# Stored data for newform 27.7.b.c, downloaded from the LMFDB on 08 December 2024. {"Nk2": 1323, "analytic_conductor": 6.211460257735977, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 3, "char_degree": 1, "char_is_minimal": true, "char_is_real": true, "char_orbit_index": 2, "char_orbit_label": "b", "char_order": 2, "char_parity": -1, "char_values": [27, 2, [2], [1]], "cm_discs": [], "conrey_index": 26, "dim": 4, "field_disc": 26896, "field_disc_factorization": [[2, 4], [41, 2]], "field_poly": [100, 0, 21, 0, 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": [[2, [5184, 0, 225, 0, 1]]], "hecke_orbit": 3, "hecke_orbit_code": 9007268091658267, "hecke_ring_generator_nbound": 5, "hecke_ring_index": 6561, "hecke_ring_index_factorization": [[3, 8]], "hecke_ring_index_proved": true, "inner_twist_count": 2, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 3, 2, -1, 2, 0]], "is_cm": false, "is_largest": true, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": false, "is_self_twist": false, "is_twist_minimal": true, "label": "27.7.b.c", "level": 27, "level_is_powerful": true, "level_is_prime": false, "level_is_prime_power": true, "level_is_prime_square": false, "level_is_square": false, "level_is_squarefree": false, "level_primes": [3], "level_radical": 3, "minimal_twist": "27.7.b.c", "nf_label": "4.0.26896.1", "prim_orbit_index": 2, "qexp_display": "q-\\beta _{1}q^{2}+(-7^{2}+\\beta _{3})q^{4}+(7\\beta _{1}+\\beta _{2}+\\cdots)q^{5}+\\cdots", "related_objects": [], "relative_dim": 4, "rm_discs": [], "sato_tate_group": "6.2.3.c2", "self_twist_discs": [], "self_twist_type": 0, "space_label": "27.7.b", "trace_display": [0, 0, 0, -676], "trace_hash": 816549841479237342, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.827", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "72.033", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1927.614", "prec": 27}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.509", "prec": 17}, "traces": [0, 4, 0, 0, -194, 0, 0, -676, 0, 0, 3258, 0, 0, -3448, 0, 0, 10498, 0, 0, -3664, 0, 0, -58014, 0, 0, 17392, 0, 0, 152342, 0, 0, -153244, 0, 0, 65988, 0, 0, 128960, 0, 0, -338058, 0, 0, 126008, 0, 0, -116568, 0, 0, 121872, 0, 0, -71884, 0, 0, 54180, 0, 0, 567036, 0, 0, 167696, 0, 0, -28994, 0, 0, 8, 0, 0, -2104830, 0, 0, -1881676, 0, 0, 3764384, 0, 0, 1188728, 0, 0, -1366344, 0, 0, -176472, 0, 0, 27342, 0, 0, -373736, 0, 0, 1381140, 0, 0, 975212, 0, 0, 1786720, 0, 0, -2914264, 0, 0, -5242806, 0, 0, 1792160, 0, 0, -5719510, 0, 0, 5061888, 0, 0, 7995204, 0, 0, -6612224, 0, 0, 3247874, 0, 0, -1318780, 0, 0, 300060, 0, 0, 14965936, 0, 0, -949860, 0, 0, -7547248, 0, 0, -20345364, 0, 0, 1446840, 0, 0, -2667880, 0, 0, 6331148, 0, 0, 13510602, 0, 0, -1831024, 0, 0, -262710, 0, 0, -17340040, 0, 0, 24289830, 0, 0, -14422164, 0, 0, -3481156, 0, 0, 7581680, 0, 0, 6659604, 0, 0, -2773216, 0, 0, 39679128, 0, 0, 13628952, 0, 0, -49611168, 0, 0, -10423828, 0, 0, -46320720, 0, 0, 521324, 0, 0, 14875578, 0, 0, 7051680, 0, 0, -1158580, 0, 0, 34473824, 0, 0, 21863034, 0, 0, 9160396, 0, 0, -55830150, 0, 0, -9352936, 0, 0, 75712176, 0, 0, -19854280, 0, 0, 15543972, 0, 0, 114984, 0, 0, -19042668, 0, 0, -13831912, 0, 0, -32044456, 