# Stored data for newform 97.8.h.a, downloaded from the LMFDB on 24 September 2025.
{"Nk2": 6208, "analytic_conductor": 30.30134747195981, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 97, "char_degree": 8, "char_is_minimal": true, "char_is_real": false, "char_orbit_index": 8, "char_orbit_label": "h", "char_order": 16, "char_parity": 1, "char_values": [97, 16, [5], [1]], "cm_discs": [], "conrey_index": 8, "dim": 440, "has_non_self_twist": 1, "hecke_cutters": [], "hecke_orbit": 1, "hecke_orbit_code": 481170554977, "inner_twist_count": 2, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 97, 8, 1, 16, 0]], "is_cm": false, "is_largest": true, "is_maximal": true, "is_rm": false, "is_self_dual": false, "is_self_twist": false, "is_twist_minimal": true, "label": "97.8.h.a", "level": 97, "level_is_powerful": false, "level_is_prime": true, "level_is_prime_power": true, "level_is_prime_square": false, "level_is_square": false, "level_is_squarefree": true, "level_primes": [97], "level_radical": 97, "minimal_twist": "97.8.h.a", "prim_orbit_index": 8, "related_objects": [], "relative_dim": 55, "rm_discs": [], "sato_tate_group": "7.2.3.c16", "self_twist_discs": [], "self_twist_type": 0, "space_label": "97.8.h", "trace_display": [-8, 96, -8, -8], "traces": [440, -8, 96, -8, -8, 0, -8, -8, -13424, -1672, -8, -18952, -8, -35264, -99880, 0, -7504, 103208, -157440, -163024, -8, 0, -24864, 131064, 622480, 545952, 541728, -390928, 569064, 624992, 794608, 824776, -883792, 1648632, -2744016, -12317200, 3569744, -8, 616104, -3314696, 811784, 2239480, 29216, -198656, -6587360, -8, -2112824, -6598728, -5733648, -813224, -3365640, 2658616, -3485560, 12041400, -8947976, -8, -8, 13776824, 1676992, -5499800, -10895104, 15252976, 25948152, 131064, -17361184, 48819920, -19791704, 13118208, 6247272, 27438344, -16305664, 13210616, -16094504, -19490184, 0, -37511768, -8, 2239480, -9349400, 3392088, 0, -12587776, -2546576, -45237664, -10401808, -116319448, -13419368, -54022152, -17892288, -30251528, 0, 38536992, -10997592, 78366136, -66954656, 103569392, 13098752, 212211344, -243024, -55364616, -17235552, 54609304, 0, 276087008, -61814672, -61409672, -45317616, -41448032, 13930728, 119040480, 219871472, -101988608, 0, 244872976, -49131384, 42119776, -10743128, 3148200, 0, -240608528, 260449488, -37901960, 218580600, 203420664, 234461968, -251365040, -65249360, 113602664, -87762912, -175516040, -67411560, -216317968, 268731440, 132164664, -422267272, -327398528, -93660144, 166929616, -5190792, -422789752, -89132040, -425834376, -173436280, -234387520, 4113416, 415122608, 235732016, -411990872, -108088448, 184907088, -478636208, 255479880, 6501240, 922486544, 117272128, -293380488, -105456192, -252435984, 512085072, 688760824, -324618296, -191783224, 224532336, -703232208, -1065303192, 195985272, -104494896, 171447584, 395882864, 638394272, 78029168, 0, -71473048, 1289680112, 458681088, -895401584, 584660816, 0, 513785728, -2107149592, -934516416, 154728824, 391506000, -542001800, 666417144, -963160144, -363168072, 0, 1494842720, 2249664280, 396544608, -124494616, -2589419168, 539746480, 2520601584, -345867104, -356442080, -55794568, 628204696, 0, 103863288, -930843488, -1785422232, -893919480, -1227786192, -1529470688, 538069888, -2353275608, 18191192, 0, 951905432, -517111112, 99474120, -1390139072, 1795557696, 0, -1209508232, -1295295040, -152432736, -790804176, 480767264, 1140056304, -342189752, 3271958064, -4391023408, -2602351264, 1694066296, 620614984, 