# Stored data for newform 48.11.e.d, downloaded from the LMFDB on 19 April 2024.
{"label": "48.11.e.d", "space_label": "48.11.e", "level": 48, "weight": 11, "hecke_orbit": 4, "hecke_orbit_code": 13511073944567856, "dim": 4, "is_polredabs": true, "nf_label": "4.0.462400.3", "trace_hash": 1704094766661730052, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[5, [306009247334400, 0, 36397440, 0, 1]]], "qexp_display": "q+(-21-\\beta _{1})q^{3}+(4\\beta _{1}-2\\beta _{2}-\\beta _{3})q^{5}+\\cdots", "char_order": 2, "char_parity": -1, "char_degree": 1, "char_conductor": 3, "char_orbit_label": "e", "char_is_real": true, "Nk2": 5808, "analytic_conductor": 30.497148128338758, "hecke_ring_index": 11943936, "level_radical": 6, "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": "0.508", "prec": 17}, "analytic_rank_proved": true, "char_values": [48, 2, [31, 37, 17], [2, 2, 1]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 2, "level_primes": [2, 3], "conrey_indexes": [17], "field_disc": 462400, "field_disc_factorization": [[2, 6], [5, 2], [17, 2]], "field_poly": [531, 38, -37, -2, 1], "hecke_ring_index_factorization": [[2, 14], [3, 6]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.040", "prec": 17}, {"__RealLiteral__": 0, "data": "3.720", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "66.487", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1619.108", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "10.2.3.c2", "trace_display": [0, -84, 0, 45112], "traces": [0, 4, 0, -84, 0, 0, 0, 45112, 0, 159012, 0, 0, 0, 275240, 0, 1180800, 0, 0, 0, 1568728, 0, 9628008, 0, 0, 0, -33732380, 0, -34619508, 0, 0, 0, 21785848, 0, 25974144, 0, 0, 0, -71014168, 0, -217287240, 0, 0, 0, 470688664, 0, 312318720, 0, 0, 0, -50058420, 0, 708576768, 0, 0, 0, -2701359360, 0, -1058753208, 0, 0, 0, -1184038744, 0, 905007096, 0, 0, 0, 297365848, 0, 596268288, 0, 0, 0, 6534269000, 0, 5150031180, 0, 0, 0, -199282568, 0, 1458964548, 0, 0, 0, -12880512000, 0, -210268800, 0, 0, 0, -8317232080, 0, 31744468392, 0, 0, 0, -39176355064, 0, 2626912512, 0, 0, 0, -11068379336, 0, 23088695040, 0, 0, 0, -20319756760, 0, 61601643768, 0, 0, 0, -63919296000, 0, 28708220520, 0, 0, 0, -12876724124, 0, 39726238464, 0, 0, 0, -18119605256, 0, 61848204936, 0, 0, 0, -37701621296, 0, 133205109120, 0, 0, 0, -285612668264, 0, -41441840640, 0, 0, 0, -251427375360, 0, 239589046980, 0, 0, 0, -306503151944, 0, 306226013184, 0, 0, 0, -123678139480, 0, -28899545472, 0, 0, 0, 463047039064, 0, 453812163840, 0, 0, 0, -304066926996, 0, 148529677464, 0, 0, 0, -140584616840, 0, 61975322496, 0, 0, 0, 242284516712, 0, -182877558216, 0, 0, 0, -19313150976, 0, -136788801624, 0, 0, 0, -133525897720, 0, -114181804800, 0, 0, 0, 122794896952, 0, -534134927928, 0, 0, 0, -737600647680, 0, 52951186944, 0, 0, 0, -1256070856232, 0, 203725428480, 0, 0, 0, 1984607238544, 0, 351615791640, 0, 