# Stored data for newform 72.8.d.a, downloaded from the LMFDB on 24 April 2024.
{"label": "72.8.d.a", "space_label": "72.8.d", "level": 72, "weight": 8, "hecke_orbit": 1, "hecke_orbit_code": 206292648008, "dim": 2, "is_polredabs": true, "nf_label": "2.0.8.1", "trace_hash": 31420157089583468, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[5, [310472, 0, 1]]], "qexp_display": "q+4\\beta q^{2}-2^{7}q^{4}+197\\beta q^{5}-754q^{7}+\\cdots", "char_order": 2, "char_parity": 1, "char_degree": 1, "char_conductor": 8, "char_orbit_label": "d", "char_is_real": true, "Nk2": 4608, "analytic_conductor": 22.491721834856765, "hecke_ring_index": 2, "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": 1, "is_self_dual": false, "is_self_twist": true, "is_cm": true, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.758", "prec": 17}, "analytic_rank_proved": true, "char_values": [72, 2, [55, 37, 65], [2, 1, 2]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 4, "level_primes": [2, 3], "conrey_indexes": [37], "field_disc": -8, "field_disc_factorization": [[-1, 1], [2, 3]], "field_poly": [2, 0, 1], "hecke_ring_index_factorization": [[2, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.047", "prec": 17}, {"__RealLiteral__": 0, "data": "1.937", "prec": 17}, {"__RealLiteral__": 0, "data": "0.413", "prec": 17}, {"__RealLiteral__": 0, "data": "23.450", "prec": 20}, {"__RealLiteral__": 0, "data": "3.117", "prec": 17}, {"__RealLiteral__": 0, "data": "313.751", "prec": 24}], "related_objects": [], "self_twist_discs": [-24], "cm_discs": [-24], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "7.2.1.d2", "trace_display": [0, 0, 0, -1508], "traces": [0, 2, 0, 0, -256, 0, 0, -1508, 0, 0, -12608, 0, 0, 0, 0, 0, 32768, 0, 0, 0, 0, 0, -152192, 0, 0, -464694, 0, 0, 193024, 0, 0, 662740, 0, 0, 0, 0, 0, 0, 0, 0, 1613824, 0, 0, 0, 0, 0, 0, 0, 0, -510054, 0, 0, 0, 0, 0, -7495456, 0, 0, 5696704, 0, 0, 0, 0, 0, -4194304, 0, 0, 0, 0, 0, 9506432, 0, 0, -5638724, 0, 0, 0, 0, 0, -15122540, 0, 0, 0, 0, 0, 0, 0, 0, 19480576, 0, 0, 0, 0, 0, 0, 0, 0, -23490428, 0, 0, 59480832, 0, 0, 36220996, 0, 0, -5420480, 0, 0, 0, 0, 0, -24707072, 0, 0, 0, 0, 0, -33499904, 0, 0, -51503802, 0, 0, -84830720, 0, 0, -3420692, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 280562672, 0, 0, 0, 0, 0, -91362596, 0, 0, 114752768, 0, 0, 0, 0, 0, -206569472, 0, 0, 0, 0, 0, -189236864, 0, 0, 125497034, 0, 0, 0, 0, 0, 350379276, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -325398476, 0, 0, 65286912, 0, 0, 210475972, 0, 0, -164335808, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -452311808, 0, 0, -499705960, 0, 0, 959418368, 0, 0, -593604596, 0, 0, 0, 0, 0, 0, 0, 0, -729178112, 0, 0, 0, 0, 0, 0, 0, 0, 650784940, 0, 0, 0, 0, 0, 0, 0, 0, 1944430976, 0, 0, 0, 0, 0, 536870912, 0, 0, 0, 0, 0, 565806592, 0, 0, -266958640, 0, 0, 0, 0, 0, -1201856084, 0, 0, 0, 0, 0, 0, 0, 0, -1216823296, 0, 0, 0, 0, 0, 0, 0, 0, -820677346, 0, 0, 721756672, 0, 0, -1649870272, 0, 0, 1327063744, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4177912960, 0, 0, 831472924, 0, 0, 1935685120, 0, 0, 3386690528, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2745788012, 0, 0, 0, 0, 0, 1626483560, 0, 0, -965671616, 0, 0, 0, 0, 0, -2493513728, 0, 0, 0, 0, 0, 297446656, 0, 0, 1787743478, 0, 0, 0, 0, 0, 2361987508, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5651573824, 0, 0, 3006774784, 0, 0, 0, 0, 0, 2556028480, 0, 0, 0, 0, 0, -7613546496, 0, 0, 0, 0, 0, -4295314816, 0, 0, 5447242060, 0, 0, -4636287488, 0, 0, -9319915552, 0, 0, 0, 0, 0, 0, 0, 0, 693821440, 0, 0, 0, 0, 0, 0, 0, 0, -4556123684, 0, 0, 0, 0, 0, 2379393508, 0, 0, 0, 0, 0, 0, 0, 0, 3162505216, 0, 0, 0, 0, 0, 6217459840, 0, 0, -8012698772, 0, 0, 0, 0, 0, 8417492044, 0, 0, 0, 0, 0, 0, 0, 0, 