# Stored data for newform 81.10.c.f, downloaded from the LMFDB on 19 July 2025.
{"Nk2": 8100, "analytic_conductor": 41.717902729273725, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 9, "char_degree": 2, "char_is_minimal": false, "char_is_real": false, "char_orbit_index": 3, "char_orbit_label": "c", "char_order": 3, "char_parity": 1, "char_values": [81, 3, [2], [1]], "cm_discs": [], "conrey_index": 28, "dim": 4, "field_disc": 28224, "field_disc_factorization": [[2, 6], [3, 2], [7, 2]], "field_poly": [196, 0, 14, 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, [254016, 0, 504, 0, 1]]], "hecke_orbit": 6, "hecke_orbit_code": 22518135743578193, "hecke_ring_generator_nbound": 7, "hecke_ring_index": 36, "hecke_ring_index_factorization": [[2, 2], [3, 2]], "hecke_ring_index_proved": true, "inner_twist_count": 4, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 9, 3, 1, 3, 0], [1, 1, 3, 2, -1, 2, 0], [1, 1, 9, 4, -1, 6, 0]], "is_cm": false, "is_largest": false, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": false, "is_self_twist": false, "is_twist_minimal": false, "label": "81.10.c.f", "level": 81, "level_is_powerful": true, "level_is_prime": false, "level_is_prime_power": true, "level_is_prime_square": false, "level_is_square": true, "level_is_squarefree": false, "level_primes": [3], "level_radical": 3, "minimal_twist": "27.10.a.a", "nf_label": "4.0.28224.6", "prim_orbit_index": 3, "qexp_display": "q+\\beta _{1}q^{2}-8\\beta _{2}q^{4}+(22\\beta _{1}+22\\beta _{3})q^{5}+\\cdots", "related_objects": [], "relative_dim": 2, "rm_discs": [], "sato_tate_group": "9.2.3.c3", "self_twist_discs": [], "self_twist_type": 0, "space_label": "81.10.c", "trace_display": [0, 0, 0, 1526], "trace_hash": 182637693209168521, "trace_moments": [{"__RealLiteral__": 0, "data": "0.070", "prec": 17}, {"__RealLiteral__": 0, "data": "3.553", "prec": 17}, {"__RealLiteral__": 0, "data": "1.210", "prec": 17}, {"__RealLiteral__": 0, "data": "72.113", "prec": 20}, {"__RealLiteral__": 0, "data": "50.627", "prec": 20}, {"__RealLiteral__": 0, "data": "2276.556", "prec": 27}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.509", "prec": 17}, "traces": [0, 4, 0, 0, 16, 0, 0, 1526, 0, 0, -44352, 0, 0, 146030, 0, 0, 515968, 0, 0, -2392516, 0, 0, 2554272, 0, 0, 3418378, 0, 0, 24416, 0, 0, 3648200, 0, 0, -7553952, 0, 0, 57088700, 0, 0, -11531520, 0, 0, -15513808, 0, 0, 215554752, 0, 0, 79542876, 0, 0, -1168240, 0, 0, 112387968, 0, 0, 208954368, 0, 0, 305532986, 0, 0, 544995328, 0, 0, 641504138, 0, 0, -16920288, 0, 0, 265855940, 0, 0, -9570064, 0, 0, 230714906, 0, 0, 2678215680, 0, 0, 166186944, 0, 0, -1328221440, 0, 0, 222841780, 0, 0, -1391461344, 0, 0, 470613686, 0, 0, 54694048, 0, 0, -201598834, 