# Stored data for newform 8.8.b.a, downloaded from the LMFDB on 16 April 2024. {"label": "8.8.b.a", "space_label": "8.8.b", "level": 8, "weight": 8, "hecke_orbit": 1, "hecke_orbit_code": 68853694472, "dim": 6, "is_polredabs": true, "trace_hash": 1021484256660776700, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [], "qexp_display": "q+(1+\\beta _{1})q^{2}+\\beta _{4}q^{3}+(19+\\beta _{1}+\\beta _{3}+\\cdots)q^{4}+\\cdots", "char_order": 2, "char_parity": 1, "char_degree": 1, "char_conductor": 8, "char_orbit_label": "b", "char_is_real": true, "Nk2": 512, "analytic_conductor": 2.4990802038729742, "hecke_ring_index": 32768, "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": false, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.506", "prec": 17}, "analytic_rank_proved": true, "char_values": [8, 2, [7, 5], [2, 1]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 2, "level_primes": [2], "conrey_indexes": [5], "field_disc": -385925773754399, "field_disc_factorization": [[-1, 1], [239, 1], [677, 2], [1877, 2]], "field_poly": [32768, -3072, -320, -24, -10, -3, 1], "hecke_ring_index_factorization": [[2, 15]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.011", "prec": 17}, {"__RealLiteral__": 0, "data": "5.453", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "152.589", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "6076.668", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 6, "sato_tate_group": "7.2.3.c2", "trace_display": [6, 0, 0, -688], "traces": [0, 6, 6, 0, 116, 0, 268, -688, 1512, -2918, -1656, 0, -4088, 0, 12048, 17872, 35344, 1452, -89062, 0, -114768, 0, 152860, -1296, 282512, -39314, -316968, 0, -480800, 0, 821648, -89280, 817056, 53880, -1009108, 0, -1253556, 0, 974124, -328208, 954464, 521244, -1093088, 0, -1096344, 0, 929840, 1566432, 853920, -511050, -148626, 0, 823952, 0, -1077064, -3270256, -2468928, -1889896, 3130744, 0, 5715168, 0, -7055808, 5776816, -4792768, 1416480, 7926264, 0, 6608040, 0, -7406912, -7597104, -11363944, 2089564, 7744200, 0, 9241288, 0, -9471184, 16015904, -12600384, -723058, 10715932, 0, 4220608, 0, -5639076, -37453776, 1541200, 2169084, -121864, 0, 669600, 0, 15503712, 48537936, 21402176, -1088308, -14983242, 0, -22902876, 0, 23330392, -66477296, 14762016, -6425216, -33327512, 0, -41047600, 0, 21976656, 105923152, 35540352, -4629396, -64722152, 0, -23369136, 0, 44635004, -101313120, 68872640, 12335018, -14354760, 0, -59870336, 0, 52718576, 120534272, 17273472, 8599288, -29381600, 0, -13298160, 0, -21022068, -184124128, -576688, -42304548, -7979936, 0, 69139584, 0, 477072, 174604080, -58310416, 6476960, 134905308, 0, 14994224, 0, -44948516, -218466320, -116725488, 55703956, 44564384, 0, 50274720, 0, -209485920, 290082960, -95069824, 39285888, 90313486, 0, 254871240, 0, -82500436, -248362608, -97496704, 34330814, 236206224, 0, 74921192, 0, -140630928, 176403472, -262985952, -183689416, 31835260, 0, 43354448, 0, -199025088, -110160720, 41086784, -89915808, -50611072, 0, 251039040, 0, 182334224, 78322560, 222227072, 189123724, 174343500, 0, -211000044, 0, 229307940, 50772176, -147136440, -60920232, -224785080, 