# Stored data for newform 650.2.ba.b, downloaded from the LMFDB on 23 May 2024. {"Nk2": 2600, "analytic_conductor": 5.190276131383225, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 325, "char_degree": 8, "char_is_minimal": true, "char_is_real": false, "char_orbit_index": 27, "char_orbit_label": "ba", "char_order": 20, "char_parity": 1, "char_values": [650, 20, [27, 301], [11, 5]], "cm_discs": [], "conrey_index": 73, "dim": 144, "has_non_self_twist": 1, "hecke_cutters": [[3, [6046717133209600000000, -45276947571507200000000, -645369010948326400000000, 2832063938784473600000000, 18457889447559651072000000, 14186775498096261248000000, 593971481268436778648000000, 1081649845258033241557600000, -3301818501266588950499190000, 7753767883136871020243910000, 16536473230446439551094045000, -100963513471055286099385790000, 272751416709243572554746295500, -66688231920458087075923303000, -2034906396895882802623638792750, 7710036609925775029587485418250, -9103323543562224943273025631975, -18171601270611833438627459650200, 95578775140865963404776372128300, -172440838975300605651303924310400, 94352858467756088071843964787170, 260881589640633261806827129122100, -751002758537078890517082277237560, 937905337386125749758787417242560, -394905892042613898609069004910789, -852067896045131348041343619146162, 2263133996662410597178913826993302, -2997174261341175360058908691155580, 2156963505129818426857090485106967, 508013786785189608277193631174086, -4123773895568247533350407513191046, 6400835415141792161837462482220772, -4647064890059133720774138197610447, -1301552609548571616644573620507846, 8318442963423011163396269631047656, -11136876591055534927199705355975394, 6270922653442596274629222821798385, 3911451473543922690223008331146156, -13293006074230510154431855894762990, 15495035485112490918719566436599458, -8297905887785868895955518674878809, -3217918911718314975857224054373968, 12637240281192498346202969744862882, -15880859863301115956367283461000200, 12515135184207502209579200499090615, -7195306127394540065807307898391184, 3276529515505093390274719182050450, -1752173961353063664115287375722314, 2762935797310777926096235525108687, -3872436875638145810947226360093674, 4158756055770397426037271952062222, -3800140515451070504722142211897948, 2493078893829348139596708842810717, -1505036415499834861880984325944042, 911971644430674938252087629361454, -324846007359275941210959966794276, 347417753854533527956203404623926, -348462617302543057533053863702180, 200432088398179280539099801431752, -241894988485781555480413202234482, 124732801280606519158190403995698, -40597720874879717788142800971352, 45727670948775881517713633987694, 9659440731987299862836664078688, 519823550626419253611119270543, -8201584592652033443960862010668, -5757656560874033364682024792046, -6524594757608955118856176201512, 1717103696891662340013226661473, 1848028824268007222344426695484, 2304542174796374185994219966758, 1221573335984819598634867032700, -391277436275601407463831946131, -495320655058074272553151799700, -498129173925040911540939590158, -171510282893655714035930326314, 57814166866490796207228786321, 77446206006444610980217422974, 65569679536467864357712667056, 18827226760151587982745584400, -3152091170547706384455367620, -6499465669435910732855393960, -4990674262387923342583213706, -1483965681794795297308693736, 