# Stored data for newform 5.12.a.a, downloaded from the LMFDB on 25 April 2024.
{"label": "5.12.a.a", "space_label": "5.12.a", "level": 5, "weight": 12, "hecke_orbit": 1, "hecke_orbit_code": 201326597, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 350246086223072610, "analytic_rank": 1, "is_twist_minimal": true, "hecke_cutters": [[2, [-34, 1]]], "qexp_display": "q+34q^{2}-792q^{3}-892q^{4}+5^{5}q^{5}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 720, "fricke_eigenval": -1, "atkin_lehner_string": "-", "analytic_conductor": 3.841715902797944, "hecke_ring_index": 1, "level_radical": 5, "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": 0, "analytic_rank_proved": true, "char_values": [5, 1, [2], [1]], "hecke_ring_generator_nbound": 1, "inner_twist_count": 1, "level_primes": [5], "conrey_indexes": [1], "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": "0.989", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.938", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "4.768", "prec": 17}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "11.2.3.c1", "atkin_lehner_eigenvals": [[5, -1]], "trace_display": [34, -792, 3125, -17556], "traces": [0, 1, 34, -792, -892, 3125, -26928, -17556, -99960, 450117, 106250, -468788, 706464, -374042, -596904, -2475000, -1571824, -3724286, 15303978, -379460, -2787500, 13904352, -15938792, -32458092, 79168320, 9765625, -12717428, -216192240, 15659952, 69696710, -84150000, 171448632, 151276064, 371280096, -126625724, -54862500, -401504364, -291340546, -12901640, 296241264, -312375000, 191343242, 472747968, -1759857392, 418158896, 1406615625, -1103575128, 1623469924, 1244884608, -1669113607, 332031250, 2949634512, 333645464, -644888642, -7350536160, -1464962500, 1754897760, 300532320, 2369688140, 925569220, 2207700000, -10898589338, 5829253488, -7902254052, 8362481728, -1168881250, 12623523264, 3795674064, 3322063112, 25706808864, -1865325000, -22966943728, -44993695320, 9880820458, -9905578564, -7734375000, 338478320, 8230042128, 10072202976, -20768886240, -4911950000, 91487377881, 6505670228, 3204862008, -12402681984, -11638393750, -59835151328, -55199794320, 46860048480, 63176321130, 47824931250, 6566681352, 28952618064, -135787316544, 55197977416, -1185812500, -119810642688, 126494473874, -56749862638, -211009448196, -8710937500, 32890510302, 100287573408, 76222392308, 37389238320, 43451100000, -21926213828, 55856572344, 192843478080, -166136788330, -49808725000, 230741712432, 27594942144, -179451654542, 10218098880, -101431537500, -62169465320, -168362662914, 31469353480, 65383565016, 247401000000, -65549481667, -370552037492, -151543847664, -152932179744, 30517578125, -268676637768, -53794877516, -25489000320, 1393807054464, -39741962500, 531507278532, -331181845632, 6661799760, 129052918176, -675600750000, 372279628560, 392827630554, 874031501376, -1046036929420, 48937350000, -1285788179808, -780876086752, 175346401096, -707504703408, 217802218750, 335947895572, 1321937976744, 259875767032, 445288935950, -262968750000, 266614824352, 37930821600, -1676364441462, 279821432352, 535776975000, -264247207488, -1619587062106, -706142132160, 510751804464, 472737700000, 569834263152, 3110570847954, 1557118038008, -170678171864, 1160250300000, 108965308272, -810193869636, -1389879025920, -1652252976273, -395705387500, -170801396820, 1569792793664, -3629196921642, -1876793006880, -171445312500, 736852229312, -733050822240, 2147994918420, -3783829650740, -1254701137500, -26382760018, 223267165968, 8631682755696, 3244510876320, -910439206250, -4616768762496, 1745900585368, -1448135172208, 3795470965440, -40317625000, 3188489846792, -6623085528576, -2172552458542, 4300812111716, 925753950000, 1488849337444, 3090424396974, -7174321238664, 4506273184600, -976171875000, -3006173858688, 1118277350268, -1223595440760, -2631073984704, 597947631250, 2591561338472, -14609938996764, 587928192608, 