0, 0, 1682678422264, 0, -1714062002940, 0, 0, 0, 2780135565032, 0, 393317713152, 0, 0, 0, 808939238400, 0, -1691711521752, 0, 0, 0, -304701658744, 0, -3248702076564, 0, 0, 0, 1215818887280, 0, -642859415424, 0, 0, 0, -2776429103616, 0, -5446802672640, 0, 0, 0, 2445060910256, 0, -1075406319360, 0, 0, 0, 4731254841600, 0, -130106462976, 0, 0, 0, 6351996198520, 0, -1483025806320, 0, 0, 0, 4451512449128, 0, -1838912765256, 0, 0, 0, -2632667035880, 0, -484759860480, 0, 0, 0, -7057958762876, 0, 1666151868504, 0, 0, 0, 2588716051200, 0, 3286550090880, 0, 0, 0, 9181990764112, 0, -4214923028352, 0, 0, 0, 5218033190104, 0, -4725366829464, 0, 0, 0, 2968727534024, 0, 9355614497280, 0, 0, 0, -13267250277120, 0, -4859960321664, 0, 0, 0, -7118108363800, 0, 740295466680, 0, 0, 0, -6610354032488, 0, -7872295304664, 0, 0, 0, 10041177926792, 0, 3113002916352, 0, 0, 0, -426540005008, 0, 10976627381760, 0, 0, 0, -16240984125016, 0, -7455168537480, 0, 0, 0, -16033751677440, 0, 17062957200384, 0, 0, 0, -18535845785748, 0, 22625241696204, 0, 0, 0, 36619855936888, 0, 17108890993152, 0, 0, 0, -10525336515736, 0, 5677537132800, 0, 0, 0, -45773794314728, 0, 32518745215656, 0, 0, 0, -9023415528960, 0, 12685742442072, 0, 0, 0, 14150965248, 0, -12227797392768, 0, 0, 0, -19802713323736, 0, -6629884395024, 0, 0, 0, -33279044695120, 0, 6683217569280, 0, 0, 0, -24889478077240, 0, 11048645373696, 0, 0, 0, 26427695719680, 0, 13215115643784, 0, 0, 0, -11028930138904, 0, -17695450321920, 0, 0, 0, -24571677034192, 0, -220345493760, 0, 0, 0, 55834526157704, 0, 76440937800960, 0, 0, 0, -8542620032072, 0, -22027149263700, 0, 0, 0, 48366071308800, 0, -12359535172992, 0, 0, 0, -1886546769408, 0, -34064852358936, 0, 0, 0, 1645024990280, 0, 69954010145280, 0, 0, 0, 13882848978040, 0, 36185803718400, 0, 0, 0, -25152381202736, 0, -110738342272200, 0, 0, 0, -36494601238760, 0, 3733296977664, 0, 0, 0, -69805658839280, 0, 8830564038144, 0, 0, 0, 106164678576952, 0, -30681400814904, 0, 0, 0, 65747319321600, 0, -140742162489600, 0, 0, 0, -28170471097640, 0, -63208480843008, 0, 0, 0, 17705530656000, 0, -22722215397084, 0, 0, 0, 100090599576560, 0, -38181198817656, 0, 0, 0, 4021230689280, 0, -78958161323136, 0, 0, 0, 18031099202200, 0, -36137796351960, 0, 0, 0, 99595029898564, 0, 41114366754048, 0, 0, 0, 336676920733440, 0, 13116213726336, 0, 0, 0, 194091135958952, 0, -171375823821192, 0, 0, 0, -110552926264232, 0, -29618732955672, 0, 0, 0, -93825917408624, 0, 34578577532160, 0, 0, 0, -45083193260560, 0, -142675998925824, 0, 0, 0, 38286417576960, 0, -124800965950536, 0, 0, 0, -173781492475880, 0, -62782244001792, 0, 0, 0, 137537548144136, 0, 308144467265880, 0, 0, 0, 219495469019904, 0, -95175028339200, 0, 0, 0, -160129907705264, 0, 48888912514176, 0, 0, 0, -454000259266560, 0, 69106183992168, 0, 0, 0, 269546118505160, 0, 56163965145624, 0, 0, 0, 280520619286264, 0, -31645826968320, 