# Stored data for newform 128.12.e.b, downloaded from the LMFDB on 23 April 2024.
{"label": "128.12.e.b", "space_label": "128.12.e", "level": 128, "weight": 12, "hecke_orbit": 2, "hecke_orbit_code": 4503874706604160, "dim": 42, "analytic_rank": 0, "is_twist_minimal": false, "char_order": 4, "char_parity": 1, "char_degree": 2, "char_conductor": 16, "char_orbit_label": "e", "char_is_real": false, "Nk2": 18432, "analytic_conductor": 98.34792711162737, "level_radical": 2, "self_twist_type": 0, "is_self_dual": false, "is_self_twist": false, "is_cm": false, "is_rm": false, "analytic_rank_proved": true, "char_values": [128, 4, [127, 5], [4, 3]], "inner_twist_count": 2, "level_primes": [2], "conrey_indexes": [33, 97], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 21, "sato_tate_group": "11.2.3.c4", "trace_display": [0, 2, 2, 0], "traces": [42, 0, 2, 0, 2, 0, 0, 0, 0, 0, 540846, 0, 2, 0, -6075004, 0, -4, 0, 11291290, 0, -354292, 0, 0, 0, 0, 0, 66463304, 0, -77673206, 0, 343549808, 0, -4, 0, 434731684, 0, 522762058, 0, 0, 0, 0, 0, -3824193658, 0, -97301954, 0, -4586900144, 0, -8474257474, 0, -7074245796, 0, 2100608058, 0, 0, 0, 0, 0, -955824746, 0, -2150827022, 0, 27758037828, 0, -1884965292, 0, 3186519018, 0, 16193060732, 0, 0, 0, 0, 0, -28890034486, 0, 22711870540, 0, 48011833792, 0, -90656394430, 0, -55713221118, 0, 84575506252, 0, 0, 0, 0, 0, 147369662716, 0, 69689773328, 0, 375702304500, 0, -4, 0, 286271331106, 0, -259392429094, 0, 0, 0, 0, 0, -507649008770, 0, -178148494454, 0, -1573165241996, 0, -10404395228, 0, -1135757971180, 0, -384697246078, 0, 0, 0, 0, 0, 2038831087776, 0, -406541918672, 0, 2043733091856, 0, 324484802380, 0, 2303154810442, 0, 999084270588, 0, 0, 0, 0, 0, -1833111997610, 0, -2682469964944, 0, -3054573475844, 0, -764380884956, 0, -2019561811226, 0, -1457913931374, 0, 0, 0, 0, 0, 1884324346160, 0, 1953853768738, 0, 1627904357652, 0, 7909306968, 0, -935806556158, 0, -2863504943732, 0, 0, 0, 0, 0, 2782787819818, 0, 6517651362818, 0, 4010645423604, 0, -3210795459156, 0, 1838764375970, 0, 925415188594, 0, 0, 0, 0, 0, -4510953457468, 0, -6799509319568, 0, 2320084436208, 0, -6031855023780, 0, -4450829445148, 0, 14344733881058, 0, 0, 0, 0, 0, -1195072986932, 0, -6347118962752, 0, 22276854442740, 0, -3634957661268, 0, 7813019109586, 0, 1782542921116, 0, 0, 0, 0, 0, -21415967537928, 0, 16064766083724, 0, -36698843124560, 0, 8198629707182, 0, -27608469430174, 0, -19180438650222, 0, 0, 0, 0, 0, 39439221551504, 0, -9077106588800, 0, 1961390001472, 0, 12236213742748, 0, 48092123362450, 0, 7438166861510, 0, 0, 0, 0, 0, -45141329547354, 0, -18712653657796, 0, -95849282758280, 0, 34751786894916, 0, -28048365120300, 0, -9009608167606, 0, 0, 0, 0, 0, 33949060617224, 0, 60155348636810, 0, 77884697989040, 0, 57788042707704, 0, 43113263811546, 0, -60665705519414, 0, 0, 0, 0, 0, 10282140704398, 0, 44609396625092, 0, 102949274050880, 0, -6550441771106, 0, 50313093321116, 0, 35425735254306, 0, 0, 0, 0, 0, -24412489855732, 0, -104281710326692, 0, -175311322860204, 0, 20162753693236, 0, -84462050685846, 0, 222942668364924, 0, 0, 0, 0, 0, 153898452236740, 0, -85701939982854, 0, 274182673128460, 0, -89263762687652, 0, 68002789351340, 0, -106012540116214, 0, 0, 0, 0, 0, -347701004114514, 0, 246796380952246, 0, -421578284725612, 0, -159177993643724, 0, -434333132250764, 0, -325641599319184, 0, 0, 0, 0, 0, -1879554964874, 0, 147927984022282, 0, 420057276833360, 0, -209161876993372, 0, 