177886294480, 1477337400000, -10473937938988, 575240668664, 18189819432576, 1899123459696, -5499554350000, 21610576310400, -3009952183392, -5648650803220, -7825609802736, 1306746550000, 1393039384012, 7845218222688, -3637981404292, -2655802579584, 4395673828125, -6101356254428, 16586396582384, -268074829440, -10279797623490, -3448672275000, -6518193365376, -6966883131600, 2927599746858, -5724330539076, 5073343512500, -825607744240, 16448957902080, 2223041210544, 13396011338080, 3890264400000, -16728195115358, -2228682376678, -34160196542472, 9721541689496, -5215980021875, -5152490820576, 141933977320, -17138005254720, -2538250710336, 1037597656250, 18833877060252, 7048810614384, 15215964032496, -1829025835544, 9217607850000, -17992988589824, -1201563096606, 47389439851776, 5114774625576, 1042642075000, 31371674015070, 18071247470088, 3796600489508, -37113158396160, -2015277006250, 226501191840, -50035646334960, -3385741265088, -25742245602410, -22970425500000, 16014429593272, 5853922117664, -5200811630784, 13356139438836, -4578007812500, -22930473506688, -23161973367666, -35565255600280, 77171943889944, 5484055500000, 37179665661882, -43716798113472, 9578058412608, 20486513805376, 939163500000, 5961777637264, -3359221956552, 68091928099488, -20401590097837, 7405275437500, -100183623308208, -8813691848536, -65105235871842, 44945891209296, 2892403812500, 29122400978160, 101348327805120, 15139823822300, 12140689647864, 6899062500000, 30896056373952, 9064904027968, -26049284159184, 596444335040, -34058091681250, -56996391009708, -33787161085856, -7341197578176, -60368134707936, 18216417150000, 31326789581712, -29612276749440, 63902725450058, -55065960111604, -24694543912500, 18525846526080, 11551720535414, 17365561351776, -32672981287480, 26132755400000, -44238405296448, 19374364947168, 1413217565560, -81606741069852, -3652753906250, 52942013292272, 131580336357360, -19126670470320, -28501637985744, 39448510200000, 117396489617532, -2858736911136, -131137332543882, -27546591567624, 11861481450000, -21855194178048, 3673996841554, -56176601193282, 142125710397264, 10381447225000, -80373061298016, -5807247491880, 64016906784600, 175915344904320, 80333777700000, -123392695335828, -59296596491576, 49238216533440, -96915614965850, -5829140625000, 80864977834080, -70916403490432, 39359396659458, -24923727956160, -71771699150000, -56353278447960, -51783783492672, -128650208125160, -53849513174280, -140605297875000, -116346269006619, -897013840612, 51915189480264, -5857479765984, 30877563931250, 293477213693664, 45567121790964, 51018407999808, 86126846059314, -30954933012500, 11321664998952, 121122286357248, 169341209790958, 59360619902512, -24169921875000, -162282053603040, -26069496801820, 129046012824960, -59380200441740, 1057744750000, 42605542992672, 108408654790928, 121002509761308, 20187288253440, 25718881650000, -73866783590428, -792141729714864, -112833070695608, 153361697488830, 31475634300000, 120883217622312, 166844596155720, -420953764597344, 105074429497116, -64902769500000, 188220427790832, 133061282073574, 153213288276400, -5276145409920, -15349843750000, -125079682705998, -102209911195392, -64128989210544, -29338335189384, 285898055878125, -41602244985840, 136576951878248, -294845465819520, 191901522661370, 20330219462500, -311119483398768, -67990373938736, -16249293226320, -496737925889976, 10015193775000, -56583601530688, 828461248100640, 6048134012320, -339088245781060, -38758381200000, 409834586687422, -356113889925592, 730751411781108, 64463068654320, -36369980468750, 618453860707584, 191335634417928, -49824062530848, -138874349668032, -186984847900000, -558967690788168, 339816151445760, -325999693255742, -102338374235328, -172499357250000, 148194015190360, 12316547590320, -266070733293024, 89133625453480, 146437651500000, -751296409442019, 47363339056408, 555014045773008, -205821607489344, 