0, -359715440, 0, -199924272, -159465968, 409569600, -104778312, -510680704, 0, 56812272, 0, 376651228, 237373584, 380253856, 140998144, -16886376, 0, -571475104, 0, 803885072, -432511296, -181170432, 390894514, -587367828, 0, -785974320, 0, -136563648, 486414912, 657630112, -39155556, -503199064, 0, 330733992, 0, 690096416, -531131808, 790587776, -723230100, 549621546, 0, -486394416, 0, 410923064, 694336624, -650025216, 199343768, -367185328, 0, -111828960, 0, -921078528, -1357275488, 155132160, 693235212, -414567304, 0, 939925440, 0, 129022220, 1500139344, 242434080, -619536928, 1179651360, 0, -153906936, 0, -249595232, -1334059616, -1546277088, -854188928, -127952676, 0, 344930368, 0, -1414146276, 2088372416, -173805312, 917952636, 372103872, 0, 1753790688, 0, -417570960, -1528775136, -328759712, 1169882098, 2304516000, 0, 566219080, 0, -280344468, 2047394832, -2278387872, -938512080, -202569176, 0, -57726488, 0, -2589325008, -2512118960, 291088032, -1840094304, 511583252, 0, 1567289280, 0, 413688576, 652293168, -108707008, 847338684, 1710010488, 0, -201076544, 0, 1779824976, -1438763920, -1641580800, 2872300536, -635774848, 0, -604979100, 0, -1547221428, 1223379824, 2007904144, -1276665600, -1415040864, 0, 1399175112, 0, 1182434896, -661963824, 753700608, -2690080468, 642184638, 0, -1906345888, 0, 1175443732, 1539490720, -571012272, 1629145216, -1193690600, 0, -3946418400, 0, -4610352, -1217440, 1560335680, 3464843724, -3186109256, 0, 866679816, 0, 2950973804, -968999664, 3144642976, -1358397766, 224041320, 0, -2264307328, 0, 1950952176, 680486752, 1073606784, -5801350108, -4122053792, 0, -2619141376, 0, 175579512, -147992544, 2276760192, 1974976224, -3048998080, 0, 1188471264, 0, 1524328832, 1401947904, 2835960064, 5652842368, 2080154892, 0, -2759616920, 0, 2196330560, -2373380384, -1914390744, -2095470760, -577324792, 0, 433943064, 0, 827882640, 3196250432, 788665808, -7441976148, 309947352, 0, 2150097456, 0, -1613484736, -5002126320, 1450197536, 944164988, 1203291600, 0, -467035040, 0, -1336954672, 4538009424, -3609982848, 10181587064, -712929480, 0, -202285824, 0, -3841192020, -6523847904, -3343109408, -2907745284, 3381256992, 0, 46314984, 0, -1456808624, 8773051872, -3994084800, -7760129556, 4557964800, 0, 5421729040, 0, -183181896, -6733663952, -2863728960, 5782007274, 2853699632, 0, 7116744672, 0, -6310470720, 7655618064, 26068480, 10849726092, 3566616626, 0, 3567703080, 0, -3020887860, -8941052160, -7486162016, -4494709668, 72102984, 0, 1188089216, 0, -5245030080, 3883206944, -1783542720, -15448709632, 7781646364, 0, -1225772944, 0, 42505344, -8453637584, -2867869488, 4760397720, 1948960576, 0, 2923265472, 0, 2651409120, 11260649664, 1097590528, 11769180704, -1539751188, 0, 2342974764, 0, -4480200956, -3056418288, 7430382240, -10062373928, -14725176, 0, 3886091984, 0, 1748759472, 5682931056, -5862251008, -13946649216, -7295303144, 0, -6497673504, 0, 541816060, -7765989456, 1992343616, 11826347104, -1282454304, 0, -5782530560, 0, 1997108768, 1928985632, 5188409856, 18830059120, -956565492, 0, 472625424, 0, 13376489664, -102470544, 