# Stored data for newform 964.1.bh.a, downloaded from the LMFDB on 25 April 2024.
{"label": "964.1.bh.a", "space_label": "964.1.bh", "level": 964, "weight": 1, "hecke_orbit": 1, "hecke_orbit_code": 2267759510468, "dim": 16, "is_polredabs": true, "nf_label": "16.0.104976000000000000.1", "trace_hash": 137646119349725831, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [], "qexp_display": "q-\\zeta_{60}^{5}q^{2}+\\zeta_{60}^{10}q^{4}+(-\\zeta_{60}+\\zeta_{60}^{23}+\\cdots)q^{5}+\\cdots", "char_order": 60, "char_parity": -1, "char_degree": 16, "char_conductor": 964, "char_orbit_label": "bh", "char_is_real": false, "Nk2": 964, "analytic_conductor": 0.48109867217821434, "hecke_ring_index": 1, "level_radical": 482, "projective_image": "D60", "projective_image_type": "Dn", "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 60, "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": "0.652", "prec": 17}, "analytic_rank_proved": true, "char_values": [964, 60, [483, 489], [30, 37]], "hecke_ring_generator_nbound": 9, "inner_twist_count": 4, "level_primes": [2, 241], "conrey_indexes": [83, 107, 123, 151, 159, 323, 331, 359, 375, 399, 491, 579, 627, 819, 867, 955], "field_disc": 104976000000000000, "field_disc_factorization": [[2, 16], [3, 8], [5, 12]], "field_poly": [1, 0, 1, 0, 0, 0, -1, 0, -1, 0, -1, 0, 0, 0, 1, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.027", "prec": 17}, {"__RealLiteral__": 0, "data": "15.152", "prec": 20}, {"__RealLiteral__": 0, "data": "6.039", "prec": 17}, {"__RealLiteral__": 0, "data": "2661.759", "prec": 27}, {"__RealLiteral__": 0, "data": "2360.280", "prec": 27}, {"__RealLiteral__": 0, "data": "692051.300", "prec": 34}], "related_objects": [], "self_twist_discs": [-4], "cm_discs": [-4], "rm_discs": [], "relative_dim": 1, "trace_display": [0, 0, 0, 0], "traces": [0, 16, 0, 0, 8, 0, 0, 0, 0, -2, 2, 0, 0, 4, 0, 0, -8, -8, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, -4, 2, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -16, -18, 0, 0, 8, 0, 0, 0, 0, 4, -2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, 0, -4, -2, 0, 0, 0, 0, 0, 0, -2, 4, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, -2, -8, 0, 0, 0, 0, 0, 0, -2, 0, 2, 0, 4, 2, 0, 0, 0, 4, 0, 0, 0, -4, 0, 0, 2, 0, 0, 0, -6, 0, 0, 0, 0, -6, -4, 0, 0, 2, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 14, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, -10, 2, 0, 0, 4, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, -16, -16, 0, 0, 2, 0, 0, 0, 0, 22, 0, 0, 0, 0, 0, -8, 2, 0, 0, -6, 10, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 16, 0, -2, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10, 10, 0, 2, 2, 0, 0, 2, 0, 8, 0, 0, 0, 0, 0, 0, 12, 4, 0, 0, 0, 0, 0, 0, 10, 2, 0, 0, 4, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 2, 0, -4, 0, 0, 0, 0, 0, -8, 0, 0, 6, 0, 0, 0, 4, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 4, 0, 0, 0, -24, -18, 0, 0, -8, 0, 0, 0, -10, 0, 0, 0, 0, 0, 0, 0, 0, -12, 0, 2, 2, 0, 0, 2, 0, 2, 0, 0, 4, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, -6, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 6, 0, 0, 18, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 16, 0, 0, 0, 0, 4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 18, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 16, 0, 0, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -4, -18, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 4, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -4, 2, 0, 0, 0, 0, 0, 4, -2, -8, 0, 0, 0, 0, 0, 2, -2, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, -4, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, -2, -12, 0, 0, 0, 0, 2, 0, 0, 4, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -10, 0, 0, -4, 0, 0, -6, 2, 0, 0, 0, 2, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, -4, 0, 0, 0, 6, 0, 0, 4, 0, 0, 0, 0, 6, 0, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -16, 0, 0, -30, 0, 0, 0, 4, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 2, 0, 0, 0, 12, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, 0, -4, 2, 0, 0, -2, 0, 0, 0, -2, 10, 0, 0, 0, 0, 0, -2, 2, 6, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, 10, 0, -20, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, 0, 0, 0, 0, 0, 2, -4, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, -20, -14, 0, 0, -2, 20, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, -10, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, -8, -4, 0, 0, -8, 0, 4, 0, 0, 0, 0, 0, 0, -8, 0, 0, -2, 16, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 14, 0, 0, 0, 0, 0, 0, 0, 0, 10, -4, 0, 0, -4, 0, 0, 0, 0, 4, 0, 0, -2, 0, 0, 8, 30, 0, 0, 4, 0, 0, 0, 0, 2, 0, 0, 0, -6, 0, 0, 12, 0, 4, 0, -10, 0, 0, 0, 0, 4, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 4, 0, 0, 0, 10, 0, 0, -2, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 8, 0, -6, 0, 0, -2, 0, 0, -4, 0, -6, 0, 0, 0, 0, 0, 0, 8, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 16, 0, -14, -20, 0, 0, 20, 0, 0, 0, 0, -2, 0, 0, -2, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 4, 0, 4, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 6, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 20, 0, 0, 0, -2, 0, 14, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 16, 0, 0, -10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, -4, 