197426003531250, -123691367745928, -352668837272400, -146811729216768, -241404543824750, 149452910156250, -89699415730696, 160070875851464, -211158940886784, 563937483801056, 20520879225000, -30041210707200, 36095403680794, -349513119198660, 805161732740640, 90476931450000, 258826949138262, -221618574422784, -564822897844692, -109550961499040, -424335364200000, 99538391393172, -388269793297936, 150179495319288, -66636853867584, 172493679425000, 1282712953187952, -92519899231200, 825000027080896, 559264568670720, -3705664062500, -58322139994272, -290275340871114, 455464385494720, 264818742090960, -374408258400000, 108973600506932, -568758633922172, -451308736416384, 58470137646964, 395295230856250, -1161446682444048, -960424464775396, 1089422990226480, -1233237486102336, -177343320743750, 237919600117292, 135177112116288, -259570481299060, 4825755228880, -659404525612500, -269487074544768, 403207664088768, -86300524151424, -926509083889700, -27221679687500, 641673544751712, 640351820048568, -221172315836092, 789909315037920, 102782844693750, 517342777104864, 1308584357208216, 47985030744272, -222666755375930, 313398666900000, -173467683960648, -559560139398656, 82036307390400, -40853145284604, 238194975962500, -1243275892581888, -761063218732112, 173902337269584, 2874323961940464, 116841369750000, -1004490588837478, 1066636916512380, -1019538444892592, -474104492450544, 135784687500000, 129084416643272, -638523739876752, -583586965615104, 100717978366537, -68519418212500, 416614440598740, -5942325385920, -71570408924164, -1701211975388640, 174551788575000, -379415579437440, 2996793083386080, -875236350481940, 782460429598316, 602635869000000, 1576723717969542, 544490606171248, 20895145934256, -563395327290304, -519177463531250, -176827595446656, -273963507086576, -350402246454168, -4905640337052546, -155652265625000, -26447113576600, -2569652614045440, 364618566829440, -787507094500644, 721067851350000, 933064941042640, 91000471705494, 2623846092258096, 658260578618464, 86234194200000, -1382753263611456, 1264108632503988, 102926393251608, 1146923056388736, -560786420443750, 325653986028672, -1606152406078836, 2295775695050880, 2339556432974490, 31931559000000, -226931239783828, -156408989777632, -2525283958659264, -114213546522768, -316973554687500, 3764095187962176, 2421511880192834, -693654063326458, 1720661547165264, -194279579125000, -56264557412448, -3406243192479072, 302316056705896, -987686812981680, -526133321606250, -2213578019642628, 1604253787184904, -1179168675255648, -65057897898720, 98341729625000, -2447616122403408, 457936062375904, -2020528622020942, 3445843145374080, 204323640675000, -397197730867400, -3568968362203200, 412783448027376, 1257878419261400, 773128125000000, -850069615091398, 1050465916714368, 1708497422665488, -237820423321984, -204842130209375, -885675661412256, -2257710792441356, -57403215245440, 969087589081920, -1157975117162500, -607245937312808, 1495317081784104, 3375833969205358, -1148763476919104, -473574523950000, -822675011114880, -1761143658313686, -2052516580069824, -536922678085660, -477913061700000, 7017187615606080, 1065110845778208, -1109123493758280, -465639128545536, 95367431640625, 2172692665301972, -140885945228160, 1444671659398552, 1085035516700156, -839614493025000, -1361520603114368, 2076057868550400, 8295358847678496, 392758498204076, -168108992237500, -455590609581888, 624318591789494, -1110881363774320, -10337811810016176, -79653126000000, -2148959139283758, -1504105780079232, -557356122582792, -508292162731584, 4355647045200000, 48049397229040, 241894180790524, -9145078292984760, -433895743505360, -124193632812500, 2383882129246464, -1388949289903136, -3139585213786042, 4473731436150240, 1660960245412500, -300757900013408, 4447525262093586, -969055691515296, 1061987922234220, -1034943267600000, -887576148441938, 3991480646996088, -1103287192137504, -320358006319680, 20818124250000, -4458669306491988, -2262222225277320, 