4600270720, -7781246244, -238850808, 0, -9807171576, 0, 789116176, 10108719744, 10509921600, -18404294378, -18550462752, 0, -1047185216, 0, 1449712376, -2546131312, 3691028880, 6610810904, -10588842536, 0, -10188793152, 0, 9073926432, -4470797680, 3477343552, 19105065504, 5558182016, 0, -20507595960, 0, 2807258028, -7723240272, -496321408, -8574839040, -10940994264, 0, 5890687336, 0, 18249151936, -6686104528, 14838999552, -22960949904, 9687033852, 0, 4503166080, 0, 3126001212, 9180664592, 9812505024, 10475012796, 1330207264, 0, -6796904160, 0, -5885729888, 300307248, -15540720192, 26757796492, -20940825102, 0, 5353330880, 0, -7280081768, 11237141840, 8994124944, -10361831200, 10058963656, 0, -5379810744, 0, 13385976528, -17119956784, -15611956800, -21648492756, 7656147504, 0, 1297417584, 0, 855230144, 5832156528, -4535605936, 6571545852, 1240063392, 0, 6115755424, 0, -34346246896, -24073542208, 19799398464, 25120692864, 5338463904, 0, 22446964440, 0, 6269886828, 32714373920, -25951136896, -11071981668, 1535904, 0, -2548219392, 0, -26506419088, -5422698720, -15849179008, -31703597802, 13274442684, 0, -5162566576, 0, -11599484608, 35934692528, -8048369280, 15936616600, 21028298424, 0, 37341640032, 0, 24840519600, -28007831760, -18993965568, 25473615372, 24960421752, 0, -372297984, 0, -29543142248, 540001872, -86748728, -5922895144, -9399091080, 0, 24826606472, 0, -22844653904, -34005567024, 2574819744, -30679877148, -6331954944, 0, 10502497728, 0, -2089464420, 32357608672, -12561226992, -1144030848, 24825974456, 0, -29004293280, 0, 764885904, -7040635152, -22073072128, 20731874124, -5613463764, 0, 32518958852, 0, 12935014104, 30454129824, 27552318144, -392182568, 15862620800, 0, -3122796872, 0, -1107143904, -48525540016, 12408794400, -21747032928, 5085244544, 0, -10826635248, 0, -3341699652, -8113594992, -32899310016, 8299364984, -49291867656, 0, -4382811552, 0, -10645448480, -14348793392, 8551954560, 40888764672, 21700837836, 0, -42553565040, 0, 23645245632, 36462701536, 6681721360, -13855882752, -2675443136, 0, -402173880, 0, 32445114320, 16935203616, 26221598784, -5328266368, -21022420422, 0, 1691567344, 0, -612905644, 38072640112, 47455501056, 7617175522, -14986125616, 0, 8839602720, 0, 31628115936, -37561345968, -2387444480, 5650348920, -52945756124, 0, -58535984832, 0, -2061133888, -27126326256, -7512410624, -11742119200, 8715393768, 0, -47090439600, 0, 35598988704, -27721935264, 14472820992, -33657806280, -27987767328, 0, 22122071936, 0, 41546088444, 17588783808, 19083838400, 23753891388, -425727488, 0, -19096670976, 0, -34711860480, 29591208624, 70731348480, 6452671244, -23734574208, 0, 17664911080, 0, -7104146716, 17039050304, -9688439088, -19194859136, -33303951736, 0, -10473708160, 0, 10964726112, 4368948960, -9918828912, 9937092768, 42853396696, 0, -30001851216, 0, 24629286784, -56698245216, -279113040, -9023945760, 4833584856, 0, 24139189984, 0, 38931022912, -4849664064, -7741415136, -18997393084, 22520574252, 0, 5832280656, 0, -28490555136, 1518492144, 31280893280, 16695030300, -21094136600, 0, 32721892224, 0, -39226606896, 107053402320, -65169314496, -6650624456, -40519968900, 