# Stored data for newform 12.21.c.a, downloaded from the LMFDB on 19 April 2024.
{"label": "12.21.c.a", "space_label": "12.21.c", "level": 12, "weight": 21, "hecke_orbit": 1, "hecke_orbit_code": 137791275020, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 2230123693358369860, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[5, [0, 1]]], "qexp_display": "q+3^{10}q^{3}-77335774q^{7}+3^{20}q^{9}+\\cdots", "char_order": 2, "char_parity": -1, "char_degree": 1, "char_conductor": 3, "char_orbit_label": "c", "char_is_real": true, "Nk2": 5292, "analytic_conductor": 30.421651812319396, "hecke_ring_index": 1, "level_radical": 6, "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": 1, "is_self_dual": true, "is_self_twist": true, "is_cm": true, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.508", "prec": 17}, "analytic_rank_proved": true, "char_values": [12, 2, [7, 5], [2, 1]], "hecke_ring_generator_nbound": 1, "inner_twist_count": 2, "level_primes": [2, 3], "conrey_indexes": [5], "field_disc": 1, "field_disc_factorization": [], "field_poly": [0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "0.962", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "2.841", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "9.346", "prec": 17}], "related_objects": [], "self_twist_discs": [-3], "cm_discs": [-3], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "20.2.1.d2", "trace_display": [0, 59049, 0, -77335774], "traces": [0, 1, 0, 59049, 0, 0, 0, -77335774, 0, 3486784401, 0, 0, 0, 217393135826, 0, 0, 0, 0, 0, -3843000838126, 0, -4566600118926, 0, 0, 0, 95367431640625, 0, 205891132094649, 0, 0, 0, 793864193940674, 0, 0, 0, 0, 0, 8665815522315698, 0, 12836847277389474, 0, 0, 0, 36742119154315826, 0, 0, 0, 0, 0, -73811444357432925, 0, 0, 0, 0, 0, 0, 0, -226925356490502174, 0, 0, 0, -1387788230779990126, 0, -269653170422461374, 0, 0, 0, -1579433466595168174, 0, 0, 0, 0, 0, 8577821547816235298, 0, 5631351470947265625, 0, 0, 0, -3262829215661625598, 0, 12157665459056928801, 0, 0, 0, 0, 0, 0, 0, 0, 0, -16812266421390839324, 0, 46876886788002859026, 0, 0, 0, -146701748198870395774, 0, 0, 0, 0, 0, -257676576635226935902, 0, 0, 0, 0, 0, -161372785248413047726, 0, 511707740777219651202, 0, 0, 0, 0, 0, 758002994882571050226, 0, 0, 0, 672749994932560009201, 0, 0, 0, 0, 0, -2155340413107716416702, 0, 2169585393943195209474, 0, 0, 0, 297201444299122919524, 0, 0, 0, 0, 0, -3781733390639874718798, 0, 0, 0, 0, 0, 0, 0, -4358491977862056788325, 0, 0, 0, -12224356281505494685726, 0, 0, 0, 0, 0, 13789305471652348836626, 0, 0, 0, 0, 0, 26371572582557549187026, 0, 0, 0, 0, 0, 28254811729380885263475, 0, -13399715375407662872526, 0, 0, 0, -7375314140319824218750, 0, 0, 0, 0, 0, 35918758264219232908274, 0, -81947507239327636950174, 0, 0, 0, 0, 0, -15922750060275921673326, 0, 0, 0, 18580285047585599226626, 0, 0, 0, 0, 0, -151492689327814927861726, 0, -93263966768978085506526, 0, 0, 0, 0, 0, 0, 0, 0, 0, 217101614651210201363474, 0, 0, 0, 0, 0, -61394101889288133871676, 0, 506511784577000878111602, 0, 0, 0, 412862181153448428825026, 0, 332525673007965087890625, 0, 0, 0, -668657708264324365858126, 0, 0, 0, 0, 0, 0, 0, -192666802355603329936302, 0, 0, 0, -1318751419552831553617726, 0, 717897987691852588770249, 0, 0, 0, -835442003182157357302076, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -670177550759498777180252, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 358294867573462584806402, 0, -992747519916707671242876, 0, 0, 0, 3217143690758411201491826, 0, 2768033287944780822626274, 0, 0, 0, 6590107934995289629613426, 0, 0, 0, 0, 0, 4064231406647572522401601, 