# Stored data for newform 25.12.a.c, downloaded from the LMFDB on 16 April 2024.
{"label": "25.12.a.c", "space_label": "25.12.a", "level": 25, "weight": 12, "hecke_orbit": 3, "hecke_orbit_code": 9007199456067609, "dim": 2, "is_polredabs": true, "nf_label": "2.2.604.1", "trace_hash": 1499357071858016000, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[2, [-5336, -20, 1]]], "qexp_display": "q+(10+3\\beta )q^{2}+(110+2^{4}\\beta )q^{3}+(3488+\\cdots)q^{4}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 3600, "fricke_eigenval": 1, "atkin_lehner_string": "+", "analytic_conductor": 19.208579513989722, "hecke_ring_index": 2, "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": {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, "analytic_rank_proved": true, "char_values": [25, 1, [2], [1]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 1, "level_primes": [5], "conrey_indexes": [1], "field_disc": 604, "field_disc_factorization": [[2, 2], [151, 1]], "field_poly": [-151, 0, 1], "hecke_ring_index_factorization": [[2, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.049", "prec": 17}, {"__RealLiteral__": 0, "data": "1.930", "prec": 17}, {"__RealLiteral__": 0, "data": "0.232", "prec": 17}, {"__RealLiteral__": 0, "data": "9.261", "prec": 17}, {"__RealLiteral__": 0, "data": "1.103", "prec": 17}, {"__RealLiteral__": 0, "data": "61.449", "prec": 20}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "11.2.3.c1", "atkin_lehner_eigenvals": [[5, 1]], "trace_display": [20, 220, 0, -57900], "traces": [0, 2, 20, 220, 6976, 0, 60184, -57900, 246240, -20846, 0, -618176, 1927040, -3414260, 1334472, 0, 6005632, -1317940, 12548020, 5325320, 0, 3836184, 89491840, -58943940, 122180160, 0, -80761736, 26769160, -163685760, 94140380, 0, 244543464, 627301120, 442259840, 445358072, 0, 182418752, -21003220, -941752240, -624203992, 0, -745743316, -1429793040, -629950100, -242725888, 0, -468194856, 1402061540, 6375522560, -1941677414, 0, 2300559784, -12841321600, -1138320580, -9205154480, 0, -3990553920, -4720910480, -7387417960, 7317515560, 0, -1516425676, 28564327440, 2848632180, 819531776, 0, -2975464192, -15734290140, 4573774720, -5837195832, 0, 32938471544, 18354067680, 29982848860, 68768198072, 0, -1325392640, 34734748800, -110356370800, -3302823120, 0, -43884431798, 74630515640, -13299102420, -15982487808, 0, -56706093896, -34064940920, 80794874880, -12674770860, 0, 90637859064, -203171571840, 166200542640, -60289765528, 0, 105515416064, 3080703740, -130206802940, 118700272448, 0, 86236921404, 35235003280, 9745519820, -496819074240, 0, -688179643816, -296543215500, -96086091520, -16217462540, 0, 365573540584, 14728753920, 458453908940, -2268025760, 0, 161785210240, -19112954260, -563986667120, 118856958072, 0, 462375122266, 178966175240, 355770628840, 1375345458432, 0, -360757892856, 305724984820, 7429294080, -338129673112, 0, -862499305536, 1394641070080, -329288971440, -489632795928, 0, 589736681280, 61675297980, -1753937766960, -43332251960, 0, -242095262216, 527994411440, 645058398080, 1194681966464, 0, 1530603598744, -804464669140, 1306305374080, 1848547439300, 0, 1737588248504, -976155523200, 551754189100, -3013834465536, 0, -4259510141696, -1590893704900, 2053077212640, -3734796266552, 0, 1727766102744, -2964538062620, -1558077182260, -959393710208, 0, -4122356267976, 3267506815860, -1935463029120, 2444167740894, 0, -1222978859960, -3205397806720, -1498071986340, 1472498094160, 0, 7573321232384, -2593269676240, 5147191650120, -284499503720, 0, -4049980496036, -1010542877520, 868555479640, -7058336840640, 0, 11624887742688, 4442489192320, 