92194462603495522068465321, 309478236750515805255660838, 268057096120366971576329626, 73197382348864475697097272, 1676958672025410414445056, -10443949937834432423677590, -10761531866845206429038972, -2565842351948508989630084, -162880474497981906315354, 309291543718517066252062, 380339265577045851737308, 73937629331683576425364, 7355897148224458129160, -7547618566383398538862, -12136962586261379298946, -1729569006186851557710, -304669259271589084657, 125549925784146424918, 343138026101064961650, 22855159775156082510, 12993934041888274398, -1141100741445203892, -8203262473114322338, 111404875725144736, -342376526304017390, 16277796149271270, 181245981038402298, -8351216812359510, 8629944701876241, 335678181840510, -3307503709056394, 284475854152616, -163419951077128, -8962003178470, 54045545503134, -6710332292830, 3110927384522, 56938317440, -729540233240, 102282825686, -45159435892, 344470246, 8055339192, -974115122, 505059340, -11254, -69778082, 7496506, -4151921, 75274, 536206, -40818, 36372, -1188, -3048, 136, -251, 8, 10, 0, 1]]], "hecke_orbit": 2, "hecke_orbit_code": 4505386367320714, "inner_twist_count": 2, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 325, 26, 1, 20, 0]], "is_cm": false, "is_rm": false, "is_self_dual": false, "is_self_twist": false, "is_twist_minimal": true, "label": "650.2.ba.b", "level": 650, "level_is_powerful": false, "level_is_prime": false, "level_is_prime_power": false, "level_is_prime_square": false, "level_is_square": false, "level_is_squarefree": false, "level_primes": [2, 5, 13], "level_radical": 130, "minimal_twist": "650.2.ba.b", "prim_orbit_index": 26, "related_objects": [], "relative_dim": 18, "rm_discs": [], "sato_tate_group": "1.2.3.c20", "self_twist_discs": [], "self_twist_type": 0, "space_label": "650.2.ba", "trace_display": [36, 0, 0, 0], "traces": [144, 36, 0, -36, 0, 0, 0, 36, -20, 0, 0, 0, 6, 0, 8, -36, -6, 0, -20, 0, -6, 0, 12, 0, 2, 14, -24, 0, 20, 12, -6, -144, -54, 6, 40, 20, -60, 0, 20, 0, 52, 6, -12, 0, -6, 28, 50, 0, -160, -22, 0, 6, 20, -6, -32, 0, -28, 20, -16, -12, 12, 6, -70, -36, 44, -16, -8, -6, 26, 10, 72, 0, -52, 0, 32, 0, -56, -50, -20, 0, 124, -22, 70, -6, -18, -8, 8, 0, 28, -14, -26, 12, 0, 50, -46, 0, 28, -20, 40, 2, 0, 100, -50, -6, 16, 50, -70, 6, 8, -48, 56, 0, 88, 28, 28, -10, -10, 16, 26, -28, 80, 18, -110, -6, -42, -140, -134, 36, -4, -44, -116, 76, -114, 28, 128, -24, 70, 34, 100, 0, -6, -12, 84, 0, -28, -58, 148, 60, -28, -2, 24, 0, 46, -4, 68, -30, 58, -20, 30, 0, 34, 16, 38, -8, -96, 100, 140, 6, -18, -2, -120, 18, -210, -88, 276, 0, -10, 2, 32, 64, -50, -54, -220, 8, -40, -30, -20, 30, -66, -54, 106, 0, 28, -28, -4, 60, 36, 10, 128, -22, 0, 80, -76, -10, -58, -50, 68, -4, -80, 104, -38, 50, -400, -10, -118, -36, 44, -178, 44, -2, -174, -46, -40, 0, 82, 32, 38, 42, -10, 12, -20, 0, 38, 30, -116, -16, 98, 144, -156, -12, -230, 80, 8, -18, -48, 70, 46, -24, 20, 42, 0, -70, -50, 24, -258, -36, 6, 4, 106, -6, 64, -74, -92, -16, 30, 44, -60, 72, -40, 22, 6, -6, -336, 0, 98, 16, 76, -60, 446, 0, 152, 6, -32, -148, 16, 96, 20, 20, -200, -132, 136, 58, 112, 2, 70, -30, -200, 28, -194, 12, -152, 56, 372, 20, 4, -16, 0, 64, -98, 42, -170, 60, -22, 112, 630, -20, 78, 0, 110, 0, -76, -94, 188, -216, -144, 112, 36, 78, -160, 176, -38, 0, 198, 100, 82, 24, 82, 68, 80, 82, 40, -200, 0, 