# Stored data for newform 25.10.b.a, downloaded from the LMFDB on 24 April 2024.
{"label": "25.10.b.a", "space_label": "25.10.b", "level": 25, "weight": 10, "hecke_orbit": 1, "hecke_orbit_code": 68887248921, "dim": 2, "is_polredabs": true, "nf_label": "2.0.4.1", "trace_hash": 357992214747874470, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[2, [64, 0, 1]]], "qexp_display": "q+4iq^{2}-57iq^{3}+448q^{4}+912q^{6}+\\cdots", "char_order": 2, "char_parity": 1, "char_degree": 1, "char_conductor": 5, "char_orbit_label": "b", "char_is_real": true, "Nk2": 2500, "analytic_conductor": 12.875895904096827, "hecke_ring_index": 2, "level_radical": 5, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 4, "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": "0.508", "prec": 17}, "analytic_rank_proved": true, "char_values": [25, 2, [2], [1]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 2, "level_primes": [5], "conrey_indexes": [24], "field_disc": -4, "field_disc_factorization": [[-1, 1], [2, 2]], "field_poly": [1, 0, 1], "hecke_ring_index_factorization": [[2, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.914", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "15.137", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "153.558", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "9.2.3.c2", "trace_display": [0, 0, 0, 0], "traces": [0, 2, 0, 0, 896, 0, 1824, 0, 0, 13374, 0, -92416, 0, 0, 67872, 0, 335872, 0, 0, 2017480, 0, -967176, 0, 0, 1751040, 0, 1854944, 0, 0, -8392780, 0, -6730056, 0, 0, 7917472, 0, 5991552, 0, 0, -26432952, 0, 22112524, 0, 0, -41402368, 0, 8520864, 0, 0, 44718086, 0, -112823976, 0, 0, 48098880, 0, 65157120, 0, 0, 170371240, 0, 91497284, 0, 0, 87556096, 0, -84283392, 0, 0, -121422312, 0, -379934936, 0, 0, -238901728, 0, 903831040, 0, 0, -190081680, 0, -422168598, 0, 0, -433294848, 0, 102348704, 0, 0, 39877260, 0, -983584056, 0, 0, -568946528, 0, 1202847744, 0, 0, -617985792, 0, -433343796, 0, 0, 1780746240, 0, -635817376, 0, 0, 4993182140, 0, 3404349624, 0, 0, 1839941760, 0, -3759965440, 0, 0, -4198239528, 0, -445536854, 0, 0, -3015065088, 0, 453860064, 0, 0, -1458469032, 0, -5634022656, 0, 0, -724578528, 0, 7600773120, 0, 0, -5046454840, 0, 8107488024, 0, 0, 2245976064, 0, -6594735136, 0, 0, -2930610100, 0, 7310304104, 0, 0, -3136229376, 0, -11841962496, 0, 0, 9060397608, 0, -4518188136, 0, 0, 9906410752, 0, -4187301216, 0, 0, -5672385966, 0, 13490888760, 0, 0, -7654215360, 0, -15519973376, 0, 0, 50380319320, 0, 20896304044, 0, 0, 8180029440, 0, -6137811072, 0, 0, -25504431120, 0, -19372501976, 0, 0, -312053728, 0, 20033702528, 0, 0, -16134726800, 0, 10325244024, 0, 0, -50545141248, 0, 11971745824, 0, 0, -93223715840, 0, -16091779616, 0, 0, 16913741472, 0, 46174924800, 0, 0, 93974975688, 0, -114738024856, 0, 0, 44758597632, 0, -17850621856, 0, 0, -41220201180, 0, 44691268608, 0, 0, 12404010528, 0, 76326315520, 0, 0, -4438325840, 0, 51595386524, 0, 0, 40990783232, 0, 20166621888, 0, 0, 59669042328, 0, -178369610496, 0, 0, 4992861472, 0, -3992977408, 0, 0, 126677641272, 0, -56122519860, 0, 0, -80912056320, 0, 68465201280, 0, 0, 52977927580, 0, 68800796264, 0, 0, -114449826528, 0, -54397195776, 0, 0, -45003884472, 0, 200597970444, 0, 0, -170210851328, 0, -85713252352, 0, 0, -252561456934, 0, 4446765624, 0, 0, 40782894432, 0, -229345658880, 0, 0, -123482230872, 0, -54270400296, 0, 0, 338807521280, 0, 52944135264, 0, 0, -170597377992, 0, 542505351384, 0, 0, 88830503072, 0, -85156592640, 0, 0, 387813578240, 0, -241020815976, 0, 0, -189131531904, 0, 