0, 0, -444564288, 0, 0, -9069331960, 0, 0, -393683584, 0, 0, 2371102272, 0, 0, -11243808576, 0, 0, -1756629866, 0, 0, -29185600, 0, 0, -10447782832, 0, 0, -1619180640, 0, 0, -912744854, 0, 0, -7856110080, 0, 0, -13597949074, 0, 0, -4900900032, 0, 0, 9193992192, 0, 0, 228354800, 0, 0, -9918434542, 0, 0, 3897819072, 0, 0, -11381897884, 0, 0, 183085056, 0, 0, 31555275524, 0, 0, 27597213504, 0, 0, 10546618296, 0, 0, -248220928, 0, 0, -2608222414, 0, 0, 15167047392, 0, 0, 4680578420, 0, 0, 56044235520, 0, 0, 19141714368, 0, 0, 26528217408, 0, 0, 23479099250, 0, 0, -636343008, 0, 0, 92526150212, 0, 0, 41135915520, 0, 0, 29460372480, 0, 0, 75346807040, 0, 0, -51581321626, 0, 0, -67748226336, 0, 0, 5567153200, 0, 0, 449551872, 0, 0, 2006735864, 0, 0, 104133234240, 0, 0, -62181817492, 0, 0, -108656271360, 0, 0, -61224299136, 0, 0, 5763665376, 0, 0, 154678583678, 0, 0, 4888527776, 0, 0, -87344777870, 0, 0, -81215475264, 0, 0, -546215741568, 0, 0, 6440869888, 0, 0, 21779339050, 0, 0, -293543099136, 0, 0, 9780414336, 0, 0, -5132033104, 0, 0, -281355229828, 0, 0, 2545302816, 0, 0, 268654507340, 0, 0, -17597099520, 0, 0, -280575249664, 0, 0, -186500170080, 0, 0, -361132873412, 0, 0, 1063423760, 0, 0, -123681894336, 0, 0, 131062038912, 0, 0, 11837035504, 0, 0, -308615423872, 0, 0, 794128410944, 0, 0, -40451241600, 0, 0, 119195507354, 0, 0, 3691438496, 0, 0, -529490368512, 0, 0, 82234137888, 0, 0, 499185739340, 0, 0, 696336076800, 0, 0, -90096442978, 0, 0, 830655354816, 0, 0, 204960464006, 0, 0, -1329495552, 0, 0, 244541637340, 0, 0, 832558228992, 0, 0, 435918483122, 0, 0, -42176139264, 0, 0, 107819800704, 0, 0, 825848630208, 0, 0, 140282411448, 0, 0, 891367120, 0, 0, -650690073922, 0, 0, -632999505600, 0, 0, 1027798533842, 0, 0, 723559898880, 0, 0, 2596938797996, 0, 0, 465833509344, 0, 0, 42876009792, 0, 0, 7529818976, 0, 0, -807683655744, 0, 0, -1172617175520, 0, 0, -1200659519368, 0, 0, -881886829952, 0, 0, -266373323000, 0, 0, 318864365568, 0, 0, -356893914226, 0, 0, 1612790672, 0, 0, 1214277394176, 0, 0, -1527784157088, 0, 0, -340921979122, 0, 0, -462346859520, 0, 0, -233121668318, 0, 0, 172017103104, 0, 0, -3578431236472, 0, 0, -36277327840, 0, 0, -1632328458376, 0, 0, -1103103610560, 0, 0, -333675042624, 0, 0, 207915717632, 0, 0, -6786598533120, 0, 0, -2370315326400, 0, 0, 2511303894356, 0, 0, 37937636352, 0, 0, 3764950691414, 0, 0, 1532577642624, 0, 0, 978935314588, 0, 0, -2923390229760, 0, 0, -2044631014762, 0, 0, -8105957661312, 0, 0, 2084165715250, 0, 0, 14053038928, 0, 0, 38663953460, 0, 0, -881971409088, 0, 0, 1565904033792, 0, 0, 1882354457600, 0, 0, -1595292152512, 0, 0, -2034472035456, 0, 0, 1809980282880, 0, 0, -41791131328, 0, 0, 101424041110, 0, 0, 12202622893440, 0, 0, 