# Stored data for newform 26.8.a.b, downloaded from the LMFDB on 29 April 2024. {"label": "26.8.a.b", "space_label": "26.8.a", "level": 26, "weight": 8, "hecke_orbit": 2, "hecke_orbit_code": 4503599761588250, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 492202133335733010, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[3, [87, 1]]], "qexp_display": "q+8q^{2}-87q^{3}+2^{6}q^{4}+321q^{5}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 1664, "fricke_eigenval": 1, "atkin_lehner_string": "--", "analytic_conductor": 8.122010662587165, "hecke_ring_index": 1, "level_radical": 26, "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": [26, 1, [15], [1]], "hecke_ring_generator_nbound": 1, "inner_twist_count": 1, "level_primes": [2, 13], "conrey_indexes": [1], "field_disc": 1, "field_disc_factorization": [], "field_poly": [0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.013", "prec": 17}, {"__RealLiteral__": 0, "data": "0.995", "prec": 17}, {"__RealLiteral__": 0, "data": "0.044", "prec": 17}, {"__RealLiteral__": 0, "data": "2.017", "prec": 17}, {"__RealLiteral__": 0, "data": "0.154", "prec": 17}, {"__RealLiteral__": 0, "data": "5.125", "prec": 17}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "7.2.3.c1", "atkin_lehner_eigenvals": [[2, -1], [13, -1]], "trace_display": [8, -87, 321, -181], "traces": [0, 1, 8, -87, 64, 321, -696, -181, 512, 5382, 2568, 7782, -5568, 2197, -1448, -27927, 4096, 9069, 43056, -37150, 20544, 15747, 62256, 19008, -44544, 24916, 17576, -277965, -11584, 174750, -223416, 29012, 32768, -677034, 72552, -58101, 344448, 323669, -297200, -191139, 164352, 795312, 125976, -314137, 498048, 1727622, 152064, -447441, -356352, -790782, 199328, -789003, 140608, -1469232, -2223720, 2498022, -92672, 3232050, 1398000, 1627770, -1787328, -2399608, 232096, -974142, 262144, 705237, -5416272, -64066, 580416, -1653696, -464808, -322383, 2755584, -4454782, 2589352, -2167692, -2377600, -1408542, -1529112, 753560, 1314816, 12412521, 6362496, -1219092, 1007808, 2911149, -2513096, -15203250, 3984384, 3390330, 13820976, -397657, 1216512, -2524044, -3579528, -11925150, -2850816, 1628774, -6326256, 41882724, 1594624, -15350268, -6312024, 6876428, 1124864, 5054787, -11753856, -15202716, -17789760, 6732605, 19984176, -28159203, -741376, -11529222, 25856400, 6101568, 11184000, 11824254, 13022160, -1641489, -14298624, 41072353, -19196864, -69192144, 1856768, -17080089, -7793136, 20669924, 2097152, 27329919, 5641896, -19094853, -43330176, 6724150, -512528, -89226765, 4643328, 29690064, -13229568, 15565235, -3718464, 38927367, -2579064, 17097054, 22044672, 56094750, -35638256, 68798034, 20714816, -2496750, -17341536, 23980157, -19020800, 48809358, -11268336, 9312852, -12232896, 17055014, 6028480, 127823184, 10518528, -3440448, 99300168, -73458592, 50899968, -217327914, -9752736, 46686024, 8062464, 4826809, 23289192, -199941300, -20104768, -78093072, -121626000, -4509796, 31875072, -141615990, 27122640, -55616325, 110567808, -119434588, -3181256, 208765896, 9732096, 103897749, -20192352, 70574958, -28636224, 50311665, -95401200, 105484662, -22806528, 21205868, 13030192, -61355619, -50610048, -166535241, 335061792, -126350710, 12756992, 5573742, -122802144, -31629750, -50496192, 255295152, 55011424, 102301056, 8998912, -289101300, 40438296, 108570947, -94030848, 28047321, -121621728, -100837977, -142318080, -5251172, 53860840, 387566034, 159873408, 19924593, -225273624, -125602687, -5931008, 134097912, -92233776, 190774224, 206851200, -52891105, 48812544, 122543154, 89472000, 151253973, 