3404183032960, -2442188092080, 0, -7475911020616, 6937864069120, -6931095694900, 16505041830872, 0, -8988371396032, 4617051692940, -3753078098560, 5291158372400, 0, -3502984686216, 12134911089240, -4191236630760, 8268940635392, 0, 13341380651384, 756632951580, -14847176600320, -10402040380160, 0, 8107665113824, -17506390943360, 4682483581840, -3628683124728, 0, -12239648592000, -2482608150000, 43070749119880, 9862247295368, 0, 283686232264, 10634415381520, -10352919702340, -16955461759488, 0, 5518771267064, -11909114012780, -15567714173440, 7211155027980, 0, -14105481384192, -2068704100800, 227108556780, -21482187990472, 0, 12780257818880, 10762585157280, -13347010877520, -2961890940560, 0, -10237234559716, -54519372130940, -23039730522380, -1406684117888, 0, -9033209561072, -4824430204880, 72943175479680, -22739515899672, 0, 16999064925504, 2151144750720, 19285816513920, -935451099128, 0, 1669612838912, 12062176821900, -27189535248880, 12748211746872, 0, -10753709379140, 11120133210240, 22933478508940, 42318208849920, 0, 30607443129120, 26733451785240, -61527001898880, -25752748710380, 0, 2117313290744, 41235921921280, -253416666480, 5347610019672, 0, -54271455234816, -52350921656580, -72651085240880, 28097291026728, 0, 54357167321964, 30053473643440, 18598009852380, 118861582665472, 0, -142467273279232, 36036747987000, 1494344856320, -48336033274394, 0, 88201462976584, 129195679026560, 45871580501100, -76524661446088, 0, 110538381199680, -91635071630080, -701813901400, 100105071687528, 0, 9365495045304, 73040409416240, 69606284688840, -82076780065280, 0, -7667931805256, 7095506707300, 53931164743680, 71706276263848, 0, -85888436624376, -247599498138240, -53524508750260, -42167176533928, 0, 30201861834240, -101865234960740, -144797761102640, -102391293261440, 0, -36157092210216, -42626157901200, -45474575557840, -203582773004224, 0, -86626977043336, 228791672428760, 42808318966080, -53668308626328, 0, 19078464335664, -126174574116480, 81153373414540, 236201554142472, 0, -133181990278656, -56499349988420, 183611528688300, 55412501597608, 0, 154260806439168, 32107322138320, 151199734486200, -160226268661440, 0, 140811747573144, -111353857720060, -82555563861760, -61760518869700, 0, -5078872119760, -133645965352960, 83888059299420, 116128913853920, 0, 61269186414720, -64448830389360, -264207488863760, -39011853936240, 0, -127738103376438, 274366883295640, -264568727769940, 277806423052032, 0, -13924310882192, 295977305329860, -165047943878400, 104089409174668, 0, -86161792299816, 778965139054080, -12609032273540, -160349570414336, 0, 50752792082880, -124995879202520, 275428032156960, 349903011273080, 0, 12335343277784, -178268578090960, -214175800003620, 18277067550720, 0, -23832136844296, -52577765772340, 340230190514560, -434199125486460, 0, 43955898029544, -420754970443680, 10432416474240, 234583048580472, 0, 315224933837824, 13626729180940, 274489971384800, 144579988307040, 0, -98600769721596, -527750274999120, -529465296024720, 526245219361152, 0, 289274514244080, 613500269656960, 303301145527680, -630089623911140, 0, 32015520323784, 298870882195840, -323982556260720, -369655998231912, 0, -1100240444448256, -389927948895760, 458270105413120, 743572175739320, 0, -791014101920956, -348187160682560, -101804534386940, -1250096188155840, 0, 1023624069382048, 78067479352200, -1047607755058560, -723272148264704, 0, -199292677728936, -853260847690240, 869146806094780, -547004492486496, 0, 808091965566080, -168043971947280, 1103270489218640, 64186628782640, 0, -109755530105878, -749225600202800, -308921303339700, 1414694109070592, 0, 136469871945944, 