3525963045696, 0, 0, 841973932800, 0, 0, 3709847776076, 0, 0, -2162967412032, 0, 0, -7921467273746, 0, 0, -14603917664, 0, 0, 1490460979392, 0, 0, 6005109174624, 0, 0, 7980242361092, 0, 0, -62365427712, 0, 0, 299656236686, 0, 0, 8731467210816, 0, 0, -176035473278, 0, 0, 108783592592, 0, 0, -2265481382240, 0, 0, 5201710214400, 0, 0, 1145465576640, 0, 0, -5096936033280, 0, 0, 8466204785090, 0, 0, 1021739281920, 0, 0, 16934695500428, 0, 0, 36775968768, 0, 0, 1126525905792, 0, 0, -14362735310784, 0, 0, -2182094217800, 0, 0, 7363985590400, 0, 0, 253601276544, 0, 0, 7869365108640, 0, 0, 1474088715788, 0, 0, -158694952672, 0, 0, -3747781537402, 0, 0, -3387749748768, 0, 0, -6501603513556, 0, 0, 1013432958720, 0, 0, -5289781089982, 0, 0, -2018800018368, 0, 0, -4889779075442, 0, 0, 91055183072, 0, 0, -10142440264324, 0, 0, -13588682788800, 0, 0, -5807823091140, 0, 0, -5855429099520, 0, 0, 1195380959504, 0, 0, 4518237755808, 0, 0, 28491810931584, 0, 0, 126221102096, 0, 0, -3228974090496, 0, 0, -2123370010944, 0, 0, -17996384568694, 0, 0, -14350551022080, 0, 0, -44683637870592, 0, 0, -7112997882144, 0, 0, 7602984737114, 0, 0, 168745892736, 0, 0, -359078242418, 0, 0, -4659247555200, 0, 0, 111993323904, 0, 0, 4002314243072, 0, 0, -2284955052880, 0, 0, -17146995868800, 0, 0, -10035274152960, 0, 0, 20865779312, 0, 0, -34146407042300, 0, 0, 14068446864192, 0, 0, 20299307211230, 0, 0, 15773729287680, 0, 0, 4103003741760, 0, 0, -10685420538912, 0, 0, -307639820684, 0, 0, 18722313680, 0, 0, 22033877874152, 0, 0, -2947810662720, 0, 0, 3513438996764, 0, 0, -889810016256, 0, 0, -18116024950720, 0, 0, 339202551744, 0, 0, 1441682428032, 0, 0, 306267429888, 0, 0, 18584830550570, 0, 0, -15256803179520, 0, 0, 29140204836068, 0, 0, 6897336526080, 0, 0, -3459950142740, 0, 0, 51023569830912, 0, 0, -9259992928606, 0, 0, -187832794000, 0, 0, 12470926619600, 0, 0, 8340514420896, 0, 0, 12418880681088, 0, 0, 41041578643968, 0, 0, -7141572449518, 0, 0, -2558166877728, 0, 0, 44616981945580, 0, 0, 370104600848, 0, 0, -10427611311936, 0, 0, 55048182037632, 0, 0, -1809151033536, 0, 0, -21390676070400, 0, 0, -4180267792288, 0, 0, 36455016981600, 0, 0, 9279258465232, 0, 0, 471365959680, 0, 0, -14065955451742, 0, 0, -4289512971744, 0, 0, 9086193822356, 0, 0, 19896416936960, 0, 0, 9137208902976, 0, 0, 10183777136064, 0, 0, -14301112717190, 0, 0, 412650573008, 0, 0, -2680617175516, 0, 0, 12911131664928, 0, 0, 44020466967218, 0, 0, -70458155389440, 0, 0, -85361695114, 0, 0, 27210116898720, 0, 0, 36632562075648, 0, 0, 22268612800, 0, 0, -46839424636070, 0, 0, -128929548259008, 0, 0, 32809296772562, 0, 0, 14497148768256, 0, 0, -31034855346076, 0, 0, -11484370070208, 0, 0, -3985829150408, 0, 0, 32107773824, 0, 0, -18168669864576, 0, 