94594032, -143628561, 104177280, -65559720, -13131912, 261916755, -114388992, -131751658, 328578824, -471979872, -153574912, -253841022, -553537152, -81618550, 14854144, 106061004, -136640712, 247061472, -62345088, 147920256, 165359392, -253269963, 16777216, 227286009, 218639352, -58584089, 45135168, 940504500, -152758824, -425872092, -346641408, -471623472, 53793200, -294958710, -4100224, -514154280, -713814120, 45709607, 37146624, 34596159, 237520512, 193896312, -105836544, -273963916, 124521880, 156142584, -29747712, 421707162, 311418936, 381957188, -20632512, 1037488050, 136776432, -143951472, 176357376, -328091912, 448758000, -141703338, -285106048, -404832687, 550384272, 522514170, 165718528, -2163123630, -19974000, 41760576, -138732288, 56858797, 191841256, 1335473316, -152166400, -770274168, 390474864, -47551966, -90146688, -598249236, 74502816, -302841318, -97863168, -631685377, 136440112, -312699582, 48227840, 793332354, 1022585472, 1359904500, 84148224, 1322636292, -27523584, -336913350, 794401344, 54740452, -587668736, -585736635, 407199744, 80986821, -1738623312, -1216276408, -78021888, 1741986558, 373488192, -20565186, 64499712, -151220641, 38614472, 1003042314, 186313536, 225771384, -1599530400, 292192825, -160838144, -530836416, -624744576, -597234381, -973008000, 119599865, -36078368, -610689105, 255000576, -466414392, -1132927920, -103484943, 216981120, 142809543, -444930600, -770101560, 884542464, 486250761, -955476704, -3573294711, -25450048, -1429985022, 1670127168, -855319006, 77856768, 4280369184, 831181992, 265930992, -161538816, -529609252, 564599664, 1485967743, -229089792, 383925750, 402493320, 1983575540, -763209600, -1798283388, 843877296, 898756473, -182452224, -452141982, 169646944, -1690685334, 104241536, 1824748770, -490844952, 172383552, -404880384, 1661252211, -1332281928, 241892760, 2680494336, 493083254, -1010805680, -585001050, 102055936, -568279548, 44589936, 63739364, -982417152, 3984419241, -253038000, 2518792158, -403969536, -1284720160, 2042361216, -2583035568, 440091392, -294626370, 818408448, -391328532, 71991296, -1354175445, -2312810400, 274847265, 323506368, 751367717, 868567576, -2408127462, -752246784, 225963204, 224378568, 434329048, -972973824, -1487443698, -806703816, -130756173, -1138544640, 1667358623, -42009376, -4880243250, 430886720, -706147200, 3100528272, 2314776050, 1278987264, -4255988724, 159396744, -690047187, -1802188992, 1088295930, -1004821496, 217217250, -47448064, 2638062870, 1072783296, 6189117984, -737870208, -2086273659, 1526193792, -127647897, 1654809600, -616221946, -423128840, -2520864585, 390500352, 1236212397, 980345232, 67846928, 715776000, -810218124, 1210031784, -1175015556, 756752256, 11595946, -1149028488, -1483786218, 833418240, -2444614134, -524477760, -925629400, -105055296, -7907406624, 2095334040, 396154455, -915111936, 711100793, -1054013264, 299318976, 2628630592, 522836454, -3775838976, -3036647896, -1228599296, 6390897504, -2030728176, -2919740913, -4428297216, 1584807750, -652948400, 13444354404, 118833152, 58351323, 848488032, -1623425080, -1093125696, -4061684088, 1976491776, 4758875898, -498760704, -4927436028, 1183362048, -419932383, 1322875136, -919375290, -2026159704, 806315542, 134217728, 10326399750, 1818288072, 2207333388, 1749114816, -3481985862, -468672712, 6794097264, 361081344, -1460886633, 7524036000, 2128561868, -1222070592, 392352252, -3406976736, 263109828, -2773131264, -3043521383, -3772987776, 8760658140, 430345600, 1747300464, -2359669680, -4880071836, -32801792, 4838620275, -4113234240, -6153865524, -5710512960, -17247913, 