101008014086200, 202249169018880, 557532894580300, 0, 952874259495808, 1617771877936000, 488012184301840, 183069443641672, 0, -507535128672000, -518659127330900, -1174920223149960, -417166829635280, 0, -31289693618676, 496245008478720, -401041738541460, -538202433355520, 0, -1540263893234376, 1239115376161060, -492487153416320, 397024678116072, 0, -315042251458616, -144012873513600, -248868000976000, 241342002500160, 0, 123861460590336, -782243105200100, 461763598234720, 617225567149680, 0, -259923424447736, 1054999804226840, -129432762984240, 429901959391808, 0, -102434799288056, 145611909126980, 131671579250880, -550301584559192, 0, 600348960133184, 989109636404480, -413312072758360, 1526228426076640, 0, 3308597100762624, -918613444702800, -1051792913172720, 1390848735969800, 0, 1444900341658584, 671064386375040, 1094823994019020, -287636918034240, 0, -2664306537468672, 1117764324988260, 986514728105600, -2192854371749540, 0, -651387055111656, -2554918993838080, 938232044807200, -773931517102728, 0, -1655561070169856, -1087291749441920, -1889532185595600, 666105241164168, 0, 416907368500244, 579724152744280, 1231494927004060, -2613495052397568, 0, 306548939273464, 940443616260720, 598871874641920, -167073365311366, 0, -823873670006680, -470553275512320, 921087662588680, 480000890538480, 0, -2482161229062720, -1425228245817520, -3979155087600440, -374803064901568, 0, 2390273550653484, -1808734300647760, 1233791149468040, -124633407077888, 0, 2414377281821088, 169852451779540, 309740580151680, 243585411700948, 0, 1012917591686000, -3499403477005440, 462771287439840, -1124825561957928, 0, -1595498149262080, -1267586917893300, 1568492594436240, 1291550184551048, 0, -603456654644992, 3496591766800440, 851834334434940, -194939749297408, 0, 95890059744024, 825932201495460, 4381104517937280, -414116623191780, 0, -878368549743056, -728393452697600, -1374400707653360, -2729558115066576, 0, 1497955446525952, -925460858500180, -1087685208591620, -519866819213912, 0, -317119267845576, 2783496219877840, -5603967423109760, 5709959532279360, 0, -6136019528010696, 2015197557508980, -4175573061054080, -1739264969201760, 0, 1512742521695784, 6735425570540800, -2004825760921700, 3292143285962240, 0, 6063987702390400, 1763778821821600, 2168028296094480, 2108384615004800, 0, -2226919870159796, 950229875918640, -225888303450300, 7173998349405952, 0, 4436223278505168, -5621613646610300, 1043738654632960, 1305294000225360, 0, -2074858403360936, 1660809137655680, 5758806421402540, -3480685894335128, 0, -1235796131543040, 1017261985825260, 2456436673110160, -1880222402597480, 0, -894581059929360, -5396389296246960, 1295147943531720, -12135878185974272, 0, 7569782315875064, 1854658273994240, -6074202032389760, 2923066331835272, 0, 5458273241287064, 3014569345363200, -1397563833856960, 2703025090920472, 0, -15175965346475776, 3789763407256220, 6053800457524480, -110282312263112, 0, -2990787316303716, -9031909432548240, -876894192538500, 4828371787798272, 0, 1421862364413920, 3829100524464740, -9545188984179360, -7868780289345280, 0, -3058038421761312, -6855497316137600, -2555851599246980, 6573361662308720, 0, 5851258272550144, 1131598228901180, 2956005191135760, 1515103560763960, 0, -5889426489171676, -10274356510236960, -3979794314586640, -8179944489743040, 0, -41389937912456, -2867385475416120, 15467593493397120, 141173867245768, 0, 2177056780943488, 278730004546560, -1151793101483940, -16389736659637928, 0, 11708654105825472, -880995689947380, 13948386283507600, 2810278950378072, 0, 301520572031384, 5167748505300480, -518013310782420, -3379008048782080, 