# Stored data for newform 16.12.a.b, downloaded from the LMFDB on 23 April 2024.
{"label": "16.12.a.b", "space_label": "16.12.a", "level": 16, "weight": 12, "hecke_orbit": 2, "hecke_orbit_code": 4503599828697104, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 1431951470455822875, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[3, [-36, 1]]], "qexp_display": "q+6^{2}q^{3}-3490q^{5}+55464q^{7}-175851q^{9}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 2304, "fricke_eigenval": 1, "atkin_lehner_string": "+", "analytic_conductor": 12.293490888953421, "hecke_ring_index": 1, "level_radical": 2, "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": [16, 1, [15, 5], [1, 1]], "hecke_ring_generator_nbound": 1, "inner_twist_count": 1, "level_primes": [2], "conrey_indexes": [1], "field_disc": 1, "field_disc_factorization": [], "field_poly": [0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.024", "prec": 17}, {"__RealLiteral__": 0, "data": "1.002", "prec": 17}, {"__RealLiteral__": 0, "data": "0.064", "prec": 17}, {"__RealLiteral__": 0, "data": "1.973", "prec": 17}, {"__RealLiteral__": 0, "data": "0.133", "prec": 17}, {"__RealLiteral__": 0, "data": "4.867", "prec": 17}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "11.2.3.c1", "atkin_lehner_eigenvals": [[2, 1]], "trace_display": [0, 36, -3490, 55464], "traces": [0, 1, 0, 36, 0, -3490, 0, 55464, 0, -175851, 0, 597004, 0, 1373878, 0, -125640, 0, 10140850, 0, 7297396, 0, 1996704, 0, 32057464, 0, -36648025, 0, -12707928, 0, -13605402, 0, -233160800, 0, 21492144, 0, -193569360, 0, -257786178, 0, 49459608, 0, -221438598, 0, 1697758892, 0, 613719990, 0, -527509392, 0, 1098928553, 0, 365070600, 0, 3277379822, 0, -2083543960, 0, 262706256, 0, 3001908988, 0, -11630023610, 0, -9753399864, 0, -4794834220, 0, 17189000548, 0, 1154068704, 0, -26169539608, 0, -7039021094, 0, -1319328900, 0, 33112229856, 0, 4199910416, 0, 30693991689, 0, 39739936436, 0, -35391566500, 0, -489794472, 0, 10565331594, 0, 76200769392, 0, -8393788800, 0, -25467912040, 0, -69851645662, 0, -104983750404, 0, 74519412606, 0, -78664150648, 0, -6968496960, 0, -78848972820, 0, -70868029994, 0, -9280302408, 0, 19681604562, 0, -111880549360, 0, -241597820178, 0, 562452104400, 0, 71102105405, 0, -7971789528, 0, 298311763500, 0, 190251579008, 0, 61119320112, 0, -114524784988, 0, 404742771744, 0, 44350668720, 0, 117101162394, 0, -989560526196, 0, -18990338112, 0, 820210661512, 0, 47482852980, 0, 39561427908, 0, -797579218418, 0, -1183229001992, 0, -1783278613350, 0, 813731192000, 0, -753512032922, 0, 117985673592, 0, 1778035183296, 0, -834305483964, 0, -75007582560, 0, 1015135845576, 0, 95380364847, 0, -1283254383996, 0, 2894963106966, 0, -2032646058600, 0, 108068723568, 0, 4092633678996, 0, 508615079022, 0, -418680849960, 0, 899673761220, 0, 6054128013400, 0, -704832518592, 0, -2999513064000, 0, -2181925750462, 0, -172614031920, 0, -4774752410466, 0, -295210163608, 0, 618804019728, 0, -754610016528, 0, 772820707020, 0, -5637337101864, 0, 4356574601584, 0, -4768855897804, 0, -942103425888, 0, -5925178533080, 0, -12932030611200, 0, -253404759384, 0, 13932290716300, 0, 9214548039008, 0, 6444591844275, 0, 5854438063236, 0, -14027335387394, 0, 1192040274816, 0, -5296101013318, 0, 1841007778080, 0, 151196774976, 0, 13164628430384, 0, 22589663991378, 0, 3356155022220, 0, -3835260649970, 0, 10025731821688, 0, 1430637711696, 0, -26118547450180, 0, 19138434237856, 0, -1274096394000, 0, -12657981060350, 0, -14297852576592, 0, 2392523547102, 0, -5370231542360, 0, -11438055578780, 0, 380351937384, 0, -8601398737994, 0, 6013709361616, 0, 2743227698112, 0, -21879017517100, 0, -26331197092466, 0, 41001559840800, 0, -51174845289782, 0, -8948955462308, 0, -916844833440, 0, -12281870399472, 0, 68564942414867, 0, -2514659243832, 0, -26847972185154, 0, -10476662368120, 0, -7586683847712, 0, 44043044525392, 0, 94164499185888, 0, 2682698853816, 0, 40588782398900, 0, -6624331875564, 0, -2831909423328, 0, -40285233723624, 0, -21542297569494, 0, 34039365525360, 0, -2794787240634, 0, -8122479415608, 0, -2838563021520, 