# Stored data for newform 256.9.d.h, downloaded from the LMFDB on 07 October 2026.
{"Nk2": 20736, "analytic_conductor": 104.28892417564856, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 8, "char_degree": 1, "char_is_minimal": false, "char_is_real": true, "char_orbit_index": 4, "char_orbit_label": "d", "char_order": 2, "char_parity": -1, "char_values": [256, 2, [255, 5], [1, 1]], "cm_discs": [], "conrey_index": 127, "dim": 4, "field_disc": 24336, "field_disc_factorization": [[2, 4], [3, 2], [13, 2]], "field_poly": [100, 0, -19, 0, 1], "field_poly_is_cyclotomic": false, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 0, "has_non_self_twist": 1, "hecke_cutters": [[3, [-8688, -72, 1]]], "hecke_orbit": 8, "hecke_orbit_code": 31525403701018880, "hecke_ring_generator_nbound": 7, "hecke_ring_index": 4096, "hecke_ring_index_factorization": [[2, 12]], "hecke_ring_index_proved": true, "inner_twist_count": 2, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 8, 4, -1, 2, 0]], "is_cm": false, "is_largest": false, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": false, "is_self_twist": false, "is_twist_minimal": false, "label": "256.9.d.h", "level": 256, "level_is_powerful": true, "level_is_prime": false, "level_is_prime_power": true, "level_is_prime_square": false, "level_is_square": true, "level_is_squarefree": false, "level_primes": [2], "level_radical": 2, "minimal_twist": "32.9.c.a", "nf_label": "4.0.24336.2", "prim_orbit_index": 4, "qexp_display": "q+(6^{2}+\\beta _{2})q^{3}+(91\\beta _{1}+2\\beta _{3})q^{5}+(236\\beta _{1}+\\cdots)q^{7}+\\cdots", "related_objects": [], "relative_dim": 4, "rm_discs": [], "sato_tate_group": "8.2.3.c2", "self_twist_discs": [], "self_twist_type": 0, "space_label": "256.9.d", "trace_display": [0, 144, 0, 0], "trace_hash": 339139415931339613, "trace_moments": [0, {"__RealLiteral__": 0, "data": "3.674", "prec": 14}, 0, {"__RealLiteral__": 0, "data": "67.644", "prec": 17}, 0, {"__RealLiteral__": 0, "data": "1755.846", "prec": 24}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.507", "prec": 10}, "traces": [0, 4, 0, 144, 0, 0, 0, 0, 0, 18876, 0, 40208, 0, 0, 0, 0, 0, -391992, 0, -664752, 0, 0, 0, 0, 0, 791028, 0, 2610144, 0, 0, 0, 0, 0, 3084864, 0, -3857984, 0, 0, 0, 0, 0, -2953352, 0, -3046768, 0, 0, 0, 0, 0, 2839044, 0, -31044576, 0, 0, 0, 0, 0, -9354432, 0, 14178512, 0, 0, 0, 0, 0, -71183216, 0, 1669264, 0, 0, 0, 0, 0, 5920824, 0, -29669808, 0, 0, 0, 0, 0, 71748, 0, 157116752, 0, 0, 0, 0, 0, -132647880, 0, -398190016, 0, 0, 0, 0, 0, 56444872, 0, 307632624, 0, 0, 0, 0, 0, -374190336, 0, 298739856, 0, 0, 0, 0, 0, -499671032, 0, -320312512, 0, 0, 0, 0, 0, -386132292, 0, 1415081184, 0, 0, 0, 0, 0, -1808041920, 0, -1000903280, 0, 0, 0, 0, 0, 137398648, 0, -44553200, 0, 0, 0, 0, 0, 415300496, 0, -727185264, 0, 0, 0, 0, 0, -3068976456, 0, -596147968, 0, 0, 0, 0, 0, -1775108864, 0, 2312496144, 0, 0, 0, 0, 0, -5227426572, 0, -2087446608, 0, 0, 0, 0, 0, -4019713728, 0, 2324802000, 0, 0, 0, 0, 0, 483395952, 0, -4634551008, 0, 0, 0, 0, 0, -2015298104, 0, -5401566144, 0, 0, 0, 0, 0, 2642874432, 0, 1910945344, 0, 0, 0, 0, 0, -6084444864, 0, 2894068048, 0, 0, 0, 0, 0, -4714511360, 0, 4403873760, 0, 0, 0, 0, 0, -453709620, 0, 5141630224, 0, 0, 0, 0, 0, -6801882568, 0, 635879296, 0, 0, 0, 0, 0, 12164100296, 