0, -921863361320400, -5857609071880920, -6859698035311360, 4845364337948008, 0, -8405992332561616, -2109425739623040, -4305827112224640, 11343599520476072, 0, -1220513620560000, 3953563801533320, 9402856979111000, -8201871279032472, 0, 2192065068905204, 15496613452029920, -6368812068258640, 11045423259123712, 0, 2979776253528984, -512591504610600, -6204092418398720, 6849760988390060, 0, 2482122379485360, 7088742760017600, -6915899742198480, 1202498774123424, 0, -6219584145506560, 2294898703953440, -26543687098036320, -2251459973492880, 0, 2048798080971384, -6576103403505180, 5046555664159240, -7828998205053568, 0, 4253748698140472, -1997555212418380, 8015582000177280, 5922091780582474, 0, -1710830244584696, 2577324199412480, 12176253440049980, -4051160590048728, 0, -18411452585227776, 1939129198945920, -4571238446439560, -9060621062469160, 0, 7866500560798880, 17642566679138160, 11017868390191100, 36801737808549120, 0, 11270895434173144, -4542238674840180, 11399913056061440, 8468193918052872, 0, 804212839315304, -3113898318967040, 4542290406445440, 10774051109967760, 0, -2521353803619840, 12717323410097500, -12272228237108560, -13116771930710784, 0, 12228182972175924, 8547735088473200, 8078490119702280, -28146166997604608, 0, -14221405350374376, -9759800442119440, -13450475536793600, 7019915104463620, 0, -3444111404640216, -23266085381717120, -16693426527176340, -4018362665792392, 0, 27397041305762880, -9355106324187120, -15115770761009880, -9498349971956560, 0, -8433120967791872, -13154340155524080, 8516987372306800, -16749965244125824, 0, -22729291812141312, -3332377965101420, 19872526937996160, 2934491458298408, 0, -13107815800544136, 6512644994012160, 1756304471853880, 6727383516593272, 0, 22887128156147200, 21031064578785340, -4371909364130880, -4058031119033128, 0, 6320197984238580, -10085894519718360, 1563482180827520, -22072819148260608, 0, -55583200928974752, -22681482894123880, 29104458438588480, 15857486067699860, 0, 26351557294576224, -7995295757057280, -9526601850312560, -16190067376238336, 0, 8113487928518144, 2935868448575920, 11702820062361880, -3193906260998472, 0, 30553856882534244, 2628639716659920, 15925384903966460, 22919906143460160, 0, 22206939771948960, 10140250428082820, -4905310819843200, -7997157752246220, 0, -8965621890981816, -6904610602065920, -3393173089165220, -13099522037122720, 0, -25036506661703680, -19484453865206880, -13656108679775440, 18538291468703840, 0, -13589270184238658, -8621620807164760, 21728728904513640, 19694259680602112, 0, 8699176753432744, -23794949499834300, -70123224181610240, 1565300876936328, 0, 1388251493736744, 35868487404730880, 7038410049220620, -6290220248431536, 0, -37598132282713920, 38169790670527100, -4912152704115200, 4366388187980360, 0, -12515560894425072, 31834606119216240, 5517034623352540, 2431148739537920, 0, -9773172864171176, -8540029664704300, -19102905446929920, 19378590898306560, 0, 28285337794434264, 68905300954334400, 19297658649258460, 27967163755571040, 0, 54492478891542784, -5664521812676580, -13168879328987680, -30126047920994712, 0, -9785070032172836, -12327275379947740, -40997768707972420, -14051751672371968, 0, 23268997122902904, 25033602940550580, 56454449476817280, -9553453677268728, 0, -8661953697251776, -31311002542375040, 10534099242626960, 52492565788663600, 0, 361096828047360, 17235438308130480, 62636156943614200, -8498454082485840, 0, -27794447457160216, -51517631182565120, 5598604057466640, 57976986040061760, 0, 61379378306078368, -56213124353406300, -35495778001187200, 12327601701774108, 0, -29245244707960376, -9746632773729280, -30995821176435840, -70125313500582728, 0, 