251555928078708, 0, 168334008464264, 0, 0, 0, 0, 0, -115610220929474, 0, -413664672405704, 0, -129727401064368, 0, -134439893558016, 0, 303585855771252, 0, 672624931980858, 0, 0, 0, 0, 0, 99733006102678, 0, -595183521148944, 0, 360591463424480, 0, 229516838265080, 0, -245416020050550, 0, -1581467467478, 0, 0, 0, 0, 0, 973536822541248, 0, 539134180474746, 0, 16202885022296, 0, 149793231986844, 0, 426561375935664, 0, -1377873570697286, 0, 0, 0, 0, 0, -154665218830736, 0, 1144901821182908, 0, -432324938318076, 0, 494868771067564, 0, -1122398294676710, 0, -732892366881422, 0, 0, 0, 0, 0, 697799793618396, 0, -961414305216820, 0, -394170737520000, 0, 417189325577052, 0, 931996852670356, 0, 1084374115557804, 0, 0, 0, 0, 0, -1531372917765362, 0, -2162592812965304, 0, -713663170123292, 0, -1015068352326980, 0, -475429883398624, 0, 1695536315578524, 0, 0, 0, 0, 0, 1157856086674672, 0, 834973322050458, 0, 185679999272352, 0, -52658636681056, 0, 1636332474858346, 0, -2095432779006052, 0, 0, 0, 0, 0, -1880343570991294, 0, 3808379134293958, 0, 1837298002327600, 0, 643732834404004, 0, -2417131645074728, 0, -1458095230209972, 0, 0, 0, 0, 0, 2184482925167222, 0, -1596115808299524, 0, -1473703903507516, 0, -1904453668009064, 0, 2448803081042834, 0, 4902463380135948, 0, 0, 0, 0, 0, -4473645275628762, 0, -3244016172915662, 0, 1359803522748976, 0, 2516043259641072, 0, -3547238296654252, 0, 1565465950164496, 0, 0, 0, 0, 0, 1662063673619646, 0, 1797169245657412, 0, -1866589788169952, 0, -740582752728610, 0, 3937264165780090, 0, -5124538635152064, 0, 0, 0, 0, 0, -1198865348512470, 0, 4786338506245618, 0, 6566115691073316, 0, -2880203913258844, 0, -2581695924673302, 0, -1356892809238670, 0, 0, 0, 0, 0, 3196778650301748, 0, 794873109859026, 0, -8972011378151700, 0, 4457673585679784, 0, 157399897956858, 0, 7222512582227220, 0, 0, 0, 0, 0, -2829062519091090, 0, -6572167184489968, 0, 14035246893786596, 0, -2296485979291724, 0, -1213119519219524, 0, -818326672482676, 0, 0, 0, 0, 0, 3961165179608830, 0, 4891986523550672, 0, -22185834712207420, 0, 4209016104710292, 0, 4300675051632632, 0, -8538640004158228, 0, 0, 0, 0, 0, -3263749523345286, 0, 2494433677644146, 0, 17918576444747840, 0, 3879589195895384, 0, -4477307167229680, 0, 53929856318546, 0, 0, 0, 0, 0, 6112252485501326, 0, -11155464555792976, 0, -22544976606082096, 0, -3400654980630294, 0, 14011506403038732, 0, 4062799016954044, 0, 0, 0, 0, 0, -9008218920818608, 0, -5528752658866874, 0, 27193082046154324, 0, 3143457023692444, 0, -10561452461180534, 0, -2028361333001956, 0, 0, 0, 0, 0, 21033665636746656, 0, 9721323695522474, 0, -25317863418427308, 0, -7842252570832680, 0, 10110052265321378, 0, -3761802086667662, 0, 0, 0, 0, 0, -21525551328314980, 0, 2021286537310928, 0, 16839025265851356, 0, -9548706764681892, 0, -39029300554305256, 0, 5651855378160458, 0, 0, 0, 0, 0, 23326521958261126, 0, -11595798952372272, 0, -29711400015224220, 0, 6147218977301636, 0, 38476671920824018, 0, 501217910101644, 0, 0, 0, 0, 0, -52821784161167752, 0, 8424165833219138, 0, 39071567479802404, 0, -15349687350889120, 0, -44716421451686604, 0, -2492797984097798, 0, 0, 0, 0, 0, 55357489338143996, 0, -703727019603328, 0, -20507169127071808, 0, 9179490273350232, 0, 59955129477257020, 0, 7341949407207090, 0, 0, 0, 0, 0, -45127960030300908, 0, -4120606554821414, 0, 80351383375854028, 0, 13491971823492428, 0, -50583657913028974, 0, 2693284277906044, 0, 0, 0, 0, 0, 76643185477293778, 0, 