0, 74001798226600, 0, -50349915290950, 0, -2551249079784, 0, -29257780917888, 0, 44856017296972, 0, 45331957187478, 0, -59989611912520, 0, -52342753988238, 0, 708537764232, 0, -139197930243200, 0, -48719477210160, 0, -4027699776960, 0, -162474635223396, 0, 56070596402598, 0, -17459142704784, 0, 121433098473250, 0, 91331693231920, 0, 20248275758400, 0, -99308194169208, 0, -63238270517403, 0, 2559675794580, 0, 24566183618060, 0, -58096458156880, 0, 38940198896898, 0, 181776594447408, 0, 10633630708910, 0, 10739223486000, 0, -18692162488956, 0, 194563767957820, 0, 6849056844288, 0, 219102152231808, 0, -115561682197440, 0, -298552598917092, 0, 258688254353630, 0, 325089933804400, 0, -4122892259568, 0, -14657687351840, 0, -253970045277898, 0, 14570739782784, 0, 176194300155186, 0, -320334493582400, 0, -107122030994610, 0, -153899379410712, 0, 254652202822986, 0, 4215641846184, 0, 166497880110432, 0, -138692378161640, 0, -35624178943056, 0, 10976383980612, 0, -306791483729602, 0, 92763054092592, 0, -371642124321250, 0, -645047629505040, 0, 29527583814432, 0, 194136614783984, 0, -197020802576750, 0, 1709382707280, 0, 233936009563744, 0, 481833288711576, 0, -193247684973603, 0, 472499076448892, 0, -36873007263060, 0, -28712851863048, 0, -35241370012606, 0, -132199728760392, 0, -42596244071712, 0, -265940685178080, 0, 541522131945818, 0, -128869191658800, 0, -263903025105418, 0, 34496762783632, 0, 29294322912000, 0, 588837802998324, 0, 953370726394272, 0, -27126433185192, 0, 1013568849559568, 0, -267435151042900, 0, -576330519078522, 0, 173689784193632, 0, -354166758658284, 0, 64009266598656, 0, 243782243360380, 0, -842617287500536, 0, -30034997422704, 0, 538407736241004, 0, -137970340871700, 0, 366393288909960, 0, -1451467344818112, 0, 136233889206996, 0, 36544890440736, 0, -488252435324712, 0, -260072749994940, 0, 3433693134492, 0, -488013674701434, 0, -390412265957616, 0, -92734782955488, 0, 274537885761520, 0, -314925217061568, 0, 104218671850776, 0, 1107897067126810, 0, 618140078509580, 0, -73175258109600, 0, -2364448698680000, 0, 74871240197369, 0, -527888697448788, 0, -304229618143044, 0, 275182915141800, 0, 147334812443856, 0, 656064741855212, 0, 761294937204198, 0, 18310142844792, 0, 247329424679060, 0, 565709123299012, 0, 2045151281842110, 0, -99284006133192, 0, 232943831313024, 0, 32388255403920, 0, -1880894854259434, 0, 2332513591023176, 0, 217948608482400, 0, 176230678421524, 0, -68688799921380, 0, 1702411555038696, 0, -491855357914582, 0, -918553298629380, 0, -107982470304000, 0, -1174842742108600, 0, -1538421618029374, 0, -78549327016632, 0, 2204135834486304, 0, 1956608863253288, 0, 843176392421220, 0, -5660273583284, 0, -1701466689276800, 0, -171891086776776, 0, -411514325733262, 0, -1962957844356000, 0, -10627565889888, 0, -3353751804185160, 0, 1025019084513418, 0, -3022702935366348, 0, -248146347863450, 0, 1990791782045920, 0, -27165960595008, 0, -724733548462176, 0, -516975009730690, 0, 27821545452720, 0, -678132802269894, 0, 655793062849004, 0, -407383944374592, 0, 585995551529616, 0, 748346291088125, 0, 156836685657024, 0, -2614170963171300, 0, -336387833915560, 0, -171678812320944, 0, -663978010737920, 0, 1509793762538534, 0, 4601939709606408, 0, -2680164396379006, 0, -163908120381276, 0, -213306427190880, 0, 3113190842401064, 0, 1792151673471952, 0, -465553102003200, 0, 3156735277314102, 0, 399691499608120, 0, 1237818898400994, 0, 2219965096229364, 0, 2945325261081614, 0, 501562465786800, 0, -1412552273386560, 0, -436154684820528, 0, 331723729404288, 0, -6943170615264440, 0, 2039719577287138, 0, 465720463042200, 0, 147928819164734, 0, -3874251674997168, 0, 210759770276496, 0, 4940163148028716, 0, -408683056755060, 0, -504984073946184, 0, 4502720035089716, 0, -2964030774710636, 0, -5822818732407456, 0, 3453566236424040, 0, -2245575606528300, 0, -190659636479448, 0, 845017864698822, 0, -1881167824192488, 0, 66276280010880, 0, 4133144700779184, 0, -6161944565636962, 0, -738558446564016, 0, -7474543952211200, 0, -2862535208676880, 0, 473926623493824, 0, -7674671417903984, 0, -4363028451540672, 