# Stored data for newform 27.10.a.a, downloaded from the LMFDB on 24 April 2024.
{"label": "27.10.a.a", "space_label": "27.10.a", "level": 27, "weight": 10, "hecke_orbit": 1, "hecke_orbit_code": 167772187, "dim": 2, "is_polredabs": true, "nf_label": "2.2.56.1", "trace_hash": 1853757316730140178, "analytic_rank": 1, "is_twist_minimal": true, "hecke_cutters": [[2, [-504, 0, 1]]], "qexp_display": "q+\\beta q^{2}-8q^{4}-22\\beta q^{5}-763q^{7}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 2700, "fricke_eigenval": 1, "atkin_lehner_string": "+", "analytic_conductor": 13.905967576424574, "hecke_ring_index": 6, "level_radical": 3, "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": true, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.509", "prec": 17}, "analytic_rank_proved": true, "char_values": [27, 1, [2], [1]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 2, "level_primes": [3], "conrey_indexes": [1], "field_disc": 56, "field_disc_factorization": [[2, 3], [7, 1]], "field_poly": [-14, 0, 1], "hecke_ring_index_factorization": [[2, 1], [3, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.835", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "13.681", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "129.794", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "9.2.3.c1", "atkin_lehner_eigenvals": [[3, 1]], "trace_display": [0, 0, 0, -1526], "traces": [0, 2, 0, 0, -16, 0, 0, -1526, 0, 0, -22176, 0, 0, -146030, 0, 0, -515968, 0, 0, -1196258, 0, 0, -2554272, 0, 0, -3418378, 0, 0, 12208, 0, 0, -3648200, 0, 0, 7553952, 0, 0, 28544350, 0, 0, 11531520, 0, 0, 15513808, 0, 0, 107777376, 0, 0, -79542876, 0, 0, 1168240, 0, 0, 56193984, 0, 0, -208954368, 0, 0, -305532986, 0, 0, 272497664, 0, 0, -641504138, 0, 0, 16920288, 0, 0, 132927970, 0, 0, 9570064, 0, 0, -230714906, 0, 0, 1339107840, 0, 0, -166186944, 0, 0, 1328221440, 0, 0, 111420890, 0, 0, 1391461344, 0, 0, -470613686, 0, 0, 27347024, 0, 0, 201598834, 0, 0, 444564288, 0, 0, -4534665980, 0, 0, 393683584, 0, 0, -2371102272, 0, 0, -5621904288, 0, 0, 1756629866, 0, 0, 29185600, 0, 0, -5223891416, 0, 0, 1619180640, 0, 0, 912744854, 0, 0, -3928055040, 0, 0, 13597949074, 0, 0, 4900900032, 0, 0, 4596996096, 0, 0, -228354800, 0, 0, 9918434542, 0, 0, 1948909536, 0, 0, 11381897884, 0, 0, -183085056, 0, 0, 15777637762, 0, 0, -27597213504, 0, 0, -10546618296, 0, 0, -124110464, 0, 0, 2608222414, 0, 0, -15167047392, 0, 0, 2340289210, 0, 0, -56044235520, 0, 0, -19141714368, 0, 0, 13264108704, 0, 0, -23479099250, 0, 0, 636343008, 0, 0, 46263075106, 0, 0, -41135915520, 0, 0, -29460372480, 0, 0, 37673403520, 0, 0, 51581321626, 0, 0, 67748226336, 0, 0, 2783576600, 0, 0, -449551872, 0, 0, -2006735864, 0, 0, 52066617120, 0, 0, 62181817492, 0, 0, 108656271360, 0, 0, -30612149568, 0, 0, -5763665376, 0, 0, -154678583678, 0, 0, 2444263888, 0, 0, 87344777870, 0, 0, 81215475264, 0, 0, -273107870784, 0, 0, -6440869888, 0, 0, -21779339050, 0, 0, -146771549568, 0, 0, -9780414336, 0, 0, 5132033104, 0, 0, -140677614914, 0, 0, -2545302816, 0, 0, -268654507340, 0, 0, -8798549760, 0, 0, 280575249664, 0, 0, 186500170080, 0, 0, -180566436706, 0, 0, -1063423760, 0, 0, 123681894336, 0, 0, 65531019456, 0, 0, -11837035504, 0, 0, 308615423872, 0, 0, 