2, -16, -110, 100, 8, 190, 244, 120, 0, -220, 30, 134, -2, -48, -32, 260, 86, 80, -360, -86, -16, 56, -20, -66, 12, 232, 120, 82, 70, 110, -120, -266, 0, 26, 186, -196, -6, -320, 44, 190, 0, -64, 32, 154, -72, -134, 384, -170, -60, -6, -36, -38, 40, -110, -78, 0, -48, -78, -230, -42, -10, -482, 76, 0, -10, 42, 48, -20, 0, -86, 122, -106, -6, 34, 0, -30, -24, 8, -72, -276, 10, 8, 0, 330, 80, -124, 68, 350, -24, -200, -104, -184, -52, -60, -104, 170, 12, 520, -76, -8, -64, -296, 0, -68, 0, 222, 88, -396, 18, -206, 2, 14, -42, 132, -180, 90, -32, -262, -50, 10, 10, 198, 22, 50, 20, -170, -94, -196, -34, 600, -48, 186, 46, -354, 106, 32, -8, 158, 30, 0, 0, 28, 112, 54, -12, -30, -272, -200, 70, -126, 114, 238, -6, 166, -140, -248, 18, 156, -190, -60, 0, 282, -50, -62, 56, -136, 38, 30, 36, 50, 34, -188, 36, 86, -36, 4, 56, 56, 26, 126, 84, -338, -28, 480, -54, -120, -50, -316, 96, 166, 170, -62, 28, 42, -60, 4, 8, -218, -86, 260, 6, -276, -64, 36, -70, 0, 152, 48, 34, 134, -216, -464, -60, 0, 154, 408, -30, -196, 28, 296, -6, -364, 52, 90, -12, 180, -16, 210, 34, 236, 40, -22, 0, -130, -170, 44, -128, 236, 44, 88, 52, -488, 68, -62, -132, -278, -110, -122, -30, 40, -200, -214, 12, -296, -116, 0, 78, 84, 132, 90, 24, 20, 328, -44, 20, -324, 106, 22, 26, 610, -120, -630, 16, 108, -132, -222, -92, -170, 220, 396, 20, -314, -88, -16, 8, -2, -110, -116, 0, 298, -78, 72, -30, 294, -40, 684, 0, 110, 76, 0, -86, 1120, 52, -246, 16, -88, -56, 208, 38, 522, -116, 68, 12, 0, 160, -20, 74, 276, 18, 608, -100, 304, 32, -566, 0, -606, 128, -194, 6, 324, 188, 486, -58, -60, -80, 120, 108, -234, -320, -150, 150, 678, -30, -770, -12, -320, -114, 146, 10, 16, 200, -342, 162, -20, 130, -144, -14, 0, -280, -48, 0, -162, -220, -132, 30, -406, -4, 52, -58, -132, -62, 488, 12, -30, 0, 100, 14, 516, -180, -202, 0, -288, 56, -82, -24, 220, -36, 276, -80, 280, -154, -288, -12, 116, -222, 170, 0, -102, 38, 0, 70, -42, -150, 12, -20, 44, 56, 0, -30, 20, -86, 120, 294, -470, -384, 54, -44, -64, -60, -204, 106, -298, 40, -134, 0, 142, -376, 410, 18, -440, 246, -642, -88, -330, -46, -54, 6, -120, 40, -842, 20, 138, -454, -310, 16, 120, 228, -38, -40, 152, -110, -112, -142, 332, 560, -112, -2, 406, -22, -48, 0, 556, -28, -124, -10, -60, -38, -62, -36, 54, -140, -218, 100, 310, 78, 412, -68, -46, 30, -516, 0, 1038, 116, -340, 48, 38, -4, -270, -14, -24, -224, -124, 80, -90, 430, 28, -136, 304, 132, 204, 72, 74, -154, -190, -10, 544, -128, 24, 400, -390, 80, -8, 30, 400, -166, 60, -98, -92, 10, -640, 24, -64, -530, 224, -156, -254, -646, -488, 22, -500, 0, 164, -56, 180, 130, -4, -2, -160, 0, 28, -4, -422, 8, 216, 124, -392, -24, -166, 0, 196, 68, 50, 0, -18, -102, 28, -58, 0, -164, -820, 42, -564, 206, 112, -2, 228, -384, -138, -28, -244, -182, 12, 10, 10, 540, 330, 52, -8, -8, -866, 0, 246, -160, 596, -20, 788, 582, 376, 178, -190, -310, -222, 140, -106, 170, -100, -226, 14, 196, 248, 14, 238, -60, -160, -2, -256, -116, -340, -76, 658, 154, -124, -46, 0, 248, -596, -12, -800, 262, 206, 240, 1186, -40, -76, 0, -90, 322, -22, -2, 238, 176, 374, 12, 128, 450, -86, 102, 184, 0, 396, -110, 200, 156, 474, 286, 290, 12, -42, 6, 0, 34, 242, -230, 372, 288, 674, -18], "weight": 2, "weight_parity": 1, "id": null, "is_polredabs": null, "nf_label": null, "trace_hash": 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}