0, 813227903689608, 0, 498611112631050, 0, -2553817398932424, 0, -5316526964931363, 0, 17216718259938200, 0, 10663897197233702, 0, -138069383398920, 0, 10261902083158192, 0, -4939672509585788, 0, 360926345580768, 0, -10483772357498360, 0, 2783551472278820, 0, -6988307562207036, 0, -4373279428488480, 0, 9786966289594416, 0, -940267708206480, 0, 4129469216952080, 0, -493316791880914, 0, 688983632562816, 0, 8971679370118762, 0, -3930624415587216, 0, 6223642360591500, 0, 4124256716615464, 0, 3726504971788802, 0, -455687318172600, 0, 1123373503759710, 0, 8544882827420000, 0, -514722692757312, 0, -1615925139290808, 0, -15623319824134432, 0, 172896469027056, 0, 2629756994897780, 0, 13968284524139636, 0, -193328335524960, 0, 1091620515426768, 0, -15978233577259580, 0, -411770000836080, 0, 17722640561243366, 0, -5349393617863200, 0, -1857924126136494, 0, -4202323749202376, 0, -6205342789703040, 0, -309650354567784, 0, -13527097038061958, 0, -11163406521710164, 0, 216493537018176, 0, 2911726139034360, 0, 12389218947445232, 0, -13399981498352592, 0, -12963905005939218, 0, 3202381470941464, 0, -787644630615600, 0, -9928785760151044, 0, 11793494274289990, 0, -947923095328776, 0, 11144069616690050, 0, -3542824101060240, 0, 2962990658822400, 0, 290602147861224, 0, -12015402802124225, 0, -1842294430432152, 0, -332877473316030, 0, 3943607174182920, 0, -322162396643088, 0, -8263971120932592, 0, -15798108662290354, 0, 4478557800146040, 0, 16482619724756106, 0, 62183817984156, 0, -442147334380992, 0, 17713423825522144, 0, -10103421243311340, 0, 2468337926935212, 0, 2507363317993664, 0, 23615589694885144, 0, 12283481741308362, 0, 16545563650764000, 0, 8215556356233942, 0, -966526998665544, 0, -19185753602969390, 0, -10441168811139500, 0, -377159845252320, 0, -9339120463680424, 0, 10552113578099712, 0, 18324435814299756, 0, -3849444927143232, 0, -14283291539696040, 0, 1585549602914112, 0, 3172246414641600, 0, 33235417167928700, 0, 3389921970691968, 0, -1775066625786780, 0, 13597564581061004, 0, -13104313226177706, 0, -24491838693488048, 0, 23724901012037744, 0, 1461196166360400, 0, -6352002674574432, 0, -19471493195311624, 0, -238475947520304, 0, -35953754737559824, 0, 9447354295998450, 0, 13833169555601448, 0, -37246532785572638, 0, 8019316826947988, 0, -1450268414050464, 0, -21128906766766000, 0, -3425214069982470, 0, -775522712501784, 0, -26922797018900586, 0, -7098759883595472, 0, 2459865489886080, 0, 28732237659322260, 0, -9670756222582532, 0, -100612340662824, 0, -17745400909311318, 0, 10468300593360000, 0, -292409258961888, 0, 6494898871020816, 0, 28955481760235169, 0, 13865670719369820, 0, 7614920869112380, 0, -24560234585384600, 0, 2664064736157600, 0, 4691582779295436, 0, -54884985024934944, 0, -1812596950474200, 0, -27787204933173774, 0, 6307545222944376, 0, 12462213942474894, 0, 10951940338723128, 0, 16663885912526340, 0, -1053280113043968, 0, 54425844560969888, 0, -33627950376561568, 0, 1614816622690992, 0, 1030283470991920, 0, 52710991601358334, 0, 3275928189419184, 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": "8.12.a.a", "char_is_minimal": false, "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], [0], [36], [0], [-3490], [0], [55464], [0], [-175851], [0], [597004], [0], [1373878], [0], [-125640], [0], [10140850], [0], [7297396], [0], [1996704], [0], [32057464], [0], [-36648025], [0], [-12707928], [0], [-13605402], [0], [-233160800], [0], [21492144], [0], [-193569360], [0], [-257786178], [0], [49459608], [0], [-221438598], [0], [1697758892], [0], [613719990], [0], [-527509392], [0], [1098928553], [0], [365070600], [0], [3277379822], [0], [-2083543960], [0], [262706256], [0], [3001908988], [0], [-11630023610], [0], [-9753399864], [0], [-4794834220], [0], [17189000548], [0], [1154068704], [0], [-26169539608], [0], [-7039021094], [0], [-1319328900], [0], [33112229856], [0], [4199910416], [0], [30693991689], [0], [39739936436], [0], [-35391566500], [0], [-489794472], [0], [10565331594], [0], [76200769392], [0], [-8393788800], [0], [-25467912040], [0], [-69851645662], [0], [-104983750404], [0]]}