0, -8850069072, 0, 0, 0, 0, 0, -1897252032, 0, 3078276048, 0, 0, 0, 0, 0, -686909432, 0, 308305344, 0, 0, 0, 0, 0, 1355098992, 0, 13245396960, 0, 0, 0, 0, 0, -20231151360, 0, 5567394000, 0, 0, 0, 0, 0, 11617495864, 0, 22666340176, 0, 0, 0, 0, 0, 17690936588, 0, -16365701088, 0, 0, 0, 0, 0, 27465199488, 0, -37445654336, 0, 0, 0, 0, 0, 29972789392, 0, -21494746416, 0, 0, 0, 0, 0, 52522220920, 0, -35147636160, 0, 0, 0, 0, 0, 52210159680, 0, 58963871136, 0, 0, 0, 0, 0, -7598121472, 0, 22340198416, 0, 0, 0, 0, 0, 1177856264, 0, 45508165920, 0, 0, 0, 0, 0, -25304218368, 0, -80353321136, 0, 0, 0, 0, 0, 2806976264, 0, -25003494464, 0, 0, 0, 0, 0, 47860026812, 0, 19017044592, 0, 0, 0, 0, 0, 95604065544, 0, 9834522048, 0, 0, 0, 0, 0, 30765569392, 0, 80024907728, 0, 0, 0, 0, 0, -48427874560, 0, -136659493776, 0, 0, 0, 0, 0, 65183237184, 0, -38438231936, 0, 0, 0, 0, 0, 5144391368, 0, -133931462912, 0, 0, 0, 0, 0, 29753222008, 0, 147075699936, 0, 0, 0, 0, 0, 8979803712, 0, 149195125520, 0, 0, 0, 0, 0, -52864911960, 0, 143606196800, 0, 0, 0, 0, 0, -83083825464, 0, 56179466304, 0, 0, 0, 0, 0, -46318692420, 0, -39044698160, 0, 0, 0, 0, 0, 59991417288, 0, 32690381792, 0, 0, 0, 0, 0, -27608661640, 0, -268488539712, 0, 0, 0, 0, 0, 37325104128, 0, 179445684816, 0, 0, 0, 0, 0, -100258801088, 0, -152682949104, 0, 0, 0, 0, 0, -51433605744, 0, -96684665856, 0, 0, 0, 0, 0, -208028905920, 0, 75590298512, 0, 0, 0, 0, 0, -175880454400, 0, 83954531024, 0, 0, 0, 0, 0, -137917241488, 0, -72158899632, 0, 0, 0, 0, 0, -422842131072, 0, 77600659136, 0, 0, 0, 0, 0, 123047978872, 0, 56463621904, 0, 0, 0, 0, 0, 147862304772, 0, -259261693392, 0, 0, 0, 0, 0, 135978560832, 0, -5466954480, 0, 0, 0, 0, 0, -180553591920, 0, -82972759792, 0, 0, 0, 0, 0, -166541155840, 0, 180041454528, 0, 0, 0, 0, 0, -497512558464, 0, -341988096304, 0, 0, 0, 0, 0, -455420385928, 0, -12842455600, 0, 0, 0, 0, 0, 344784917256, 0, 31870406688, 0, 0, 0, 0, 0, -540319462800, 0, -38277179888, 0, 0, 0, 0, 0, -227145697272, 0, 477843150720, 0, 0, 0, 0, 0, -253072247752, 0, 193837483632, 0, 0, 0, 0, 0, 257609044224, 0, -432105228160, 0, 0, 0, 0, 0, 232928877880, 0, -297520521584, 0, 0, 0, 0, 0, -60263161708, 0, -344627872512, 0, 0, 0, 0, 0, 675384228672, 0, 499951595520, 0, 0, 0, 0, 0, -3562899512, 0, 719488034704, 0, 0, 0, 0, 0, -43213343936, 0, 297767768064, 0, 0, 0, 0, 0, 329672503368, 0, 31724432464, 0, 0, 0, 0, 0, 555265082112, 0, 141424385216, 0, 0, 0, 0, 0, -383238781496, 0, 472564135008, 0, 0, 0, 0, 0, 1163872260672, 0, 32437434000, 0, 0, 0, 0, 0, 264276898704, 0, 41120922064, 0, 0, 0, 0, 0, -355651797648, 0, -1740616978464, 0, 0, 0, 0, 0, 715768794624, 0, -635914693184, 0, 0, 0, 0, 0, -571486409728, 0, -831931472320, 0, 0, 0, 0, 0, 501039794944, 0, 1412906712096, 0, 0, 0, 0, 0, -217061864964, 0, 1018681077792, 0, 0, 0, 0, 0, 122673459776, 0, 134149377296, 0, 0, 0, 0, 0, 334916468848, 0, 197585185200, 0, 0, 0, 0, 0, 1540407448896, 0, -187259410624, 0, 0, 0, 0, 0, 362752109944, 0, -698337192384, 0, 0, 0, 0, 0, 470747442632, 0, -1130162331360, 0, 0, 0, 0, 0, 948627422976, 0, 1046123339616, 0, 0, 0, 0, 0, -599182475632, 0, -834853567408, 0, 0, 0, 0, 0, 2479519246448, 0, -32065430592, 0, 0, 0, 0, 0, 671526540360, 0, 231335810784, 0, 0, 0, 0, 0, 86511188856, 0, 1428945216912, 0, 0, 0, 0, 0, -113564488896, 