# Stored data for newform 324.8.e.h, downloaded from the LMFDB on 01 June 2024. {"Nk2": 20736, "analytic_conductor": 101.21274825685545, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 9, "char_degree": 2, "char_is_minimal": false, "char_is_real": false, "char_orbit_index": 5, "char_orbit_label": "e", "char_order": 3, "char_parity": 1, "char_values": [324, 3, [163, 245], [3, 1]], "cm_discs": [], "conrey_index": 109, "dim": 4, "field_disc": 608400, "field_disc_factorization": [[2, 4], [3, 2], [5, 2], [13, 2]], "field_poly": [4225, 0, -65, 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": [[5, [63867398400, 0, 252720, 0, 1]], [7, [2411809, 1553, 1]]], "hecke_orbit": 8, "hecke_orbit_code": 31525472403718468, "hecke_ring_generator_nbound": 7, "hecke_ring_index": 3888, "hecke_ring_index_factorization": [[2, 4], [3, 5]], "hecke_ring_index_proved": true, "inner_twist_count": 4, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 9, 3, 1, 3, 0], [1, 1, 3, 2, -1, 2, 0], [1, 1, 9, 4, -1, 6, 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": "324.8.e.h", "level": 324, "level_is_powerful": true, "level_is_prime": false, "level_is_prime_power": false, "level_is_prime_square": false, "level_is_square": true, "level_is_squarefree": false, "level_primes": [2, 3], "level_radical": 6, "minimal_twist": "108.8.a.d", "nf_label": "4.0.608400.8", "prim_orbit_index": 3, "qexp_display": "q-\\beta _{2}q^{5}+(-1553+1553\\beta _{1})q^{7}+\\cdots", "related_objects": [], "relative_dim": 2, "rm_discs": [], "sato_tate_group": "7.2.3.c3", "self_twist_discs": [], "self_twist_type": 0, "space_label": "324.8.e", "trace_display": [0, 0, 0, -3106], "trace_hash": 60837863313677756, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.658", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "78.947", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "2687.175", "prec": 27}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.509", "prec": 17}, "traces": [0, 4, 0, 0, 0, 0, 0, -3106, 0, 0, 0, 0, 0, 1598, 0, 0, 0, 0, 0, -142132, 0, 0, 0, 0, 0, -349190, 0, 0, 0, 0, 0, -155656, 0, 0, 0, 0, 0, 949532, 0, 0, 0, 0, 0, 52400, 0, 0, 0, 0, 0, -3176532, 0, 0, 0, 0, 0, 13141440, 0, 0, 0, 0, 0, -846118, 0, 0, 0, 0, 0, -3900046, 0, 0, 0, 0, 0, -13880956, 0, 0, 0, 0, 0, -9357166, 0, 0, 0, 0, 0, -11625120, 0, 0, 0, 0, 0, -4963388, 0, 0, 0, 0, 0, 16600166, 0, 0, 0, 0, 0, 10542182, 0, 0, 0, 0, 0, -79628824, 0, 0, 0, 0, 0, 106647840, 0, 0, 0, 0, 0, -46445018, 0, 0, 0, 0, 0, 107598320, 0, 0, 0, 0, 0, 110365498, 0, 0, 0, 0, 0, -60225034, 0, 0, 0, 0, 0, -299220480, 0, 0, 0, 0, 0, -53013862, 0, 0, 0, 0, 0, -14715820, 0, 0, 0, 0, 0, -126693004, 0, 0, 0, 0, 0, 124220232, 0, 0, 0, 0, 0, -542292070, 