4287987712, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6592486656, 0, 0, -3181128548, 0, 0, 3215380416, 0, 0, 0, 0, 0, 10858332160, 0, 0, 0, 0, 0, -10782042752, 0, 0, -8093538544, 0, 0, 437848576, 0, 0, 4251597896, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6809650894, 0, 0, 0, 0, 0, -22276356544, 0, 0, -9149501504, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 35361354624, 0, 0, 11402395160, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1910297012, 0, 0, -35912022016, 0, 0, -3222475360, 0, 0, -3116511680, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5997650396, 0, 0, 11694412288, 0, 0, -2160258452, 0, 0, 0, 0, 0, 0, 0, 0, -14688354304, 0, 0, 0, 0, 0, 0, 0, 0, 59459006818, 0, 0, 0, 0, 0, 19570786300, 0, 0, -23496131648, 0, 0, 0, 0, 0, 26440892416, 0, 0, 0, 0, 0, 0, 0, 0, -19915692928, 0, 0, 0, 0, 0, 27865974656, 0, 0, 0, 0, 0, 0, 0, 0, 24222318592, 0, 0, 0, 0, 0, 0, 0, 0, -30313035716, 0, 0, -16063620352, 0, 0, 17711782712, 0, 0, -50431863040, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8670296960, 0, 0, 0, 0, 0, -44848547328, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -27310630984, 0, 0, 0, 0, 0, -10640671268, 0, 0, 35546516096, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4087041920, 0, 0, 65357889392, 0, 0, 0, 0, 0, 44538437140, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 13642626868, 0, 0, 41651004928, 0, 0, -153985650780, 0, 0, -4098695744, 0, 0, 0, 0, 0, -8356724736, 0, 0, 0, 0, 0, 95332492160, 0, 0, 0, 0, 0, -26940924416, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 21034983424, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14464717756, 0, 0, 25258927616, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -15256282496, 0, 0, -92267577318, 0, 0, 0, 0, 0, 38833866708, 0, 0, 0, 0, 0, 0, 0, 0, 57895911424, 0, 0, 0, 0, 0, 0, 0, 0, -47559327088, 0, 0, 63962362880, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -122805551104, 0, 0, 0, 0, 0, -74739616640, 0, 0, 2579201768, 0, 0, 75981388288, 0, 0, 14649247808, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -112501315648, 0, 0, 0, 0, 0, -45467591300, 0, 0, -20102898368, 0, 0, 0, 0, 0, 93334798336, 0, 0, 0, 0, 0, -96376122752, 0, 0, 65653142572, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 164586925578, 0, 0, -83300472320, 0, 0, 95771323492, 0, 0, 148083658112, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 67943429632, 0, 0, 125884402640, 0, 0, 0, 0, 0, 115356122164, 0, 0, 0, 0, 0, 0, 0, 0, -248887164928], "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, 24, 8, -1, 2, -24], [1, 1, 8, 2, 1, 2, 0], [1, 1, 3, 2, -1, 2, 0]], "char_orbit_index": 4, "prim_orbit_index": 2, "minimal_twist": "72.8.d.a", "char_is_minimal": true, "conrey_index": 37, "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, 0], [-128, 0], [0, 197], [0, 0], [-754, 0], [0, -512], [0, 0], [-6304, 0], [0, 2378], [0, 0], [0, 0], [0, -3016], [0, 0], [16384, 0], [0, 0], [0, 0], [0, 0], [0, -25216], [0, 0], [-76096, 0], [0, 0], [0, 0], [-232347, 0], [0, 0], [0, 0], [96512, 0], [0, -89011], [0, 0], [331370, 0], [0, 65536], [0, 0], [0, 0], [0, -148538], [0, 0], [0, 0], [0, 0], [0, 0], [806912, 0], [0, 0], [0, 0], [0, 0], [0, -304384], [0, 0], [0, 0], [0, 0], [0, 0], [-255027, 0], [0, -929388], [0, 0], [0, 0], [0, 84695], [0, 0], [-3747728, 0], [0, 386048], [0, 0], [2848352, 0], [0, 523436], [0, 0], [0, 0], [0, 1325480], [0, 0], [-2097152, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [4753216, 0], [0, 0], [0, 0], [-2819362, 0], [0, 0], [0, 0], [0, 0], [0, -1793012], [0, 0], [-7561270, 0], [0, 3227648], [0, 0], [0, 0], [0, 2956826], [0, 0], [0, 0], [0, 0], [0, 0], [9740288, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [-11745214, 0], [0, -1020108], [0, 0], [29740416, 0]]}