0, 0, 0, 31928078342888, 0, -300843008202240, 0, 0, 0, 70189279805848, 0, 76064418420480, 0, 0, 0, -325682485667900, 0, 449603981568, 0, 0, 0, 48035894122936, 0, 168832272065352, 0, 0, 0, -261065365653000, 0, 40483901606400, 0, 0, 0, 56318121416536, 0, 205228277809920, 0, 0, 0, 191506580713728, 0, 379095375560496, 0, 0, 0, -36566203979520, 0, 218694618543240, 0, 0, 0, -12709832715160, 0, -132675400811520, 0, 0, 0, -317972325542400, 0, 128482223816616, 0, 0, 0, -176964656505592, 0, 398482603849260, 0, 0, 0, -396284718155152, 0, 200667285251712, 0, 0, 0, -1091408963258880, 0, -360793684052232, 0, 0, 0, -110422895811368, 0, 162753265737216, 0, 0, 0, -844099078035456, 0, 348443592327936, 0, 0, 0, -342708472039696, 0, 302260397644800, 0, 0, 0, 956593409222120, 0, 134533222351416, 0, 0, 0, -614730844224000, 0, -119422516889088, 0, 0, 0, -392550533109488, 0, 858677318784984, 0, 0, 0, 493822331891896, 0, 1016397230436, 0, 0, 0, 883407190298024, 0, 205631700243840, 0, 0, 0, -187215223146920, 0, -179067493938480, 0, 0, 0, 1024234510199040, 0, -220963702885632, 0, 0, 0, -37641575448200, 0, -215230959167616, 0, 0, 0, -882078640928920, 0, 595089218658816, 0, 0, 0, -212232865704400, 0, -31786345866240, 0, 0, 0, 22545825171464, 0, -647971318480896, 0, 0, 0, 546618580976440, 0, 438828107854224, 0, 0, 0, -646735143882240, 0, 61942165568640, 0, 0, 0, -313296051705896, 0, -316190754480384, 0, 0, 0, 142888055612560, 0, -1010785335287040, 0, 0, 0, 871075654594560, 0, 121204228787712, 0, 0, 0, -200628423336960, 0, -274673981722752, 0, 0, 0, 29157923281816, 0, -279865171847640, 0, 0, 0, -191140087492592, 0, -191389161756240, 0, 0, 0, -1363358758873160, 0, -176882270705280, 0, 0, 0, 1353221215883432, 0, -609408863209608, 0, 0, 0, 2755037685542400, 0, 583810444451304, 0, 0, 0, -131779266273116, 0, 619596550427904, 0, 0, 0, 1061937151767928, 0, -1409140066827000, 0, 0, 0, 364177404301928, 0, -443342765145600, 0, 0, 0, 186986763930904, 0, 955022128630272, 0, 0, 0, 991573056357120, 0, -2797727567644884, 0, 0, 0, 590583208730480, 0, -1628227309480632, 0, 0, 0, 444940966624808, 0, -232388497768320, 0, 0, 0, 1302871568919256, 0, -1565516709953280, 0, 0, 0, 1531111701207952, 0, -205317416037888, 0, 0, 0, -2909072897176320, 0, -1087784824320, 0, 0, 0, -392667245171712, 0, 1860604728456048, 0, 0, 0, 2299687821653656, 0, -2048802862853376, 0, 0, 0, 784095234064128, 0, -541482188808960, 0, 0, 0, -2081143916769608, 0, -1874170798242744, 0, 0, 0, 1962171877813160, 0, -23545848920328, 0, 0, 0, -1269093113270520, 0, -475584373350144, 0, 0, 0, -1994896888175800, 0, -939455980053864, 0, 0, 0, -18461494711296, 0, 2331725607394560, 0, 0, 0, -78319226001200, 0, 1326423461505408, 0, 0, 0, 3022196227706880, 0, 3481317265063680, 0, 0, 0, 2135112769762572, 0, -1142477661595392, 0, 0, 0, -573169190162888, 0, -602056901827584, 0, 0, 0, -2831408193728432, 0, 2238770605495800, 