268219786144, 0, 0, 301683896472, 0, -480128025456, 0, 0, 223278922272, 0, -162423668736, 0, 0, 254371361448, 0, 310982427648, 0, 0, 98254755840, 0, -251200184736, 0, 0, -933184966700, 0, -697036944240, 0, 0, 155378570880, 0, 17865012480, 0, 0, 332894940240, 0, 1389737379642, 0, 0, -440645657088, 0, 83445523008, 0, 0, 147866447988, 0, 337142163624, 0, 0, -365850546176, 0, -546188666880, 0, 0, 334018547320, 0, -71148275976, 0, 0, 695709204480, 0, 327089694304, 0, 0, -1584498908340, 0, -527060172936, 0, 0, -403890018528, 0, -276857634816, 0, 0, -975629118240, 0, -644202145596, 0, 0, -194138020608, 0, -284817382080, 0, 0, 792845897540, 0, 1630910028024, 0, 0, 56979017568, 0, 1223253950464, 0, 0, 2463233836280, 0, -2350007329036, 0, 0, -610384680960, 0, -346500661632, 0, 0, 1221413846016, 0, -464654171256, 0, 0, -228391180416, 0, 2236945598720, 0, 0, 1042770286960, 0, 299029841082, 0, 0, 1525148631552, 0, -509788874336, 0, 0, -1171343823500, 0, -1021775508992, 0, 0, 484193639072, 0, 1766344089600, 0, 0, -2975168247120, 0, -1520557546116, 0, 0, -1409449902080, 0, -57877619616, 0, 0, 384207764472, 0, -1265834668776, 0, 0, -173354492160, 0, -1880811308544, 0, 0, 1391476620720, 0, 3462104116744, 0, 0, -199600510592, 0, 561712493664, 0, 0, -3822131952552, 0, 2399772845824, 0, 0, 1871156210560, 0, -1130218684416, 0, 0, -2862913945400, 0, -3181724642376, 0, 0, 435705661440, 0, -393732083712, 0, 0, 2329267989940, 0, 3496858305864, 0, 0, -1760931858528, 0, -653394126336, 0, 0, 3579602632488, 0, -1673891556236, 0, 0, -2524042149888, 0, -330198834656, 0, 0, 3035077797094, 0, 1139272481880, 0, 0, 36368061120, 0, -695595386880, 0, 0, -2066333317888, 0, 6148127468124, 0, 0, 5221224415232, 0, -897028659072, 0, 0, 611842338108, 0, -8466132897200, 0, 0, -1696366252128, 0, -2260811768320, 0, 0, -1483211831192, 0, 5213370283008, 0, 0, 3632154634752, 0, 39887421984, 0, 0, 9145567837380, 0, -4646097121136, 0, 0, 750410614464, 0, 585487613952, 0, 0, -4661028143832, 0, 2220316469784, 0, 0, -6330945730560, 0, 1355308891104, 0, 0, -6788876689440, 0, 5755432764024, 0, 0, -2222553047040, 0, -1312913324800, 0, 0, -9027935027200, 0, -2884238770196, 0, 0, 3275016238592, 0, -395209541952, 0, 0, 4058647694640, 0, 8245030847144, 0, 0, 101681104672, 0, -3010780200960, 0, 0, -3788752562920, 0, -3201906367440, 0, 0, -4439044227072, 0, -2615982762656, 0, 0, 14777326110872, 0, -2203192318456, 0, 0, 4057697274272, 0, 4059058128384, 0, 0, -2540624917032, 0, -9705039987876, 0, 0, -2024148284928, 0, 7986670705280, 0, 0, -7872514257920, 0, 3254574320928, 0, 0, 4553782111680, 0, 3713488830464, 0, 0, 5851057813240, 0, -3258411678316, 0, 0, -4019809167360, 0, -1597535855136, 0, 0, 7264491459288, 0, -4227906499072, 0, 0, -822098421728, 0, -2541228912768, 0, 0, 165466489272, 0, -6899759356776, 0, 0, 6043918164480, 0, 4256432980800, 0, 0, 9214106458648, 0, 1181991803024, 0, 0, 4424953360672, 0, -7348046745600, 0, 0, 824756079528, 0, 14254769491204, 0, 0, -4045792083968, 0, 1615961997024, 0, 0, -1818537742460, 0, -1271076194160, 0, 0, -3828794449536, 0, 22570383055360, 0, 0, -21603332861520, 0, -6348018223176, 0, 0, 9361544211712, 0, -406329610848, 0, 0, -16313947549146, 0, -6330804673096, 0, 0, -4758090412128, 0, 5619134889984, 0, 0, 5442484711960, 0, -26663976000480, 0, 0, -5892298629120, 0, -3131416133536, 0, 0, -8968511415528, 0, -10274455469896, 0, 0, -7784068452160, 0, -11425985141760, 0, 0, 5610682192896, 0, 20787157027284, 0, 0, -8678880885248, 0, -1153251045216, 0, 0, 7833272131580, 0, 25093278984024, 0, 0, 684405783648, 0, -299571578880, 