722692931715312, 2881281272199264, 403290369300000, 5109127898582344, 2103395643030528, -2923985063350542, 124915892612836, -2111252343750000, 1473809654835516, -3201435506787666, 4832274153506976, -2220736983331944, 1163373839250000, -13136426093248128, -2732684084132544, 2374358013548208, 152354845963440, 1227586345481250, 2176574830676400, 8141599717804080, 2766186085323008, 241215437430964, 2731348441800000, -446381960099708, 3237243654104664, 3704481872528976, -2016084280713584, -3268865404437500, 5517771440227200, -712616957375212, -3295130908838900, -2318658999511536, 152929218750000, 5799298780282502, 2749409246358720, 110552083585160, -3920231084305664, -4018088061900000, 1338219486421572, -577425798861912, 653881333438080, 3711496215295870, -2440237771100000, -9348428767690080, -6315105060154800, -5564895470730144, -1760648638750848, 547957503425000, 3375176048460080, -10609640979759360, -1830883447925520, 254073503735040, -2210952198150000, -1338160319359248, -3955773146225046, 13248730531363536, 23533421936056, 680631933593750, 1765116442328976, 3407257530559484, -656405467945920, 10848161132152317, 1049837173662500, 6554212247022112, -7699461018080832, -3167081741102842, 1549282140892776, 4131056177325000, -4910132402709888, -1779366453114432, 2928312766016676, 3825929969969980, 812111771975000, -112411710037440, 384936609964368, -2209953962739692, 13573300161738240, 1391527924843750, 5757601132892572, 1442562872454936, -1557343322148256, -980617984071264, -821777343750000, 1226064105604552, -2551808989821376, -14916430631719584, -886362891261880, 833171326100000, -3385560101172480, 6709291091329294, -2018926815019160, -12051043513736832, 118533817500000, -5226981453900438, 1448588461750848, 2916697455921480, -2844132943338464, -5238638879568750, 4114085331884472, -346201762187240, 14250446963140608, 9722515805477090, 874441976100000, 951637972511952, 1937916793019464, 9828292307784558, -26932818810305376, 1674303046875000, -12644387608445040, -4050901503456192, 5214297714620220, -72607106609320, -825772523400000, 10766627616361664, 4110029399158608, -15067887855530400, 2623552826209168, -5061209569081250, -14312427996309696, 2540306642769904, -2756658562100808, -3006907587690336, -2206694163000000, 3150453247139352, 21092504441672160, 4076530153164196, 4524083590501516, 1596099388950000, -4019595680663200, -3634047718991626, -179388943937280, -6046266309374264, 1477305312500000, 28436736138072210, -4252709212003932, -4632010060864904, 2681507081949696, 1780732072350000, -2180385633158496, 20387858517108720, -3287735409787920, -4024893340628230, 9720533899856250, -11209452324103188, 1091447133157920, -12683428237871424, 4643616363860432, 4865993868775000, -4636306317189888, 667795485968320, 6524651770486580, 2955774910118184, -533369287075000, -21142690373861778, -10578062435558112, -3765892141086892, -7619190335107680, 3625782187500000, -552475969694880, 1794186154640584, 13032065585113488, -11161486852296090, 340516588350000, 18344282907191472, -3127919390504576, 6216256438959602, 28167682435421760, -2531855842612500, -158674574676160, -37065863797015680, -11529000356556040, 3475139435319080, -4343371956000000, -7342878380881729, 13934375947372348, -29446295204210544, 9342752641577296, -5163290550853125, 24845548000557672, 1150786700145852, 1013651444823008, -7585822262785536, -1236579335937500, 9456358245398232, -16225318933857792, 16412214205681758, 6505411570209552, -533754365062500, -5583422971506240, 4919205017661994, -4721727888713088, -19688991000557180, 4905602480200000, 2660503789589184, -19004901486797712, 24406755096212108, -32704711134543360, -11341240380131250, -11083989570695228, 16158059357486904, 2684877347585664, 9736204642677120, -5864978146500000, -1419741518246688, 16607033361466800, 56937313096743258, 418762618070880, -535766601562500, 6980443944040512, 28874389996366134, 3030543265418320, 51563346810498864, 