19802854996179244, 0, -58936171941684864, 0, -32320315878989940, 0, 63377511275144372, 0, -3668925299233102, 0, 0, 0, 0, 0, -66002193485702580, 0, 9303789871461620, 0, 58155858137856012, 0, 23826860051373020, 0, -80887105588321132, 0, -6511280906351174, 0, 0, 0, 0, 0, 57147614905121696, 0, -23898060820597412, 0, -137811417277871856, 0, -18953649689160428, 0, 66663411892419682, 0, 16422626348047996, 0, 0, 0, 0, 0, -114003233520573740, 0, -19643718705875502, 0, 99875227192862816, 0, 7476600962575272, 0, -81915117580083272, 0, -1169586156770184, 0, 0, 0, 0, 0, 83123600853907390, 0, 28677759759441040, 0, -142705831633158012, 0, 48681411838768828, 0, 138719175604209444, 0, -46802716913451174, 0, 0, 0, 0, 0, -88164211639032018, 0, 23125516479209522, 0, 207453599480484340, 0, -12057335252562700, 0, -119582164862885084, 0, 13859331424044608, 0, 0, 0, 0, 0, 147045265928450328, 0, -49507371041587878, 0, -219144349469912100, 0, 23167031916883644, 0, 107898734601718148, 0, 51098005411279674, 0, 0, 0, 0, 0, -129072250962449642, 0, -32683771680957824, 0, 205570988610806448, 0, -4254479619656364, 0, -170616462954846298, 0, -9311612183527808, 0, 0, 0, 0, 0, 180161917896087584, 0, 43861528101809274, 0, -326948721762201020, 0, -15959506457175852, 0, 163096703548360714, 0, -89446720128805252, 0, 0, 0, 0, 0, -215052809784586170, 0, 57290731079644848, 0, 335009084706063428, 0, 38516703639054936, 0, -146810628911789328, 0, 18957390023099228, 0, 0, 0, 0, 0, 149847476661080902, 0, -31698539032342106, 0, -319593717975956048, 0, 10268800877862908, 0, 266238378371495684, 0, 110593951874748252, 0, 0, 0, 0, 0, -181762890754059348, 0, -43111360396049522, 0, 494644138235278772, 0, -35957428868498756, 0, -206197938344886482, 0, 8982423163541964, 0, 0, 0, 0, 0, 282808342658136448, 0, 70113379159839050, 0, -334765390524814528, 0, 18818569277073248, 0, 190802853408766058, 0, -72922968620164600, 0, 0, 0, 0, 0, -279220977102802256, 0, 62397098316806716, 0, 486676824761816160, 0, -113178931445230614, 0, -382583946642788142, 0, -55932875536687828, 0, 0, 0, 0, 0, 281618931699970294, 0, -12735372782409924, 0, -687269709012922572, 0, -20283076604084228, 0, 327380076485751624, 0, 102247355085901386, 0, 0, 0, 0, 0, -463935509647324192, 0, -142201744452582900, 0, 516355293981024960, 0, -38624648901648388, 0, -438562850821992956, 0, 37305465941818490, 0, 0, 0], "weight_parity": 1, "has_non_self_twist": 1, "level_is_prime": false, "level_is_prime_power": true, "level_is_square": false, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 16, 5, 1, 4, 0]], "char_orbit_index": 5, "prim_orbit_index": 5, "minimal_twist": "16.12.e.a", "char_is_minimal": false, "conrey_index": 33, "id": null, "is_polredabs": null, "nf_label": null, "trace_hash": null, "hecke_cutters": null, "qexp_display": null, "fricke_eigenval": null, "atkin_lehner_string": null, "hecke_ring_index": null, "projective_image": null, "projective_image_type": null, "field_poly_is_cyclotomic": null, "field_poly_root_of_unity": null, "artin_degree": null, "artin_image": null, "field_poly_is_real_cyclotomic": null, "artin_field_label": null, "projective_field_label": null, "hecke_ring_index_proved": null, "trace_zratio": null, "hecke_ring_generator_nbound": null, "field_disc": null, "field_disc_factorization": null, "field_poly": null, "hecke_ring_index_factorization": null, "trace_moments": null, "atkin_lehner_eigenvals": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null}