2, 0, 0, 0, 12, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 10, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 12, -6, 0, 0, 0, 0, 0, -2, 0, -8, 0, 0, 0, 0, 0, -2, -4, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -4, 0, 0, 0, 2, -6, 0, 0, -16, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 6, 0, 0, 0, 0, 0, -2, 0, 0, -10, 0, 0, 0, -2, 0, 0, 2, -2, 0, 0, 0, 6, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -8, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 4, 6, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, -4, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 8, -10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -20, 0, 0, 0, 0, -14, 2, 0, 0, -6, 0, 0, 0, 4, -4, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 10, -2, 0, 0, 0, 0, 0, 6, 0, -2, 0, 0, -2, 0, 0, 4, -2, 0, 0, 4, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 4, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 2, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, -4, 0, -2, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -14, 0, 0, -30, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, -6, -30, 0, 0, 0, 0, -14, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, -2, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 2, 6, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, -2, 0, 0, -12, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 12, 6, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 4, -4, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, -10, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 14, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 8, -2, 0, 0, 0, 0, 0, 0, 2, -2, -2, 0, 0, 4, 0, 0, 0, 0, -2, 0, 0, 20, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -4, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -4, 0, 0, -4, 0, -4, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 8, -2, 0, 0, -4, 0, 0, 0], "projective_field": [-33251319328124966479425840083251048235938086912, -15010053872290990475077834630985140855162011648, 16522687939332183812586706993762177046588424192, 9103833119597781933665274265560611283082936320, -11662037486712037132251110759166194885584748544, 5264024484769027679916721868186200489561423872, -2124011438147845323355248381567665827498426368, 853720208577245119861510467328910889152675840, -335910152607729203946738275556038230916726784, 134936196955849535148266125283012059692793856, -55328109045978221338842777871368624845881344, 19673760914879246034218458975231317475328000, -6188937712791456557105621391144090103185408, 1868957448818464496234956692713025433894912, -529322132740959026703971370036355053256704, 135239702574958197264948480139664599498752, -32297870256447609189980195939885830766592, 7345381441097516417383877935609580851200, -1539252282526732156770220626854417203200, 291201491912426974968798299886876037120, -51180510835918882419716499284944389120, 8164922376809500643282410003465842432, -1038785735512904905799764053024882944, 80555391912616863675212411308714208, 4892819819435765457616678383043072, -4678388305945271240291096682017416, 1550851937096941699517074776998368, -376633227420476830243991482829676, 79105488005102784514295475234412, -15608319198031905641539427619994, 2876509836940124571153758664632, -491507190438338955033559835133, 79767625981174489985200250399, -12495541185768254097395912178, 1872459134681846981922422456, -265988959132265342937858905, 36126922248259559940030131, -4759925332569137372043034, 599415484725547278470592, -70283756029536759787281, 7847846474681040153003, -860555894750864848722, 87763791855346907856, -7905165682832896981, 678557981898240807, -56903436549261822, 3529679223601592, -67661219754839, -8731859015971, 828807818650, -125780829928, 26713969653, -2317104391, 27952306, 601168, 653893, -36839, -974, 256, -27, 1], "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, 4, 2, -1, 2, -4], [1, 1, 241, 17, 1, 60, 0], [1, 1, 964, 34, -1, 60, 0]], "char_orbit_index": 34, "prim_orbit_index": 34, "minimal_twist": "964.1.bh.a", "char_is_minimal": true, "conrey_index": 83, "id": null, "fricke_eigenval": null, "atkin_lehner_string": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "sato_tate_group": null, "atkin_lehner_eigenvals": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[], [[1, 0]], [[-1, 5]], [], [[1, 10]], [[-1, 1], [1, 23]], [], [], [[-1, 15]], [[1, 26]], [[1, 6], [-1, 28]], [], [], [[-1, 12], [-1, 29]], [], [], [[1, 20]], [[-1, 10], [-1, 23]], [[1, 1]], [], [[-1, 3], [-1, 11]], [], [], [], [], [[1, 2], [-1, 16], [-1, 24]], [[-1, 4], [1, 17]], [], [], [[-1, 8], [-1, 14]], [], [], [[-1, 25]], [], [[1, 15], [1, 28]], [], [[-1, 6]], [[-1, 2], [-1, 17]], [], [], [[1, 8], [1, 16]], [[1, 4], [1, 14]], [], [], [], [[-1, 19], [-1, 27]], [], [], [], [[-1, 13]], [[-1, 7], [1, 21], [1, 29]], [], [[1, 9], [-1, 22]], [[1, 12], [-1, 20]], [], [], [], [], [[1, 13], [1, 19]], [], [], [[-1, 9], [1, 27]], [], [], [[-1, 0]], [[-1, 0], [1, 5], [1, 13], [1, 22]], [], [], [[1, 3], [-1, 20]], [], [], [], [[1, 11]], [[1, 18], [1, 21]], [[1, 7], [1, 22]], [], [], [], [], [], [[-1, 13], [-1, 21]], [[-1, 22]], [[-1, 9], [-1, 19]], [], [], [[1, 3], [1, 11], [1, 16], [1, 24]], [], [], [], [[-1, 7], [-1, 18]], [[-1, 2], [1, 24]], [], [], [], [], [], [], [[-1, 16]], [[1, 18]], [], [[1, 4], [1, 12], [-1, 26]]]}