0, -8662591529395098000058926, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2841480223199239844159324, 0, 0, 0, 0, 0, -14848283828172743270622574, 0, -15215544173733515338077198, 0, 0, 0, 11867720064079031177075426, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 20732225020027160644531250, 0, -9528901596133542055172574, 0, 0, 0, -27745613919184203536792398, 0, 30215830385154043183826898, 0, 0, 0, 4304627448588606258018626, 0, 0, 0, 0, 0, 11879061852779946356982724, 0, 0, 0, 0, 0, 9202092217523922876138002, 0, 44759318844820937944795074, 0, 0, 0, 0, 0, 0, 0, 0, 0, -22821318015708819738163725, 0, 39725214450772735983309849, 0, 0, 0, -44126411472949785029525374, 0, 0, 0, 0, 0, -93179970343473668539285774, 0, 0, 0, 0, 0, -66365350630676541881606926, 0, -127270696053597546689836398, 0, 0, 0, 0, 0, 128111847926951733924230226, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4212782437325231404508974, 0, 17549448084418909274972676, 0, 0, 0, 172580626540742949067986724, 0, 0, 0, 0, 0, 198673724829739275348907874, 0, 0, 0, 0, 0, 0, 0, -223307574983893962270303102, 0, 0, 0, 110309548987834923699284402, 0, 0, 0, 0, 0, 107325676975461160106567524, 0, 0, 0, 0, 0, 265167280972609002464889026, 0, 0, 0, 0, 0, -254040401755480376083424926, 0, -257364592800776591293802925, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -721836014066617955697434574, 0, 0, 0, 7270173075970201292318498, 0, 0, 0, 0, 0, -879009997358655908708354302, 0, 0, 0, 0, 0, 122146709620640475396456676, 0, 814244698795599546453928674, 0, 0, 0, -366497119724845886230468750, 0, 0, 0, 0, 0, 1883888810885835669365996548, 0, 0, 0, 0, 0, -831547504794500661626974, 0, 1557214989427440721944698274, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1849797534668080443288022126, 0, 0, 0, 0, 0, 0, 0, 1668418377808211893922935275, 0, 0, 0, -663372468634246566536950652, 0, -791239793202447084959787774, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2849880786888529729038551374, 0, -435504924671745300292968750, 0, 0, 0, 1716155831334586342923895201, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4245994031311294689248268526, 0, 2120966756743881484000671426, 0, 0, 0, -459720656266435082728889902, 0, -4838918354975057634270824526, 0, 0, 0, 252333422823004737719542852, 0, 0, 0, 0, 0, 7987484499849256615719382276, 0, 0, 0, 0, 0, 0, 0, -940222468309232898888226974, 0, 0, 0, 6303268057342440040563628274, 0, 0, 0, 0, 0, 7430615760719797133536449026, 0, 1097147251774882048733038674, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3050820762672231592721336924, 0, 0, 0, 0, 0, 0, 0, -8945491812118143675307058574, 0, 0, 0, 2238489882157027224187147874, 0, -5507143973741386971074853774, 0, 0, 0, -6570508187260533459627645502, 0, 0, 0, 0, 0, -9013974241437342177009620302, 0, 0, 0, 0, 0, 2737825044134086725223732274, 0, 0, 0, 0, 0, 9094947017729282379150390625, 0, 0, 0, 0, 0, -15943608921725048110969396126, 0, 12819633243539311180311776226, 0, 0, 0, -16046101348708657157209471050, 0, 0, 0, 0, 0, 18864090119646145147094204498, 0, 0, 0, 0, 0, 0, 0, -3625260322460575016988596124, 0, 0, 0, 0, 0, 29909014367487324851611986498, 0, 0, 0, -19186948881508173107597062798, 0, 0, 0, 0, 0, 0, 0, 24379098934929976273688960274, 0, 0, 0, 24397933907919678207154471298, 0, 19635308465447330474853515625, 0, 0, 0, 11345293244112747982868619076, 0, 0, 0, 0, 0, 0, 0, -39483569015300089479556482174, 0, 0, 0, -49452492834173185928431897198, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -33302736315304527870366701948, 0, 0, 0, 0, 0, -39531848478720150436385304526, 0, -11376782012296021029408696798, 0, 0, 0, 0, 0, 0, 0, 0, 0, 19927617495755590753629558148, 0, -77870952573175150409573102574, 