0, 11902080901536, 0, 0, 6663129548544, 0, 0, 27074640902400, 0, 0, -34213828366678, 0, 0, -2470869656640, 0, 0, -69931339019136, 0, 0, 497454539936, 0, 0, -168396813966160, 0, 0, -67224243991968, 0, 0, 48787689032150, 0, 0, -3450254524416, 0, 0, -47576900879004, 0, 0, -6421512498912, 0, 0, 84043895768972, 0, 0, -244897196544, 0, 0, -143180088468480, 0, 0, -39626485387776, 0, 0, 9705735729550, 0, 0, -2997105995520, 0, 0, 20496674411136, 0, 0, -17006114696256, 0, 0, 46224562701342, 0, 0, 2474857338848, 0, 0, 2214119893946, 0, 0, -5218164550368, 0, 0, -20750470286924, 0, 0, -78822621860224, 0, 0, -38433298091328, 0, 0, -62035399065024, 0, 0, 25797577861440, 0, 0, 698758222960, 0, 0, 67655161166660, 0, 0, 3739386724416, 0, 0, 80132296076564, 0, 0, -84464094274560], "weight": 10, "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], [0, 0, -8, 0], [0, 22, 0, 22], [0, 0, 0, 0], [763, 0, 763, 0], [0, 0, 0, -520], [0, 0, 0, 0], [-11088, 0, 0, 0], [0, -2534, 0, 0], [0, 0, 0, 0], [0, 0, -73015, 0], [0, 763, 0, 763], [0, 0, 0, 0], [257984, 0, 257984, 0], [0, 0, 0, 7494], [0, 0, 0, 0], [-598129, 0, 0, 0], [0, 176, 0, 0], [0, 0, 0, 0], [0, 0, -1277136, 0], [0, -106922, 0, -106922], [0, 0, 0, 0], [1709189, 0, 1709189, 0], [0, 0, 0, -73015], [0, 0, 0, 0], [6104, 0, 0, 0], [0, -207296, 0, 0], [0, 0, 0, 0], [0, 0, -1824100, 0], [0, -8256, 0, -8256], [0, 0, 0, 0], [-3776976, 0, -3776976, 0], [0, 0, 0, 16786], [0, 0, 0, 0], [14272175, 0, 0, 0], [0, -598129, 0, 0], [0, 0, 0, 0], [0, 0, 5765760, 0], [0, -1328480, 0, -1328480], [0, 0, 0, 0], [-7756904, 0, -7756904, 0], [0, 0, 0, 20272], [0, 0, 0, 0], [53888688, 0, 0, 0], [0, 1380418, 0, 0], [0, 0, 0, 0], [0, 0, -39771438, 0], [0, 1709189, 0, 1709189], [0, 0, 0, 0], [-584120, 0, -584120, 0], [0, 0, 0, 441036], [0, 0, 0, 0], [28096992, 0, 0, 0], [0, 396760, 0, 0], [0, 0, 0, 0], [0, 0, -104477184, 0], [0, 5577286, 0, 5577286], [0, 0, 0, 0], [152766493, 0, 152766493, 0], [0, 0, 0, -1824100], [0, 0, 0, 0], [136248832, 0, 0, 0], [0, 1606330, 0, 0], [0, 0, 0, 0], [0, 0, -320752069, 0], [0, 59952, 0, 59952], [0, 0, 0, 0], [-8460144, 0, -8460144, 0], [0, 0, 0, 4862004], [0, 0, 0, 0], [66463985, 0, 0, 0], [0, 14272175, 0, 0], [0, 0, 0, 0], [0, 0, 4785032, 0], [0, -1933442, 0, -1933442], [0, 0, 0, 0], [115357453, 0, 115357453, 0], [0, 0, 0, 5675648], [0, 0, 0, 0], [669553920, 0, 0, 0], [0, -27378188, 0, 0], [0, 0, 0, 0], [0, 0, -83093472, 0], [0, -7756904, 0, -7756904], [0, 0, 0, 0], [-664110720, 0, -664110720, 0], [0, 0, 0, -15046674], [0, 0, 0, 0], [55710445, 0, 0, 0], [0, -855376, 0, 0], [0, 0, 0, 0], [0, 0, 695730672, 0], [0, -13158838, 0, -13158838], [0, 0, 0, 0], [235306843, 0, 235306843, 0], [0, 0, 0, -39771438], [0, 0, 0, 0], [13673512, 0, 0, 0]]}