2302663216600000, -2519277239619518, -25544077921028646, -22947853053776392, -1242591130538704, -2290783819500000, 18870477556282272, -31202872587089796, -23064941574702720, 944422869670896, 6712484120062500, -42888184902078228, 3245079412628464, -616041897361040, -11990740467261600, -11824467658562500, 447484889617920, -9615426201108288, -8207754490041500, 11949405584400720, -3920941054687500, 2401749740959612, -3049780134843664, -24469676648169984, 17937987388018320, -82446125056250, -7179403990150656, 7971313059821544, -14795065751486528, 14804577825605334, 697709893650000, -21501767879960888, -472383913351680, -1502400851006304, 1227243725146996, 26974008611550000, 9169579480153080, -9331141781907792, 27375498913181760, -19363824928436360, 10139096488500000, 26759431579997952, 8800116270700908, 8590601565908576, 5814228481915392, -2845122519531250, -19203978526719528, 34308994558500036, 10543443962549440, -17850530406099790, -14427402382800000, 633361849312220, -2611418974197336, -24810817348715904, -13201172972129824, 5455939329275000, 16829531784883440, 7465052912682954, -2265653031497856, -50610958556445936, -4525422413150000, 30598421763809942, 43612240408390368, -6210636552414264, -1454831913657280, 11860846767000000, 28050000920750464, -23513751983906976, -14672470448655360, -3695841845751236, -125992578125000, -9148962664047888, -6535741158999360, 14874428064538858, -9869361589617876, 9964030771225000, -11949242113567360, 25877001179684160, 9003837231092640, -6896481882006024, -20697142276800000, 3986156518266593, 3705102417235688, 25141992773764248, 14921550042899336, -6789226432943750, -15344497038157056, -47403930542122036, 6552326187433320, -1119268311923520, 13440037849112500, -12108312753504228, 30470895315885024, 18364224332897520, -32654431802363464, 2892981093750000, 17130664287612512, -52395212022280766, -41930074527479424, -29616301229890440, 4652654179512500, -74780992752734610, 8089266403987928, 36425353018854708, 15148323012493440, 9657576240543750, -8825396364168040, 22573297284709248, -126605107769440, 57121613136416064, -22419753870825000, 42108794710093592, 25936074227144448, -92978019777085344, 13709060579018112, 14082103701875000, 2264119633619712, 27520915894982574, -31501308852249800, 62985565242563040, -3050537109375000], "weight_parity": 1, "has_non_self_twist": 0, "level_is_prime": true, "level_is_prime_power": true, "level_is_square": false, "level_is_squarefree": true, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "5.12.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], [1], [34], [-792], [-892], [3125], [-26928], [-17556], [-99960], [450117], [106250], [-468788], [706464], [-374042], [-596904], [-2475000], [-1571824], [-3724286], [15303978], [-379460], [-2787500], [13904352], [-15938792], [-32458092], [79168320], [9765625], [-12717428], [-216192240], [15659952], [69696710], [-84150000], [171448632], [151276064], [371280096], [-126625724], [-54862500], [-401504364], [-291340546], [-12901640], [296241264], [-312375000], [191343242], [472747968], [-1759857392], [418158896], [1406615625], [-1103575128], [1623469924], [1244884608], [-1669113607], [332031250], [2949634512], [333645464], [-644888642], [-7350536160], [-1464962500], [1754897760], [300532320], [2369688140], [925569220], [2207700000], [-10898589338], [5829253488], [-7902254052], [8362481728], [-1168881250], [12623523264], [3795674064], [3322063112], [25706808864], [-1865325000], [-22966943728], [-44993695320], [9880820458], [-9905578564], [-7734375000], [338478320], [8230042128], [10072202976], [-20768886240], [-4911950000], [91487377881], [6505670228], [3204862008], [-12402681984], [-11638393750], [-59835151328], [-55199794320], [46860048480], [63176321130], [47824931250], [6566681352], [28952618064], [-135787316544], [55197977416], [-1185812500], [-119810642688], [126494473874], [-56749862638], [-211009448196], [-8710937500]]}