0, -2303593061952, 0, 0, 0, 0, 0, -60263044800, 0, 2043113177040, 0, 0, 0, 0, 0, 73441085640, 0, -2036489289536, 0, 0, 0, 0, 0, 1747736299764, 0, -2179626437664, 0, 0, 0, 0, 0, 391906784064, 0, -193499529408, 0, 0, 0, 0, 0, -2726859002504, 0, 554993296208, 0, 0, 0, 0, 0, -237632416112, 0, 3955647329712, 0, 0, 0, 0, 0, -1058272235592, 0, -1927367302016, 0, 0, 0, 0, 0, 838284961032, 0, 2160275696592, 0, 0, 0, 0, 0, 2193254891520, 0, 339893825040, 0, 0, 0, 0, 0, -975270868224, 0, 10775568128, 0, 0, 0, 0, 0, -1401111188880, 0, -686861869552, 0, 0, 0, 0, 0, 1269645931840, 0, 3714017506368, 0, 0, 0, 0, 0, -3837484617408, 0, -4622179604416, 0, 0, 0, 0, 0, -2702413465144, 0, -774542703792, 0, 0, 0, 0, 0, -2252808339912, 0, 3648063825120, 0, 0, 0, 0, 0, -2693950631424, 0, -2067186969392, 0, 0, 0, 0, 0, -67483188360, 0, -1274504291840, 0, 0, 0, 0, 0, -289561891836, 0, 4394551170672, 0, 0, 0, 0, 0, 3508256596608, 0, 1437397009168, 0, 0, 0, 0, 0, -3220009304888, 0, -594526943520, 0, 0, 0, 0, 0, 221498508400, 0, 3958040180736, 0, 0, 0, 0, 0, 2662998654528, 0, -3592505623616, 0, 0, 0, 0, 0], "weight": 9, "weight_parity": -1, "id": null, "artin_degree": null, "artin_field": null, "artin_field_label": null, "artin_image": null, "atkin_lehner_eigenvals": null, "atkin_lehner_string": null, "embedded_related_objects": null, "fricke_eigenval": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp": [[0, 0, 0, 0], [1, 0, 0, 0], [0, 0, 0, 0], [36, 0, 1, 0], [0, 0, 0, 0], [0, 91, 0, 2], [0, 0, 0, 0], [0, 236, 0, 11], [0, 0, 0, 0], [4719, 0, 72, 0], [0, 0, 0, 0], [10052, 0, 41, 0], [0, 0, 0, 0], [0, -1579, 0, 230], [0, 0, 0, 0], [0, 23244, 0, 163], [0, 0, 0, 0], [-97998, 0, -424, 0], [0, 0, 0, 0], [-166188, 0, 365, 0], [0, 0, 0, 0], [0, 118320, 0, 632], [0, 0, 0, 0], [0, -3164, 0, 1017], [0, 0, 0, 0], [197757, 0, -1456, 0], [0, 0, 0, 0], [652536, 0, 750, 0], [0, 0, 0, 0], [0, -88187, 0, -898], [0, 0, 0, 0], [0, -339248, 0, 3412], [0, 0, 0, 0], [771216, 0, 11528, 0], [0, 0, 0, 0], [-964496, 0, -5892, 0], [0, 0, 0, 0], [0, -555381, 0, 1018], [0, 0, 0, 0], [0, 2239476, 0, 6701], [0, 0, 0, 0], [-738338, 0, 38096, 0], [0, 0, 0, 0], [-761692, 0, -42527, 0], [0, 0, 0, 0], [0, 1867125, 0, 15990], [0, 0, 0, 0], [0, -2621800, 0, 9958], [0, 0, 0, 0], [709761, 0, -20768, 0], [0, 0, 0, 0], [-7761144, 0, -113262, 0], [0, 0, 0, 0], [0, 562731, 0, -6806], [0, 0, 0, 0], [0, 1733420, 0, 23835], [0, 0, 0, 0], [-2338608, 0, -153048, 0], [0, 0, 0, 0], [3544628, 0, -113435, 0], [0, 0, 0, 0], [0, -5019883, 0, -70938], [0, 0, 0, 0], [0, 9021012, 0, 68901], [0, 0, 0, 0], [-17795804, 0, -71088, 0], [0, 0, 0, 0], [417316, 0, 64673, 0], [0, 0, 0, 0], [0, 10039824, 0, 33448], [0, 0, 0, 0], [0, -9064564, 0, 119571], [0, 0, 0, 0], [1480206, 0, 104936, 0], [0, 0, 0, 0], [-7417452, 0, 145341, 0], [0, 0, 0, 0], [0, 6875056, 0, 120248], [0, 0, 0, 0], [0, 10602344, 0, 71994], [0, 0, 0, 0], [17937, 0, 207144, 0], [0, 0, 0, 0], [39279188, 0, -189139, 0], [0, 0, 0, 0], [0, -17384250, 0, -234580], [0, 0, 0, 0], [0, -12140364, 0, -120515], [0, 0, 0, 0], [-33161970, 0, 451240, 0], [0, 0, 0, 0], [-99547504, 0, -147644, 0], [0, 0, 0, 0], [0, 21852480, 0, -216416], [0, 0, 0, 0], [0, -7834788, 0, -299161], [0, 0, 0, 0], [14111218, 0, -460680, 0], [0, 0, 0, 0], [76908156, 0, 917223, 0], [0, 0, 0, 0]]}