], [-622, 622], [240, -120], [-81, 162], [504, -315], [235, 0], [0, -45], [-743, -743], [-1035, 1035], [894, -447], [770, -1540], [91, -14], [-243, 0], [0, -1970], [-1030, -1030], [216, -216], [-70, 35], [-1626, 3252], [1155, -1365], [2798, 0], [0, 1341], [-27, -27], [-2800, 2800], [4768, -2384], [-957, 1914], [784, 1911], [-3110, 0], [0, -1386], [216, 216], [-901, 901], [-810, 405], [-149, 298], [-1225, -735], [-1854, 0], [0, 1175], [797, 797], [81, -81], [-4120, 2060], [3715, -7430], [567, -1512], [-71, 0], [0, 72], [2235, 2235], [4156, -4156], [2772, -1386], [-1680, 3360], [70, 385], [484, 0], [0, 945], [-548, -548], [9850, -9850], [-3732, 1866], [1854, -3708], [-8344, 5215], [1080, 0], [0, -4325], [-319, -319], [-729, 729], [-16260, 8130], [753, -1506], [2457, -378], [462, 0], [0, 13990], [705, 705], [5215, -5215], [2284, -1142], [135, -270], [-1848, 2184], [-5040, 0], [0, -6687], [11920, 11920], [618, -618], [-6210, 3105], [-3147, 6294], [-9555, 13475], [4023, 0], [0, -5598]]}