0, 0, 0, 2395597975045632, 0, -834112058756760, 0, 0, 0, -2926718735512320, 0, -992153284715520, 0, 0, 0, -1747917917644040, 0, 2853364915588488, 0, 0, 0, 3324928946325224, 0, 2056365543863736, 0], "weight_parity": -1, "has_non_self_twist": 1, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": false, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 3, 2, -1, 2, 0]], "char_orbit_index": 5, "prim_orbit_index": 2, "minimal_twist": "6.11.b.a", "char_is_minimal": false, "conrey_index": 17, "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, 0, 0], [1, 0, 0, 0], [0, 0, 0, 0], [-21, -1, 0, 0], [0, 0, 0, 0], [0, 4, -2, -1], [0, 0, 0, 0], [11278, -43, 5, -1], [0, 0, 0, 0], [39753, -20, -62, 7], [0, 0, 0, 0], [0, 21, -189, -35], [0, 0, 0, 0], [68810, 860, -100, 20], [0, 0, 0, 0], [295200, 743, 1877, 35], [0, 0, 0, 0], [0, 4276, 2860, -236], [0, 0, 0, 0], [392182, 4171, -485, 97], [0, 0, 0, 0], [2407002, -12952, -1674, 189], [0, 0, 0, 0], [0, 366, -4590, -826], [0, 0, 0, 0], [-8433095, -18060, 2100, -420], [0, 0, 0, 0], [-8654877, -39306, -5727, 1599], [0, 0, 0, 0], [0, -16812, -34494, -2947], [0, 0, 0, 0], [5446462, -130935, 15225, -3045], [0, 0, 0, 0], [6493536, 29456, 69146, 5033], [0, 0, 0, 0], [0, 129502, 71914, -9598], [0, 0, 0, 0], [-17753542, -244412, 28420, -5684], [0, 0, 0, 0], [-54321810, -35330, 33480, -3780], [0, 0, 0, 0], [0, 238792, 158308, -13414], [0, 0, 0, 0], [117672166, -291669, 33915, -6783], [0, 0, 0, 0], [78079680, -411492, -175386, -52581], [0, 0, 0, 0], [0, -246700, -159940, 14460], [0, 0, 0, 0], [-12514605, -969908, 112780, -22556], [0, 0, 0, 0], [177144192, 78720, 346344, -98364], [0, 0, 0, 0], [0, 81716, 437750, 59339], [0, 0, 0, 0], [-675339840, -1614564, 187740, -37548], [0, 0, 0, 0], [-264688302, -229804, 162378, -18333], [0, 0, 0, 0], [0, 600237, 739875, 23273], [0, 0, 0, 0], [-296009686, 844692, -98220, 19644], [0, 0, 0, 0], [226251774, -2903825, -924173, 130057], [0, 0, 0, 0], [0, -1412560, -2027020, -102410], [0, 0, 0, 0], [74341462, 2146431, -249585, 49917], [0, 0, 0, 0], [149067072, 698920, 1635604, 122926], [0, 0, 0, 0], [0, 478562, -803026, -213598], [0, 0, 0, 0], [1633567250, -1987632, 231120, -46224], [0, 0, 0, 0], [1287507795, 7730015, -703080, 79380], [0, 0, 0, 0], [0, 2259432, 1340556, -153146], [0, 0, 0, 0], [-49820642, 6895609, -801815, 160363], [0, 0, 0, 0], [364741137, 6742260, -4229568, 397530], [0, 0, 0, 0], [0, -2981737, -651583, 388359], [0, 0, 0, 0], [-3220128000, 23246832, -2703120, 540624], [0, 0, 0, 0], [-52567200, 3019021, 6360919, 1018345], [0, 0, 0, 0], [0, 2016028, 5538400, 587062], [0, 0, 0, 0], [-2079308020, 6740250, -783750, 156750], [0, 0, 0, 0], [7936117098, -10543792, -5097330, 575505], [0, 0, 0, 0], [0, -6617102, -9947954, -555142], [0, 0, 0, 0], [-9794088766, -3429508, 398780, -79756], [0, 0, 0, 0], [656728128, -12335547, -11748765, -2000271], [0, 0, 0, 0]]}