0, 0, 22305787459760, 0, 17556033522688, 0, 0, 7509776490496, 0, -5138228662272, 0, 0, 4705333393848, 0, 9465292239144, 0, 0, -2356602088928, 0, -7228357606400, 0, 0, 35192329726072, 0, 266659237620, 0, 0, 4625709322752, 0, -6241938498432, 0, 0, -5351611948660, 0, -46517174224416, 0, 0, 11039171047424, 0, -18947207233536, 0, 0, -6577226582472, 0, 33147965018964, 0, 0, 11492875991040, 0, 5781718400640, 0, 0, -42223218925380, 0, 24173219092824, 0, 0, -4602366814080, 0, -41764224696320, 0, 0, 6959765560160, 0, 6205086112462, 0, 0, -7209117267968, 0, -3804545432736, 0, 0, -568395763272, 0, 15903508856664, 0, 0, 3105051829824, 0, 16237191813120, 0, 0, -31402886805560, 0, -10693351256112, 0, 0, 31719095009280, 0, 2424858965984, 0, 0, 8783294269440, 0, 10500410883144, 0, 0, 8595336351360, 0, 42100789108224, 0, 0, -19313151698232, 0, -63245392462756, 0, 0, -51402635135488, 0, -17627115475296, 0, 0, -2647464795528, 0, 19507566576384, 0, 0, -2672716411200, 0, 25887705661440, 0, 0, 28241939697840, 0, 39328642746824, 0, 0, -17136596981760, 0, 6666997342848, 0, 0, -2897769963852, 0, -68328905074216, 0, 0, -9132859730528, 0, -18466650128640, 0, 0, -62873291460320, 0, -1448955741576, 0, 0, 20021688336384, 0, 11428625370144, 0, 0, 17540141899220, 0, 45108922071640, 0, 0, 12520331255072, 0, 11907850106880, 0, 0, 37277754367848, 0, -15121032808676, 0, 0, 28611464560640, 0, -4729328914432, 0, 0, 95569252907128, 0, -57822186158376, 0, 0, -4251710793312, 0, -1988369976320, 0, 0, 60687020516472, 0, -30232417439774, 0, 0, 23114733162752, 0, -4120587580032, 0, 0, -113810057550240, 0, 54532567696464, 0, 0, -26431288805728, 0, 15365687885824, 0, 0, -1842648430080, 0, 33389408970180, 0, 0, 19359957012480, 0, -33224800326080, 0, 0, -6813276463752, 0, -51277540853576, 0, 0, -12893471988096, 0, 26731730962944, 0, 0, 89772699584880, 0], "weight_parity": 1, "has_non_self_twist": 1, "level_is_prime": false, "level_is_prime_power": true, "level_is_square": true, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 5, 2, 1, 2, 0]], "char_orbit_index": 2, "prim_orbit_index": 2, "minimal_twist": "5.10.a.a", "char_is_minimal": false, "conrey_index": 24, "id": 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], [1, 0], [0, 4], [0, -57], [448, 0], [0, 0], [912, 0], [0, -2121], [0, 3840], [6687, 0], [0, 0], [-46208, 0], [0, -25536], [0, -57967], [33936, 0], [0, 0], [167936, 0], [0, -247421], [0, 26748], [1008740, 0], [0, 0], [-483588, 0], [0, -184832], [0, -266277], [875520, 0], [0, 0], [927472, 0], [0, -1503090], [0, -950208], [-4196390, 0], [0, 0], [-3365028, 0], [0, 2637824], [0, 2633856], [3958736, 0], [0, 0], [2995776, 0], [0, 7465679], [0, 4034960], [-13216476, 0], [0, 0], [11056262, 0], [0, -1934352], [0, -3198397], [-20701184, 0], [0, 0], [4260432, 0], [0, 17779579], [0, -9572352], [22359043, 0], [0, 0], [-56411988, 0], [0, -25969216], [0, 19869293], [24049440, 0], [0, 0], [32578560, 0], [0, -57498180], [0, -16785560], [85185620, 0], [0, 0], [45748642, 0], [0, -13460112], [0, -14183127], [43778048, 0], [0, 0], [-42141696, 0], [0, 22643079], [0, -110844608], [-60711156, 0], [0, 0], [-189967468, 0], [0, 25678080], [0, 206085473], [-119450864, 0], [0, 0], [451915520, 0], [0, 98007168], [0, -52865904], [-95040840, 0], [0, 0], [-211084299, 0], [0, 44225048], [0, 130853163], [-216647424, 0], [0, 0], [51174352, 0], [0, 239194230], [0, -177438720], [19938630, 0], [0, 0], [-491792028, 0], [0, -119292096], [0, 191806596], [-284473264, 0], [0, 0], [601423872, 0], [0, 9751679], [0, 89436172], [-308992896, 0], [0, 0]]}