0, 0, -25535072, 0, 0, 30879018, 0, 0, 56676960, 0, 0, -102719102, 0, 0, -7447520, 0, 0, -19609218, 0, 0, 68236668, 0, 0, 131750324, 0, 0, -37951084, 0, 0, -132092172, 0, 0, -97237936, 0, 0, 130419630, 0, 0, -42288688, 0, 0, 42595596, 0, 0, 82655860, 0, 0, 192405662, 0, 0, -4902840, 0, 0, -103240854, 0, 0, -10774424, 0, 0, -127976608, 0, 0, -19680184, 0, 0, -70419258, 0, 0, -116879788, 0, 0, -133212700, 0, 0, 167489352, 0, 0, 185643720, 0, 0, -36033760, 0, 0, 46849032, 0, 0, -36631144, 0, 0, -59314500, 0, 0, 98776376, 0, 0, 68097780, 0, 0, -102705356, 0, 0, 174914622, 0, 0, -81771472, 0, 0, -181084302, 0, 0, 170068680, 0, 0, -220866210, 0, 0, 245574300, 0, 0, -44521148, 0, 0, 170468900, 0, 0, 58411080, 0, 0, -120450664, 0, 0, 10587852, 0, 0, -138406528, 0, 0, -259936740, 0, 0, -221966100, 0, 0, 250157546, 0, 0, -41957568, 0, 0, 84641058, 0, 0, 104185016, 0, 0, -41152352, 0, 0, 165572008, 0, 0, -68809428, 0, 0, -255349900, 0, 0, 148993388, 0, 0, -262691892, 0, 0, 164327904, 0, 0, 171254384, 0, 0, 509193702, 0, 0, -123985424, 0, 0, 68440500, 0, 0, 301741964, 0, 0, -337270024, 0, 0, 39515228, 0, 0, -41100264, 0, 0, -313730280, 0, 0, -232179562, 0, 0, -224440128, 0, 0, -65751444, 0, 0, 122919092, 0, 0, -310300920, 0, 0, 133466948, 0, 0, -199249740, 0, 0, 527001496, 0, 0, 16743708, 0, 0, 299696768, 0, 0, 468504720, 0, 0, -139856960, 0, 0, -350255408, 0, 0, -548645608, 0, 0, 624593808, 0, 0, -160880688, 0, 0, -264101698, 0, 0, 59402168, 0, 0, -367871436, 0, 0, -203269860, 0, 0, 481809050, 0, 0, 722580748, 0, 0, 385149132, 0, 0, 350002008, 0, 0, 144830340, 0, 0, -798219784, 0, 0, 687696408, 0, 0, -264767612, 0, 0, -1441510112, 0, 0, 48885444, 0, 0, -1192680612, 0, 0, 674036432, 0, 0, 177492708, 0, 0, 1005878600, 0, 0, -170707680, 0, 0, -503132600, 0, 0, -263301256, 0, 0, -129660752, 0, 0, 6394932, 0, 0, -597049776, 0, 0, 1218131892, 0, 0, 103805720, 0, 0, 503021592, 0, 0, -199283752, 0, 0, 466634700, 0, 0, -161163756, 0, 0, 221221764, 0, 0, -361763696, 0, 0, 220095080, 0, 0, 267979320, 0, 0, -231405840, 0, 0, -308289916, 0, 0, 366637382, 0, 0, -6771160, 0, 0, 447433992, 0, 0, 323112680, 0, 0, -1681154586, 0, 0, -204138280, 0, 0, -681382080, 0, 0, -397731668, 0, 0, 1724808968, 0, 0, -818323876, 0, 0, -936578610, 0, 0, 218225760, 0, 0, 730079478, 0, 0, -422852608, 0, 0, -297165888, 0, 0, 1931443128, 0, 0, 381896900, 0, 0, 454463820, 0, 0, -276691932, 0, 0, 412139024, 0, 0, -1931506326, 0, 0, -941342400, 0, 0, -1712752740, 0, 0, -260403364, 0, 0, 1111704042, 0, 0, 1025010484, 0, 0, 2092856094, 0, 0, 386796888, 0, 0, 243910340, 0, 0, 68979248, 0, 0, 1146739914, 0, 0, 240129792, 0, 0, -292391200, 0, 0, 312274240, 0, 0, -169432848, 0, 0, -1674854848, 0, 0, -2463225012, 0, 0, 378916200, 0, 0, 324273564, 0, 0, 523116952, 0, 0, -724867552, 0, 0, -738327124, 0, 0, -2847501990, 0, 0, 624983696, 0, 0, 864495720, 0, 0, -810406936, 0, 0, 3247862994, 0, 0, -232496100, 0, 0, -145956924, 0, 0, 1167600644, 0, 0, -542824344, 0, 0, 16098920, 0, 0, 2508295968, 0, 0, -1304276096, 0, 0, -995975820, 0, 0, 295817948, 0, 0, 2248443026, 0, 0, -1034537392, 0, 0, -2653209126, 0, 0, -2235864168, 0, 0, 1653380688, 0, 0, 2279849552, 0, 0, 1950491052, 0, 0, 46735648, 0, 0, 700301150, 