397064205472, 0, 0, 40451241600, 0, 0, -119195507354, 0, 0, 1845719248, 0, 0, 529490368512, 0, 0, -82234137888, 0, 0, 249592869670, 0, 0, -696336076800, 0, 0, 90096442978, 0, 0, 415327677408, 0, 0, -204960464006, 0, 0, 1329495552, 0, 0, 122270818670, 0, 0, -832558228992, 0, 0, -435918483122, 0, 0, -21088069632, 0, 0, -107819800704, 0, 0, -825848630208, 0, 0, 70141205724, 0, 0, -891367120, 0, 0, 650690073922, 0, 0, -316499752800, 0, 0, -1027798533842, 0, 0, -723559898880, 0, 0, 1298469398998, 0, 0, -465833509344, 0, 0, -42876009792, 0, 0, 3764909488, 0, 0, 807683655744, 0, 0, 1172617175520, 0, 0, -600329759684, 0, 0, 881886829952, 0, 0, 266373323000, 0, 0, 159432182784, 0, 0, 356893914226, 0, 0, -1612790672, 0, 0, 607138697088, 0, 0, 1527784157088, 0, 0, 340921979122, 0, 0, -231173429760, 0, 0, 233121668318, 0, 0, -172017103104, 0, 0, -1789215618236, 0, 0, 36277327840, 0, 0, 1632328458376, 0, 0, -551551805280, 0, 0, 333675042624, 0, 0, -207915717632, 0, 0, -3393299266560, 0, 0, 2370315326400, 0, 0, -2511303894356, 0, 0, 18968818176, 0, 0, -3764950691414, 0, 0, -1532577642624, 0, 0, 489467657294, 0, 0, 2923390229760, 0, 0, 2044631014762, 0, 0, -4052978830656, 0, 0, -2084165715250, 0, 0, -14053038928, 0, 0, 19331976730, 0, 0, 881971409088, 0, 0, -1565904033792, 0, 0, 941177228800, 0, 0, 1595292152512, 0, 0, 2034472035456, 0, 0, 904990141440, 0, 0, 41791131328, 0, 0, -101424041110, 0, 0, 6101311446720, 0, 0, -3525963045696, 0, 0, -841973932800, 0, 0, 1854923888038, 0, 0, 2162967412032, 0, 0, 7921467273746, 0, 0, -7301958832, 0, 0, -1490460979392, 0, 0, -6005109174624, 0, 0, 3990121180546, 0, 0, 62365427712, 0, 0, -299656236686, 0, 0, 4365733605408, 0, 0, 176035473278, 0, 0, -108783592592, 0, 0, -1132740691120, 0, 0, -5201710214400, 0, 0, -1145465576640, 0, 0, -2548468016640, 0, 0, -8466204785090, 0, 0, -1021739281920, 0, 0, 8467347750214, 0, 0, -36775968768, 0, 0, -1126525905792, 0, 0, -7181367655392, 0, 0, 2182094217800, 0, 0, -7363985590400, 0, 0, 126800638272, 0, 0, -7869365108640, 0, 0, -1474088715788, 0, 0, -79347476336, 0, 0, 3747781537402, 0, 0, 3387749748768, 0, 0, -3250801756778, 0, 0, -1013432958720, 0, 0, 5289781089982, 0, 0, -1009400009184, 0, 0, 4889779075442, 0, 0, -91055183072, 0, 0, -5071220132162, 0, 0, 13588682788800, 0, 0, 5807823091140, 0, 0, -2927714549760, 0, 0, -1195380959504, 0, 0, -4518237755808, 0, 0, 14245905465792, 0, 0, -126221102096, 0, 0, 3228974090496, 0, 0, -1061685005472, 0, 0, 17996384568694, 0, 0, 14350551022080, 0, 0, -22341818935296, 0, 0, 7112997882144, 0, 0, -7602984737114, 0, 0, 84372946368, 0, 0, 359078242418, 0, 0, 4659247555200, 0, 0, 55996661952, 0, 0, -4002314243072, 0, 0, 2284955052880, 0, 0, -8573497934400, 0, 0, 10035274152960, 0, 0, -20865779312, 0, 0, -17073203521150, 0, 0, -14068446864192, 0, 0, -20299307211230, 0, 0, 7886864643840, 0, 0, -4103003741760, 0, 0, 10685420538912, 0, 0, -153819910342, 0, 0, -18722313680, 0, 0, -22033877874152, 0, 0, -1473905331360, 0, 0, -3513438996764, 0, 0, 889810016256, 0, 0, -9058012475360, 0, 0, -339202551744, 0, 0, -1441682428032, 0, 0, 153133714944, 0, 0, -18584830550570, 0, 0, 15256803179520, 0, 0, 14570102418034, 0, 0, -6897336526080, 0, 0, 3459950142740, 0, 0, 25511784915456, 0, 0, 9259992928606, 0, 0, 