0, -17157608480, 0, -40412537928, -20278278096, -17181001536, 9229077144, 41905135776, 0, -21238872480, 0, -26055258864, 18498433040, -29383394048, 9353224716, 37623694840, 0, 73667513232, 0, 42338996044, -115325609520, -22257763840, -7825985698, 60317705160, 0, 37886806472, 0, -70476832608, 7539355952, 8682452160, 62357073592, 25117266044, 0, 11948793024, 0, -48629793984, -49014160976, -67512427184, -8432873988, -6624433440, 0, 24475495776, 0, -6809431968, 136396945344, -39796678016, -52651124704, 64807408236, 0, -7497026560, 0, -12234866880, -20166225936, -72845730528, 16277411956, 11131714912, 0, 48504145872, 0, -14293664400, 22604598864, 37461314432, 1146948204, 53025836394, 0, 63858472992, 0, -69880927364, -130219641168, 85024493504, 1084200960, 4670339664, 0, 11444037760, 0, 52245023952, 8777473104, -85438620672, -21329392256, -42782944500, 0, 12525832476, 0, -39773350440, -23749028288, -2532916656, 17500195296, 34629299808, 0, -61575910776, 0, 23786986240, 133263044256, -47560765376, 77946267320, 64070902620, 0, 5953051696, 0, 91692926960, -23211420176, -30299651328, -99562971624, -29508726440, 0, -15296479872, 0, -113175852384, 40590558192, 78440593024, -103174931124, -105818229248, 0, 35580574920, 0, 24040735404, -141035222496, 28971701728, 66120111132, -29053004256, 0, -30220393728, 0, -26393638288, 16359114848, 12646331424, 71002767104, -29590592232, 0, -94918275200, 0, 44835600252, 18547048624, 35417389952, -8949841476, -11360911080, 0, 74620066368, 0, 137047883200, 158257475616, 123985245696, -24356255034, 54011633952, 0, -120920468696, 0, 6241726720, 40909182672, 37226872152, 58506285488, -59929904624, 0, -56959009448, 0, 22238416080, -23046092240, -28863626688, 101338164012, -238741958824, 0, 7681906992, 0, 14530612700, -164115002256, 49188360352, -90386089632, 49887548784, 0, -154697174880, 0, 79237562544, -30742152000, -1969579008, -203347615880, -20745424512, 0, 4881894864, 0, 9741807084, -12636286432, 87906994112], "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, 8, 2, 1, 2, 0]], "char_orbit_index": 2, "prim_orbit_index": 2, "minimal_twist": "8.8.b.a", "char_is_minimal": true, "conrey_index": 5, "id": null, "nf_label": null, "fricke_eigenval": null, "atkin_lehner_string": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "atkin_lehner_eigenvals": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0], [1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [19, 1, 0, 1, 0, 0], [0, 2, 0, 1, -1, -1], [44, 2, -1, 0, 6, 2], [-112, 16, 2, -6, 2, -2], [250, 10, 2, 2, -20, 4], [-481, -112, -4, -12, 4, -4], [-280, -12, -10, 8, -52, 4], [0, -208, 16, 8, -11, -8], [-682, 74, 20, -6, 88, 8], [0, 438, -32, -5, 37, 5], [2008, -88, -40, 16, 80, -16], [2960, 1040, 50, 42, -14, 14], [5908, 164, 76, -12, -56, -40], [194, -1296, -92, 108, -36, 36], [-14801, -305, -80, -96, 160, -32], [0, -1296, 80, -88, 65, 88], [-19100, -292, 120, -4, -368, -80], [0, 1320, -96, -12, -404, 12], [25532, -358, -77, -192, -434, 26], [-208, 1200, 70, -18, 6, -6], [47044, -764, 4, -12, 856, 136], [-6435, -160, 40, -264, 88, -88], [-53000, 636, 18, 472, 452, 