0, 0, -344132496, 0, 0, -530866800, 0, 0, -1114656480, 0, 0, -1522029834, 0, 0, 2242030544, 0, 0, -1759184280, 0, 0, 200204512, 0, 0, -1545935400, 0, 0, -615092500, 0, 0, -1779917292, 0, 0, 94233032, 0, 0, 499151924, 0, 0, 2212375608, 0, 0, 1960469532, 0, 0, 232319956, 0, 0, -1561749832, 0, 0, -1566327232, 0, 0, 113320512, 0, 0, 595449656, 0, 0, 544124790, 0, 0, -3059722288, 0, 0, 2758359420, 0, 0, -79743132, 0, 0, -4317415382, 0, 0, -1054012592, 0, 0, 5085088128, 0, 0, -1194884344, 0, 0, 1897875270, 0, 0, 924845264, 0, 0, 2262931812, 0, 0, 1894266700, 0, 0, -3597418108, 0, 0, 2605027500, 0, 0, 2562334128, 0, 0, 344902536, 0, 0, -4246412976, 0, 0, 417158720, 0, 0, 510007500, 0, 0, 1655274996, 0, 0, -2478367324, 0, 0, 2537504828, 0, 0, -4119143346, 0, 0, 876345920, 0, 0, 2260088028, 0, 0, -4960826112, 0, 0, -5979742434, 0, 0, -2790477964, 0, 0, 1272955140, 0, 0, 202829760, 0, 0, -1746019836, 0, 0, 812849704, 0, 0, 2010535884, 0, 0, 3076952040, 0, 0, 4314451644, 0, 0, 2906740560, 0, 0, 4748663780, 0, 0, -370690228, 0, 0, -3072609090, 0, 0, -1241886224, 0, 0, 1229187752, 0, 0, -3655194552, 0, 0, -3036653046, 0, 0, -2009475972, 0, 0, -1634240576, 0, 0, -3879502012, 0, 0, 9572306652, 0, 0, 5174202104, 0, 0, -5139700218], "weight": 7, "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, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp": [[0, 0, 0, 0], [1, 0, 0, 0], [0, -1, 0, 0], [0, 0, 0, 0], [-49, 0, 0, 1], [0, 7, 1, 0], [0, 0, 0, 0], [-171, 0, 0, 4], [0, 49, 8, 0], [0, 0, 0, 0], [821, 0, 0, -13], [0, -133, 17, 0], [0, 0, 0, 0], [-858, 0, 0, -8], [0, 427, 32, 0], [0, 0, 0, 0], [2641, 0, 0, -33], [0, 150, -14, 0], [0, 0, 0, 0], [-976, 0, 0, 120], [0, -1205, -40, 0], [0, 0, 0, 0], [-14519, 0, 0, 31], [0, -212, -196, 0], [0, 0, 0, 0], [4304, 0, 0, 88], [0, 346, -64, 0], [0, 0, 0, 0], [38267, 0, 0, -363], [0, 1322, -258, 0], [0, 0, 0, 0], [-38241, 0, 0, -140], [0, -1617, 248, 0], [0, 0, 0, 0], [16530, 0, 0, -66], [0, -4645, -135, 0], [0, 0, 0, 0], [32180, 0, 0, 120], [0, 8656, 960, 0], [0, 0, 0, 0], [-84821, 0, 0, 613], [0, -3068, 132, 0], [0, 0, 0, 0], [31458, 0, 0, 88], [0, 7991, 1336, 0], [0, 0, 0, 0], [-29836, 0, 0, 1388], [0, 3182, -470, 0], [0, 0, 0, 0], [31144, 0, 0, -1352], [0, 1328, 704, 0], [0, 0, 0, 0], [-17734, 0, 0, -474], [0, -11313, -1407, 0], [0, 0, 0, 0], [14435, 0, 0, -1780], [0, -34171, -856, 0], [0, 0, 0, 0], [141646, 0, 0, 226], [0, 18358, -2462, 0], [0, 0, 0, 0], [42324, 0, 0, -800], [0, 29281, -1120, 0], [0, 0, 0, 0], [-6257, 0, 0, -1983], [0, 890, -930, 0], [0, 0, 0, 0], [-2202, 0, 0, 4408], [0, -11154, -1424, 0], [0, 0, 0, 0], [-528935, 0, 0, 5455], [0, -44958, -1058, 0], [0, 0, 0, 0], [-472111, 0, 0, 3384], [0, -24500, 960, 0], [0, 0, 0, 0], [944464, 0, 0, -6736], [0, 28639, 5769, 0], [0, 0, 0, 0], [298446, 0, 0, -2528], [0, 46933, 2344, 0], [0, 0, 0, 0], [-342724, 0, 0, 2276], [0, 53009, 4035, 0], [0, 0, 0, 0], [-45114, 0, 0, 1992], [0, -25826, 704, 0], [0, 0, 0, 0], [13847, 0, 0, -14023], [0, 11838, 12338, 0], [0, 0, 0, 0], [-92386, 0, 0, -2096], [0, 105100, -1440, 0], [0, 0, 0, 0], [345466, 0, 0, -362], [0, -110272, 104, 0], [0, 0, 0, 0], [238827, 0, 0, 9952], [0, -117672, -10816, 0], [0, 0, 0, 0], [446640, 0, 0, 80]]}