448738688, 3416037360, 4097715624, 1590521128, -3119473136, 4184570800, -631439432, 5379442576, -3023830440, 181340552, -1385812112, 2966257520, 17010896, 1655784616, -500090200, 2284940224, 462783432, -1564968104, 2519393472, -1351145328, -2680728200, 1872736736, 132860408, -2592155168, 369990144, 1345665288, -2469102064, 671088624, 226553632, 79014280, 285689848, -4704714576, -5550953152, -44142480, 6332003016, 4028159768, 2831117472, 4032638072, 4483404472, -447220744, 0, -6971142648, -802595840, 1245959328, -2458079408, 927567888, 0, -1941094056, -2223079320, -3274388360, -4794965384, -3277349616, 527004328, -4702217880, -4109287408, 3514461624, 0, -848115184, -4067576592, 8844614544, -2178854976, 7076832496, 4529104992, 10742616592, -5960737320, 4213760352, -1197815544, 4688802000, 0, -3330028512, -930669040, 3077329912, -5986105920, 2403754144, 3107422552, -4695300848, -9398882904, 1207611928, 0, 75758896, 1595121784, -8235408816, -6843232528, 5187877640, 0, -8783036520, 11843476464, -2328410120, 7670036760, 3909528376, 8583166968, 106930456, -3741691832, -3169574768, -342943112, -13029746840, -5238470048, -9160942016, 7429124720, 8521641976, 9570733720, 8721840808, 127708952, -3336361112, -5039846592, -8539462432, 2243375400, -8515127408, 2417828032, -6578658096, 10565347488, -1305494136, 8262869768, 1631232816, 502670728, 14407272744, 1512808784, 974131968, -3815753216, -27005996968, -6532334680, 3587340088, 11768662888, -1674663840, 9679883904, -7579513216, 5012046768, 2270204656, 6613383400, -18525777808, -4907317728, -135703112, 4513221944, 17520505208, -9378936816, -5152031304, 5811653624, 0, -4460854048, -14213423200, -12444423528, -35044539672, 3246818184, 0, -7498481128, -10932866352, -388844288, -12322764848, 11902255208, 13763926216, 260486264, 206630400, 18552762056, 0, -3620617752, -11484709728, 6604964664, 3232948112, 25266745584, 27708070168, 2967726944, 6407540096, 6777261816, 358440456, 21838364312, 0, -8580599464, -24274009728, 31485552192, -9301293240, -8620592848, -3473388784, -9465466808, -21862071928, 858998656, 0, -12745871416, -10672691520, -5795091688, -26620362952, -9550448648, 0, -11842952216, 10976397224, 811357408, 36431618816, 22510442992, 40353912720, -8870479952, 24761224024, -6355650896, 6635651608, 12774924744, -3489366200, -24605642240, 3158093616, 22078242112, 29091604328, -13834696064, 9952658888, -38285973008, -20256199456, -17778022248, 48280214280, -22408864032, -6560592888, -15737136280, 27991514000, -634949728, -13100508264, -22998057056, 12528448456, 25491454072, 21531790320, 4947449280, -51475266464, -32636752832, 1808543520, -11241513472, 29274335224, -3299360576, 60691365424, 8867827600, 25723823528, 24889771392, 9610866184, -38382974632, 15410400536, -1585862984, -1807903920, -3128297888, 24339949016, -35051902872, 33896139488, 0, -56796993632, -33724244976, -9378682056, -22143177160, 28529798512, 0, -57807283080, -46045373608, -2686684688, -40180512312, 22767854360, 26798251392, 33504010824, -13173562040, 44847762672, 0, -60736917984, -8452840040, 24943768888, -7045783880, 1951970800, 41820309160, 53383134320, 34834203496, 15577395192, 2676661896, 42265154424, 0, -69713487416, 5376708152, 25022967608, 8273240696, 19169945440, 4045699256, -20307417472, -13039205272, 31449933488, 0, -23726589976, -13667460384, -111669842248, -4146509456, -27052336016, 0, -44402741144, -2347135608, -4086782848, 16028903696, 62308424408, 29091757640, 4522200824, -41372538616, -2351248328, 21262525392, -21765436832, 