187832794000, 0, 0, 6235463309800, 0, 0, -8340514420896, 0, 0, -12418880681088, 0, 0, 20520789321984, 0, 0, 7141572449518, 0, 0, 2558166877728, 0, 0, 22308490972790, 0, 0, -370104600848, 0, 0, 10427611311936, 0, 0, 27524091018816, 0, 0, 1809151033536, 0, 0, 21390676070400, 0, 0, -2090133896144, 0, 0, -36455016981600, 0, 0, -9279258465232, 0, 0, 235682979840, 0, 0, 14065955451742, 0, 0, 4289512971744, 0, 0, 4543096911178, 0, 0, -19896416936960, 0, 0, -9137208902976, 0, 0, 5091888568032, 0, 0, 14301112717190, 0, 0, -412650573008, 0, 0, -1340308587758, 0, 0, -12911131664928, 0, 0, -44020466967218, 0, 0, -35229077694720, 0, 0, 85361695114, 0, 0, -27210116898720, 0, 0, 18316281037824, 0, 0, -22268612800, 0, 0, 46839424636070, 0, 0, -64464774129504, 0, 0, -32809296772562, 0, 0, -14497148768256, 0, 0, -15517427673038, 0, 0, 11484370070208, 0, 0, 3985829150408, 0, 0, 16053886912, 0, 0, 18168669864576, 0, 0, -11902080901536, 0, 0, 3331564774272, 0, 0, -27074640902400, 0, 0, 34213828366678, 0, 0, -1235434828320, 0, 0, 69931339019136, 0, 0, -497454539936, 0, 0, -84198406983080, 0, 0, 67224243991968, 0, 0, -48787689032150, 0, 0, -1725127262208, 0, 0, 47576900879004, 0, 0, 6421512498912, 0, 0, 42021947884486, 0, 0, 244897196544, 0, 0, 143180088468480, 0, 0, -19813242693888, 0, 0, -9705735729550, 0, 0, 2997105995520, 0, 0, 10248337205568, 0, 0, 17006114696256, 0, 0, -46224562701342, 0, 0, 1237428669424, 0, 0, -2214119893946, 0, 0, 5218164550368, 0, 0, -10375235143462, 0, 0, 78822621860224, 0, 0, 38433298091328, 0, 0, -31017699532512, 0, 0, -25797577861440, 0, 0, -698758222960, 0, 0, 33827580583330, 0, 0, -3739386724416, 0, 0, -80132296076564, 0, 0, -42232047137280], "weight_parity": 1, "has_non_self_twist": 1, "level_is_prime": false, "level_is_prime_power": true, "level_is_square": false, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 3, 2, -1, 2, 0]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "27.10.a.a", "char_is_minimal": true, "conrey_index": 1, "id": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0, 0], [1, 0], [0, 1], [0, 0], [-8, 0], [0, -22], [0, 0], [-763, 0], [0, -520], [0, 0], [-11088, 0], [0, -2534], [0, 0], [-73015, 0], [0, -763], [0, 0], [-257984, 0], [0, 7494], [0, 0], [-598129, 0], [0, 176], [0, 0], [-1277136, 0], [0, 106922], [0, 0], [-1709189, 0], [0, -73015], [0, 0], [6104, 0], [0, -207296], [0, 0], [-1824100, 0], [0, 8256], [0, 0], [3776976, 0], [0, 16786], [0, 0], [14272175, 0], [0, -598129], [0, 0], [5765760, 0], [0, 1328480], [0, 0], [7756904, 0], [0, 20272], [0, 0], [53888688, 0], [0, 1380418], [0, 0], [-39771438, 0], [0, -1709189], [0, 0], [584120, 0], [0, 441036], [0, 0], [28096992, 0], [0, 396760], [0, 0], [-104477184, 0], [0, -5577286], [0, 0], [-152766493, 0], [0, -1824100], [0, 0], [136248832, 0], [0, 1606330], [0, 0], [-320752069, 0], [0, -59952], [0, 0], [8460144, 0], [0, 4862004], [0, 0], [66463985, 0], [0, 14272175], [0, 0], [4785032, 0], [0, 1933442], [0, 0], [-115357453, 0], [0, 5675648], [0, 0], [669553920, 0], [0, -27378188], [0, 0], [-83093472, 0], [0, 7756904], [0, 0], [664110720, 0], [0, -15046674], [0, 0], [55710445, 0], [0, -855376], [0, 0], [695730672, 0], [0, 13158838], [0, 0], [-235306843, 0], [0, -39771438], [0, 0], [13673512, 0]]}