0, 0, 0, 0, 0, 417718004, 0, 0, 0, 0, 0, -151126560, 0, 0, 0, 0, 0, -33919438, 0, 0, 0, 0, 0, 114975572, 0, 0, 0, 0, 0, 380090880, 0, 0, 0, 0, 0, -484034818, 0, 0, 0, 0, 0, 483467536, 0, 0, 0, 0, 0, 517838600, 0, 0, 0, 0, 0, -311915332, 0, 0, 0, 0, 0, 785453760, 0, 0, 0, 0, 0, -215998498, 0, 0, 0, 0, 0, -56781734, 0, 0, 0, 0, 0, -2772843840, 0, 0, 0, 0, 0, -737311598, 0, 0, 0, 0, 0, 1747811520, 0, 0, 0, 0, 0, -897616084, 0, 0, 0, 0, 0, 863012540, 0, 0, 0, 0, 0, 145034720, 0, 0, 0, 0, 0, -1106599172, 0, 0, 0, 0, 0, -196616160, 0, 0, 0, 0, 0, 81377200, 0, 0, 0, 0, 0, 2557825280, 0, 0, 0, 0, 0, -579883798, 0, 0, 0, 0, 0, 1944933120, 0, 0, 0, 0, 0, -558005620, 0, 0, 0, 0, 0, 650778182, 0, 0, 0, 0, 0, 1025020886, 0, 0, 0, 0, 0, 4750459276, 0, 0, 0, 0, 0, -1766822014, 0, 0, 0, 0, 0, 1624484160, 0, 0, 0, 0, 0, 1474889400, 0, 0, 0, 0, 0, -1813351114, 0, 0, 0, 0, 0, -3113844862, 0, 0, 0, 0, 0, 2035304348, 0, 0, 0, 0, 0, -10204328160, 0, 0, 0, 0, 0, 2452900320, 0, 0, 0, 0, 0, -6145944040, 0, 0, 0, 0, 0, 124369144, 0, 0, 0, 0, 0, 4044216686, 0, 0, 0, 0, 0, 3851452800, 0, 0, 0, 0, 0, 1644459038, 0, 0, 0, 0, 0, -1314021254, 0, 0, 0, 0, 0, 8066423240, 0, 0, 0, 0, 0, 60340232, 0, 0, 0, 0, 0, 2626771680, 0, 0, 0, 0, 0, -9882362880, 0, 0, 0, 0, 0, 626604500, 0, 0, 0, 0, 0, -4644980482, 0, 0, 0, 0, 0, 12113542876, 0, 0, 0, 0, 0, 12407768270, 0, 0, 0, 0, 0, 379338034, 0, 0, 0, 0, 0, -11384060188, 0, 0, 0, 0, 0, 3441035520, 0, 0, 0, 0, 0, 10177632512, 0, 0, 0, 0, 0, -12073950720, 0, 0, 0, 0, 0, 10778562334, 0, 0, 0, 0, 0, -5105449440, 0, 0, 0, 0, 0, -6562469956, 0, 0, 0, 0, 0, -15693043346, 0, 0, 0, 0, 0, -4419061920, 0, 0, 0, 0, 0, -19798813084, 0, 0, 0, 0, 0, 4278486806, 0, 0, 0, 0, 0, -14531678798, 0, 0, 0, 0, 0, 83735200, 0, 0, 0, 0, 0, -1396530720, 0, 0, 0, 0, 0, -12237481318, 0, 0, 0, 0, 0, 6364999148, 0, 0, 0, 0, 0, 22721549760, 0, 0, 0, 0, 0, 5530924648, 0, 0, 0, 0, 0, 36107622720, 0, 0, 0, 0, 0, -305008756, 0, 0, 0, 0, 0, -16474108306, 0, 0, 0, 0, 0, -22312846804, 0, 0, 0, 0, 0, -4733072326, 0, 0, 0, 0, 0, -21479328050, 0, 0, 0, 0, 0, 48046013996, 0, 0, 0, 0, 0, 2538049068, 0, 0, 0, 0, 0, -20080946800, 0, 0, 0, 0, 0, 5112020160, 0, 0, 0, 0, 0, 18169557120, 0, 0, 0, 0, 0, -14072444662, 0, 0, 0, 0, 0, 63135521280, 0, 0, 0, 0, 0, -6845172022, 0, 0, 0, 0, 0, 25780057798, 0, 0, 0, 0, 0, -100306589760, 0, 0, 0, 0, 0, 7483472624, 0, 0, 0, 0, 0, 8742090240, 0, 0, 0, 0, 0, -33739720556, 0, 0, 0, 0, 0, -25304697874, 0, 0, 0, 0, 0, 5250005280, 0, 0, 0, 0, 0, -32744017292, 0, 0, 0, 0, 0, -32610426280, 0, 0, 0, 0, 0, 35779441580, 0, 0, 0, 0, 0, 12920050304, 0, 0, 0, 0, 0, -13526585280, 0, 0, 0, 0, 0, 17411729378, 0, 0, 0, 0, 0, -37471375228, 0, 0, 0, 0, 0, 61831781836, 0, 