365676856, 10390809156, 297172992, 2161166205, 276769272, 751153769, 1900164096, -12914690256, 1551170496, -6491962500, -846692352, -136394360, -2191711328, -9039104163, 996175040, 3007006959, 1249140672, -690158989, -237981696, -6140021346, 3373657296, 2828796303, 2491351488, -3700880262, 3055657504, -2246666301, -165060096, 7672902135, 8299904400, -3093628603, 1094211456, -9177165594, -1151611776, 473603328, 1410859008, 3718145414, -2624735296, -1844910516, 3590064000, 220655652, -1133626704, -11433563424, -2280848384, 3795585534, -3238661496, -2748526536, 4403074176, -1077795800, 4180113360, 14488565967, 1325748224, -9112618782, -17304989040, -526917969, -159792000, 10992511770, 334084608, -5524932450, -1109858304, -1782188443, 454870376, -344803212, 1534730048, 13184225313, 10683786528, 9537054134, -1217331200, 2751788250, -6162193344, -983027877, 3123798912, -1186268722, -380415728, -22210678224, -721173504, 1322558904, -4785993888, -3594504700, 596022528, -5283558720, -2422730544, -613649730, -782905344, -7429271069, -5053483016, 25151813100, 1091520896, 2935354161, -2501596656, 7491017, 385822720, -9445672389, 6346658832, 6635045604, 8180683776, -1737348054, 10879236000, -1735065306, 673185792, 4063962222, 10581090336, 1565438, -220188672, 8772903999, -2695306800, 13102543794, 6355210752, 12667306140, 437923616, 456851964, -4701349888, 7633260288, -4685893080, -6129447813, 3257597952, -23975636724, 647894568, -9259001820, -13908986496, 4799624162, -9730211264, -1733439591, -624175104, 2158452150, 13935892464, 3321648000, 2987905536, 10927433769, -164521488, -18673749456, 515997696, -10899746947, -1209765128, -6925775940, 308915776, 3440991504, 8024338512, -294808094, 1490508288, -16597357488, 1806171072, 5535534408, -12796243200, 9530510544, 2337542600, 4601526135, -1286705152, -3227902704, -4246691328, 421595432, -4997956608, -7580773044, -4777875048, 4996440435, -7784064000, 7212684528, 956798920, -13159095651, -288626944, -5149945008, -4885512840, -12024303350, 2040004608, 12495684807, -3731315136, 2778398508, -9063423360, 10568287250, -827879544, 4055659920, 1735848960, 551460096, 1142476344, 5488154334, -3559444800, -22786757685, -6160812480, 15369036990, 7076339712, -1244633468, 3890006088, 11462394246, -7643813632, 4354071000, -28586357688, 4885986014, -203600384, 13916065437, -11439880176, -2848908453, 13361017344, 3598888523, -6842552048, 22084168914, 622854144, -498561612, 34242953472, 2788864580, 6649455936, 7100813850, 2127447936, -3081304917, -1292310528, -801456750, -4236874016, -6561153144, 4516797312, 2751691596, 11887741944, -641281288, -1832718336, -21494348064, 3071406000, 7697630397, 3219946560, -16021920976, 15868604320, -12869062272, -6105676800, -5736228198, -14386267104, -1218601505, 6751018368, 15667803918, 7190051784, 3576210690, -1459617792, 24587427200, -3617135856, -19773882783, 1357175552, -13151736867, -13525482672, 722862992, 833932288, 5096815743, 14597990160, -29545840800, -3926759616, -2508784506, 1379068416, -48574383750, -3239043072, 5474659494, 13290017688, -7388628376, -10658255424, 37050872004, 1935142080, 2086789182, 21443954688, -5271938776, 3944666032, 41031242064, -8086445440, -5223985746, -4680008400, -4057842429, 816447488, 18246756060, -4546236384, -34667113524, 356719488, -1104383808, 509914912, 44731422360, -7859337216, -7921016385, 31875353928, -8166071788, -2024304000, -3976735809, 20150337264, -23580208032, -3231756288, 11670189550, -10277761280, -2140189974, 16338889728, 26374934337, -20664284544, 20408499158, 