29840339840, 19141274640, 14829513248, 99596727160, 40367797664, -21568876744, 40788001056, -40248150960, -34642415792, -51052704552, 31020855088, -46976475808, 30814270248, 58882972000, 6635425080, -32739143672, 13826425016, -89852817392, 36689331384, -23034279976, 15154488368, 45379652856, 34823239312, -58755083256, -49632856000, 21082470296, 47748513536, 16931985168, 59986673424, 34373537768, 91679632536, -19997684360, 1318179808, -226659423376, -36119987984, -87840558192, 17895758840, -12272947288, 69667333872, -94254284224, -15334999840, 0, -1935361464, -32059895016, -9117141208, -30484692472, -1852725056, 0, -41235923576, -86023226072, 14671949816, -139002507920, 33415647640, 176644397664, 97678105488, -126837912816, 99355416768, 0, 14217903752, -1032586888, -58828021768, 30476749640, 66940664240, 191028556688, 53129055536, 138740360480, -108211595384, 33673975312, 25176289096, 0, -11293388928, 28033285184, -6102147568, -110297174248, 75698855616, 8003607664, -53670162920, -58176172216, 3664824536, 0, -49468555560, -114649163552, -99664936712, -56980388944, -110971524696, 0, -35113806712, -77071136056, 1040480360, 2795726200, -5514177896, -61401085368, -24204542504, -117802084392, -2358678616, 32959942264, 11822288232, 26416973080, 69465268704, 105907972320, 41653006744, 137274463000, 16624630872, 23470310968, -30412929424, -77947157760, 63013798568, 52065680864, -143158227760, -49632624152, -27758519272, 74913001600, -106789421096, 25769373384, -11666762368, 34178950976, -15486695720, 63372674904, 58804374424, 168842354456, -85380787280, 93091872008, 112665247568, -122871831704, -63870359936, 206015473648, 146907555656, 165877241944, 31416833632, 131575026840, -191066976416, 43823280160, -117618845448, 153350847832, -61528643632, 145756830936, -145109190200, -137845129296, 0, -120647389832, -20436329920, 23466576240, 15363438144, 8075124496, 0, -129646887640, -128821752048, 50391625144, -141816758208, 167382564208, 221217505312, 116411377200, -61737044464, 236728002448, 0, -64560136888, -61499135952, -37802276896, 6671686264, -68998039056, 175383355576, 174392227296, 207759713128, -151487394976, -47013693288, 137856844840, 0, -162682128912, -34189289432, -63359012632, -92030380240, 213587541376, 5763928592, 53295399632, -7011973968, -37487232456, 0, 47870206912, -64838389808, -210418026272, 14274468176, -142159985112, 0, -88178987336, 19289365112, -218324508536, 44390512376, -25576550256, -113779087288, 137423082664, -61755893320, -568886200, -36662392344, -5460899520, -93515710224, -115776854336, 6253849552, 97143201272, -11746584896, -65978261952, 169725582840, 186749064080, -85554570952, -37991473160, 51556425880, -137136355144, -85957808448, 293353493440, 135152769368, -213000604624, 32637143200, 31731035248, -8978042064, 134493585896, -27864053408, 153894168232, 162599132816, -128388941240, -55834484008, 175599767136, -21600829368, -377124075584, 205853633712, 131870012208, -19554577432, -151789306688, -10817112608, -337869329568, -263796042896, -227629087576, -42227697752, 149928884320, 13798900520, 22433300912, -44951571344, 0, -60064305816, -62955131840, -88436403152, 15748134200, -117042081880, 0, -159196770264, 50797391800, 121448335456, -317480176200, 84265987464, 313652543512, 136053306008, -293457441440, 221614617704, 0, 15738789792, 130086952512, 250115680488, 414452305352, 174113675680, 118773593344, 199640658864, 146235225816, -289234677416, 265026196376, 139310455552, 0, 95605980912, 449116303144, 