0, 0, 0, 0, -12843968926, 0, 0, 0, 0, 0, 54353518640, 0, 0, 0, 0, 0, 21118294080, 0, 0, 0, 0, 0, -6868583446, 0, 0, 0, 0, 0, -1352096564, 0, 0, 0, 0, 0, -9032718240, 0, 0, 0, 0, 0, 165624095520, 0, 0, 0, 0, 0, -24675259168, 0, 0, 0, 0, 0, -1861929200, 0, 0, 0, 0, 0, -44418234838, 0, 0, 0, 0, 0, -3522386092, 0, 0, 0, 0, 0, -61069788000, 0, 0, 0, 0, 0, -9784878422, 0, 0, 0, 0, 0, 144258225908, 0, 0, 0, 0, 0, -25973451262, 0, 0, 0, 0, 0, 2296012334, 0, 0, 0, 0, 0, 67494435840, 0, 0, 0, 0, 0, 3116136754, 0, 0, 0, 0, 0, 25038371714, 0, 0, 0, 0, 0, -29706766636, 0, 0, 0, 0, 0, -83550095480, 0, 0, 0, 0, 0, -19225926720, 0, 0, 0, 0, 0, -80399329920, 0, 0, 0, 0, 0, -42179146606, 0, 0, 0, 0, 0, -25034443200, 0, 0, 0, 0, 0, -58178940976, 0, 0, 0, 0, 0, -82891769770, 0, 0, 0, 0, 0, 112871711556, 0, 0, 0, 0, 0, -16124163988, 0, 0, 0, 0, 0, -80199175680, 0, 0, 0, 0, 0, -5545441922, 0, 0, 0, 0, 0, 176716987200, 0, 0, 0, 0, 0, 42910833054, 0, 0, 0, 0, 0, -61170165166, 0, 0, 0, 0, 0, 187058955604, 0, 0, 0, 0, 0, 34148031840, 0, 0, 0, 0, 0, -119719023840, 0, 0, 0, 0, 0, -156320556844, 0, 0, 0, 0, 0, 47092565540, 0, 0, 0], "weight": 8, "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], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, -1, 0], [0, 0, 0, 0], [-1553, 1553, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 13, -13], [0, 0, 0, 0], [0, 799, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 23], [0, 0, 0, 0], [-35533, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 211, 0], [0, 0, 0, 0], [-174595, 174595, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, -296, 296], [0, 0, 0, 0], [0, -77828, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 1553], [0, 0, 0, 0], [237383, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 752, 0], [0, 0, 0, 0], [26200, -26200, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 777, -777], [0, 0, 0, 0], [0, -1588266, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, -3458], [0, 0, 0, 0], [3285360, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, -389, 0], [0, 0, 0, 0], [-423059, 423059, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, -799, 799], [0, 0, 0, 0], [0, -1950023, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, -3214], [0, 0, 0, 0], [-3470239, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, -20189, 0], [0, 0, 0, 0], [-4678583, 4678583, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 3810, -3810], [0, 0, 0, 0], [0, -5812560, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, -5197], [0, 0, 0, 0], [-1240847, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 35533, 0], [0, 0, 0, 0], [8300083, -8300083, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]]}