3520731136, -16868979144, -2357010960, -25530736446, 6547267584, 8482083950, -3130628256, 23834860692, 575930368, -7171601958, -10833403560, 14986213704, -18502483200, -8064320580, 2198778120, -22932345240, 2588050944, 13287686191, 6010941736, -36688523094, 6948540608, 1549405689, -19265019696, -7434095893, -6017974272, -33230275356, 1807705632, 6152300352, 1795028544, 24717450023, 3474632384, -64181157300, -7783790592, 11908133094, -11899549584, -4942139980, -6453630528, 12523778064, -1046049384, -20538654777, -9108357120, -25067876112, 13338868984, 28543996344, -336075008, 5864203920, -39041946000, -140753002, 3447093760, 8766061668, -5649177600, 3091496109, 24804226176, -14258360281, 18518208400, 35220443769, 10231898112, 17839812837, -34047909792, 37995418253, 1275173952, -45458732790, -5520377496, 84519504, -14417511936, -3741256244, 8706367440, 96594238422, -8038571968, 16622433150, 1737738000, -17852840325, -379584512, -3633170112, 21104502960, 5069847000, 8582266368, -13324465008, 49512943872, -4946715339, -5902961664, -38338502748, -16690189272, 18202392899, 12209550336, -82615142376, -1021183176, -36696268698, 13238476800, -9486973944, -4929775568, 67013852616, -3385030720, 3456168393, -20166916680, 13347440480, 3124002816, 4137021042, 9889699176, -708275451, 7842761856, 8064536804, 542775424, 37008935496, 5726208000, 27177075540, -6481744992, 29377551300, 9680254272, 26347194666, -9400124448, 22654561518, 6054018048, 40433346254, 92767568, 54956627799, -9192227904, -8498425953, -11870289744, 15117290496, 6667345920, 16150044465, -19556913072, -4400818986, -4195822080, -9787156054, -7405035200, -69019914798, -840442368, -17313304377, -63259252992, 33860576502, 16762672320, -118311691500, 3169235640, -5373901584, -7320895488, -26670917967, 5688806344, -81821017512, -8432106112, 6807083628, 2394551808, 14091825029, 21029044736, 29311461450, 4182691632, -7278434283, -30206711808, -2817307535, -24293183168, -4762419324, -9828794368, 24379128954, 51127180032, 26383548060, -16245825408, 36234880110, -23357927304, 40655607843, -35426377728, -53457812361, 12678462000, -7045853427, -5223587200, -5971116096, 107554835232, -48663578518, 950665216, 105816047496, 466810584, -40558577910, 6787904256, -17668151686, -12987400640, -89968653585, -8745005568], "weight_parity": 1, "has_non_self_twist": 0, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": false, "level_is_squarefree": true, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "26.8.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], [1], [8], [-87], [64], [321], [-696], [-181], [512], [5382], [2568], [7782], [-5568], [2197], [-1448], [-27927], [4096], [9069], [43056], [-37150], [20544], [15747], [62256], [19008], [-44544], [24916], [17576], [-277965], [-11584], [174750], [-223416], [29012], [32768], [-677034], [72552], [-58101], [344448], [323669], [-297200], [-191139], [164352], [795312], [125976], [-314137], [498048], [1727622], [152064], [-447441], [-356352], [-790782], [199328], [-789003], [140608], [-1469232], [-2223720], [2498022], [-92672], [3232050], [1398000], [1627770], [-1787328], [-2399608], [232096], [-974142], [262144], [705237], [-5416272], [-64066], [580416], [-1653696], [-464808], [-322383], [2755584], [-4454782], [2589352], [-2167692], [-2377600], [-1408542], [-1529112], [753560], [1314816], [12412521], [6362496], [-1219092], [1007808], [2911149], [-2513096], [-15203250], [3984384], [3390330], [13820976], [-397657], [1216512], [-2524044], [-3579528], [-11925150], [-2850816], [1628774], [-6326256], [41882724], [1594624]]}