178112875720, -260103458608, 44124695768, -520238616, -60800316736, -116226613584, -84358944832, 0, -40449514840, -269836570456, -327532468816, 66590501912, 8041792976, 0, -36349779016, 33102879160, -179717131480, -52298746848, -284569451952, -186443357784, 26358143128, -93220198152, -61595936408, 123842098424, 105315075712, -630921553144, 168445529584, -35659635200, 158387884696, -63488121384, 286095146544, 463543243552, 117259976, -250125899216, -162904946968, 454607100400, -46910013376, 45186447528, 341756748616, 579266210064, -242264897048, -170576260200, 290001185400, 3475224016, -78439617160, -4055930680, 158520087400, -51750060440, 74429671728, -269250220528, 188543344520, -168428681760, -332713292144, 120081594992, 66859669128, -327335158120, -182774604312, 202029452152, -290953960760, -87329340840, -82396713552, -349815360992, -32593336464, -85998747928, -226176143512, -254185148352, 0, -659206318688, 33871125888, -429871131536, 284600141264, 63760149336, 0, -410156195256, 33160999704, -139545221472, -508881659344, 420177473696, 37599969184, 133797638944, -185380103688, 451835440896, 0, -348039899192, 109722008088, 389478196896, 442002238544, 34268050048, 114320048408, 266097058864, 55089523840, -641750188344, 309379933752, 431711659792, 0, 214354206696, 342742753424, 479358061616, -575101799272, -151460053168, -29262766248, 135933179056, 166877004184, 456708320768, 0, -37555942480, -245701318240, -355289836272, 391997250864, -622926980096, 0, 38640979520, -71384040528, -343828515064, -108869706960, -1032040062472, -455752964464, 399154050544, 189928864344, -299397858504, 180651314944, 1029856150832, -514376424064, -278543146288, -323955618816, -219288572280, 59238693128, 70603897808, 369458375256, 202328907040, -128978388120, -616010149464, 777912739512, 416023557976, 7176881560, 719808409496, 693691456520, 89066421960, 116477224440, 672224980656, -265318885408, -50854556816, -93961628752, 981712314360, -236770076840, 283517510848, -410179744624, 46452647648, -84272689216, -83433090624, 601966402064, 137929462456, -147536818248, -418537082448, -9240254608, -655323429920, -167401604448, 172351578080, -301102505368, -107985685840, -310992770624, -157100097584, -197981451552, 0, -560709896376, -310986705968, -262301858936, 275109967520, 166233577576, 0, -167140746224, 288666503784, 201489729072, -925029815624, 246960934848, 884877311408, -6427788320, 333937013864, 964903454728, 0, -336571861744, 469779178264, 411343607864, 1384284843248, -325062719008, -118198337408, -338976046352, 221359983688, -732671078264, 552197425384, 894660011768, 0, 196776187768, 746348047592, 389231194056, -994743521184, -446541231104, -243727250784, 271768801752, -485965336736, 183440589368, 0, 216626396864, -1071089817664, -398705762616, -76844927888, -486474999832, 0, 319433183216, 244706769272, -323445268168, -61517897032, -746668943192, -535940962872, 495500596280, -204882965192], "weight": 8, "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, "field_disc": null, "field_disc_factorization": null, "field_poly": null, "field_poly_is_cyclotomic": null, "field_poly_is_real_cyclotomic": null, "field_poly_root_of_unity": null, "fricke_eigenval": null, "hecke_ring_generator_nbound": null, "hecke_ring_index": null, "hecke_ring_index_factorization": null, "hecke_ring_index_proved": null, "is_polredabs": null, "nf_label": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp_display": null, "trace_hash": null, "trace_moments": null, "trace_zratio": null}