44], [0, 1392, -48, 360, -286, -360], [-80248, 2648, -256, 88, -256, 256], [0, -3394, 256, 95, 2209, -95], [136600, 1768, 280, 912, -560, 112], [-14656, -9024, -408, -504, 168, -168], [136136, 4648, -488, 200, -1136, -80], [9156, 10128, 636, -396, 132, -132], [-167886, 658, 720, -1184, -1440, 288], [0, 10144, -800, -528, 768, 528], [-208899, -12369, -768, -81, 2048, 0], [0, -12942, 928, 25, -7097, -25], [163148, -270, 903, -1984, 4438, -398], [-55120, -11728, -826, 942, -314, 314], [159320, -21800, -680, -136, -4208, -592], [85690, 13344, 248, 2664, -888, 888], [-182368, 848, 536, 1440, -1872, -880], [0, 7392, -608, -560, -275, 560], [-181986, 27650, 388, -526, 1912, -1688], [0, 5118, -480, -801, 14081, 801], [154632, -1160, -120, 1072, 240, -48], [260064, 18144, 588, 2268, -756, 756], [142344, 48936, 888, -1464, 8912, 1392], [-84279, -18816, -672, -2016, 672, -672], [-24515, -4611, -1760, -64, 3520, -704], [0, -32496, 2736, 2904, -4406, -2904], [136140, -56588, 1064, 852, -5584, 2704], [0, 38810, -2720, 365, -16589, -365], [-181256, -3404, -3674, 3648, -18276, 1588], [-542000, 32080, 3050, -6846, 2282, -2282], [-411920, -77200, 3760, 1968, 3360, -672], [-311756, -81584, -3188, -7260, 2420, -2420], [521240, -628, -3254, -3336, 8884, 4988], [0, -57088, 3584, -3456, 9141, 3456], [951240, 122904, 3840, 1560, -18688, 2304], [0, 22638, -1056, 3927, 7881, -3927], [-1172896, -3424, -3360, -7872, 6720, -1344], [964592, 60272, 4094, -4026, 1342, -1342], [-800432, 139792, 496, 6224, -12896, -1312], [230800, -38880, -4360, 11880, -3960, 3960], [1318356, 2676, -2640, 9120, 5280, -1056], [0, 30192, -1968, 1320, 5001, -1320], [1105206, -171342, 2816, -3406, 22528, -8192], [0, 13944, -1440, -3108, 10180, 3108], [-1236800, 19616, 5040, 8576, 28896, -1632], [-1276272, 12048, -3534, 22698, -7566, 7566], [-1891610, -191786, -2210, -10914, 13908, 3772], [347114, 171536, 9052, 2580, -860, 860], [1300264, -29292, 6822, -14648, -43732, -14044], [0, 50592, -3360, 1776, -27731, -1776], [1540326, 175034, -13580, -2070, 55960, 1736], [0, -73592, 3488, -12380, -33604, 12380], [-1575800, -50696, 6280, -10704, -12560, 2512], [2669216, -290912, -16204, 228, -76, 76], [-2091600, 162416, -3760, -17616, -37920, -7776], [-116195, 116752, 8284, -9708, 3236, -3236], [1779930, 56858, 17760, 11072, -35520, 7104], [0, 106112, -9088, -10560, -8775, 10560], [700304, -208528, -6688, 5616, -62912, 3776], [0, -288828, 22240, 11266, 74014, -11266], [-940292, 14778, 6435, 5248, 24110, -3910], [-6226320, -135696, -882, -35946, 11982, -11982], [243572, -181324, -24908, 34788, -21896, 5096], [357466, 38928, 476, 9108, -3036, 3036], [-28520, 43852, -5270, 1272, 121332, 23356], [0, 293088, -18272, 18640, 65152, -18640], [109848, 147336, 1280, 392, -21248, 4864], [0, 21024, 2304, 26640, -140560, -26640], [2576784, 229488, 15120, 15456, -30240, 6048], [8090000, 172560, 9730, -774, 258, -258], [3551056, 160528, 6256, 38736, 118944, 9184], [-164494, 223600, 19460, -38004, 12668, -12668], [-2490039, -54711, -13440, -16128, 26880, -5376], [0, -289152, 19584, -7488, 54531, 7488], [-3820665, 10557, -12800, 2365, 4096, 8192]]}