0, 0, 0, 80172708786751620772755558626, 0, 42391158275216203514294433201, 0, 0, 0, -2259004449620970286241029102, 0, 0, 0, 0, 0, 92554215806943134185213429202, 0, -49332014845903209791330285724, 0, 0, 0, 0, 0, 0, 0, 0, 0, 112900322508201695380017360002, 0, 0, 0, 0, 0, -112972259938121916661208456974, 0, 0, 0, 0, 0, 12479889249721805317589149924, 0, 0, 0, 0, 0, 108611199527700351483172457474, 0, 0, 0, 0, 0, 75708789247577095031738281250, 0, -39573314194797643293716700348, 0, 0, 0, 0, 0, 0, 0, 0, 0, 59966314616013533042980011026, 0, 0, 0, 0, 0, -301695635351678627384456854076, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -212622899824262060926681483726, 0, 21156953635345392170233231698, 0, 0, 0, -141199994704561077648105982076, 0, -58620748303561671279220584924, 0, 0, 0, -218456207520472896366040188574, 0, 0, 0, 0, 0, 288759835820040929045133824402, 0, 189969117795593423036890833474, 0, 0, 0, 0, 0, 163449597619851362795258853426, 0, 0, 0, 176994576151109753197786640401, 0, 0, 0, 0, 0, -52027641566605606113006456574, 0, 389139283453536857339043191874, 0, 0, 0, -294561325819457344780250418574, 0, 0, 0, 0, 0, 419965978983195631451219986802, 0, 0, 0, 0, 0, 0, 0, 239988800331132509875292137449, 0, 0, 0, -343357994131653428605694401724, 0, -511517367219251141805479521374, 0, 0, 0, 507930201940024655329650502226, 0, 0, 0, 0, 0, -521104272375823264955751697774, 0, 0, 0, 0, 0, 166684919081164994458155697348, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -167786565699691913557763922876, 0, 0, 0, -285320121476846073372278343502, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -165434894939507551519231146526, 0, -876776311769772317386992372126, 0, 0, 0, 826436569434709358215332031250, 0, -898462667914790347198120464702, 0, 0, 0, 283657442528905344292827698550, 0, 0, 0, 0, 0, -829096123507548959706013639774, 0, 700777002063802711975126829874, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1864759524835604393826089586148, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -41570170398006220379111027325, 0, 0, 0, 0, 0, 1380051274808803778666671588898, 0, 0, 0, 0, 0, 292463278826779066641275679652, 0, 1224217155207583808898925781250, 0, 0, 0, 0, 0, -562672110350089524815885322126, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1778120457155734682573059211326, 0, -1638350756313908034644054309502, 0, 0, 0, -1939340866384989573533388461902, 0, 1784214568412961095961794500002, 0], "weight_parity": -1, "has_non_self_twist": 0, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": false, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 3, 2, -1, 2, -3]], "char_orbit_index": 3, "prim_orbit_index": 2, "minimal_twist": "12.21.c.a", "char_is_minimal": true, "conrey_index": 5, "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], [1], [0], [59049], [0], [0], [0], [-77335774], [0], [3486784401], [0], [0], [0], [217393135826], [0], [0], [0], [0], [0], [-3843000838126], [0], [-4566600118926], [0], [0], [0], [95367431640625], [0], [205891132094649], [0], [0], [0], [793864193940674], [0], [0], [0], [0], [0], [8665815522315698], [0], [12836847277389474], [0], [0], [0], [36742119154315826], [0], [0], [0], [0], [0], [-73811444357432925], [0], [0], [0], [0], [0], [0], [0], [-226925356490502174], [0], [0], [0], [-1387788230779990126], [0], [-269653170422461374], [0], [0], [0], [-1579433466595168174], [0], [0], [0], [0], [0], [8577821547816235298], [0], [5631351470947265625], [0], [0], [0], [-3262829215661625598], [0], [12157665459056928801], [0], [0], [0], [0], [0], [0], [0], [0], [0], [-16812266421390839324], [0], [46876886788002859026], [0], [0], [0], [-146701748198870395774], [0], [0], [0]]}