211873268999040, 28444497118012800, 8207984561966560, -23588341431136480, 0, -18161579389707016, 52619581735864440, -57081891303356720, -36453922621648896, 0, -30138104179697736, 15437961645318700, 24282557158627840, 13571892856623980, 0, 4969476652614760, -30058544929994880, -33647754322031760, -4983037505487128, 0, -37270522783001280, 34199033144083980, -1463522583636720, 37339116855485608, 0, -7295743815941716, -52162019150389040, 22893969441870120, -40825516443466240, 0, -17043403968401152, -43870952089780860, 40214220047139840, -56462184446669272, 0, 8643770503800584, -9204683273688960, 11569188399826220, -8028663634739432, 0, -503425447866880, 26484762488648960, 101730697224390240, -952869037503528, 0, 41831827162469986, -119864464503907760, 2312655464008980, -12560031147809408, 0, 42207647138761248, -3096091900413340, -40067097246514080, 5006373328596640, 0, -14717205069319056, -77803329943346560, -11455857544703280, -36095905128627928, 0, 14579948095216384, -35555126501297380, -58489872087954800, 50328285932311680, 0, 50895665139849620, 98660650235450240, 32832902968479180, 23153377829646720, 0, 22938768876763280, 12724156863898800, 14661842007887360, 18003736124720808, 0, -21300659650645016, 93148156748528640, -53715455075576160, 16577536364892384, 0, -95803386541575936, -23301634781464260, 74456703192222800, -60382311169209680, 0], "weight_parity": 1, "has_non_self_twist": 0, "level_is_prime": false, "level_is_prime_power": true, "level_is_square": true, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "5.12.a.b", "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], [10, 3], [110, 16], [3488, 60], [0, 0], [30092, 490], [-28950, 528], [123120, 4920], [-10423, 3520], [0, 0], [-309088, 26400], [963520, 62408], [-1707130, -12864], [667236, -81570], [0, 0], [3002816, 295680], [-658970, 126528], [6274010, 3931], [2662660, -274560], [0, 0], [1918092, -405120], [44745920, -663264], [-29471970, 33456], [61090080, 2511120], [0, 0], [-40380868, -5250030], [13384580, -2613920], [-81842880, 104664], [47070190, -2298240], [0, 0], [122271732, 7207200], [313650560, 1889088], [221129920, -2041408], [222679036, -711630], [0, 0], [91209376, 11652380], [-10501610, 19033728], [-470876120, 5242380], [-312101996, -28729120], [0, 0], [-372871658, 22651200], [-714896520, 1703076], [-314975050, -13909104], [-121362944, 73537920], [0, 0], [-234097428, -88081350], [701030770, -20505072], [3187761280, 80569856], [-970838707, -30571200], [0, 0], [1150279892, 3374560], [-6420660800, -147297432], [-569160290, -186753984], [-4602577240, 14014540], [0, 0], [-1995276960, -77426640], [-2360455240, 12400960], [-3693708980, 118228170], [3658757780, -175817280], [0, 0], [-758212838, 53568000], [14282163720, 438887196], [1424316090, -107407344], [409765888, 354289920], [0, 0], [-1487732096, 642975680], [-7867145070, -91691472], [2286887360, 401791464], [-2918597916, -467871360], [0, 0], [16469235772, 54804000], [9177033840, 382101240], [14991424430, 339617856], [34384099036, 158832450], [0, 0], [-662696320, -797905680], [17367374400, -927478464], [-55178185400, -1223597188], [-1651411560, 575636160], [0, 0], [-21942215899, -696935360], [37315257820, -892102974], [-6649551210, -1100818224], [-7991243904, -1297973040], [0, 0], [-28353046948, -1084016190], [-17032470460, 500316640], [40397437440, 1729655040], [-6337385430, 1455281280], [0, 0], [45318929532, -528951840], [-101585785920, -1651623672], [83100271320, 2749139712], [-30144882764, 1898041590], [0, 0], [52757708032, 5226208640], [1540351870, 4545870528], [-65103401470, -3218228121], [59350136224, -1363156960], [0, 0]]}