# Stored data for newform 720.4.f.f, downloaded from the LMFDB on 19 April 2024.
{"label": "720.4.f.f", "space_label": "720.4.f", "level": 720, "weight": 4, "hecke_orbit": 6, "hecke_orbit_code": 22518341801345744, "dim": 2, "is_polredabs": true, "nf_label": "2.0.4.1", "trace_hash": 1762353070949499858, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[7, [676, 0, 1]], [11, [28, 1]]], "qexp_display": "q+(5-5i)q^{5}+13iq^{7}-28q^{11}+6iq^{13}+\\cdots", "char_order": 2, "char_parity": 1, "char_degree": 1, "char_conductor": 5, "char_orbit_label": "f", "char_is_real": true, "Nk2": 11520, "analytic_conductor": 42.48137520413324, "hecke_ring_index": 2, "level_radical": 30, "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": "0.507", "prec": 17}, "analytic_rank_proved": true, "char_values": [720, 2, [271, 181, 641, 577], [2, 2, 2, 1]], "hecke_ring_generator_nbound": 7, "inner_twist_count": 2, "level_primes": [2, 3, 5], "conrey_indexes": [289], "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": "0.043", "prec": 17}, {"__RealLiteral__": 0, "data": "1.952", "prec": 17}, {"__RealLiteral__": 0, "data": "0.481", "prec": 17}, {"__RealLiteral__": 0, "data": "15.352", "prec": 20}, {"__RealLiteral__": 0, "data": "5.853", "prec": 17}, {"__RealLiteral__": 0, "data": "149.220", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "3.2.3.c2", "trace_display": [0, 0, 10, 0], "traces": [0, 2, 0, 0, 0, 10, 0, 0, 0, 0, 0, -56, 0, 0, 0, 0, 0, 0, 0, -120, 0, 0, 0, 0, 0, -150, 0, 0, 0, 180, 0, 256, 0, 0, 0, 520, 0, 0, 0, 0, 0, -484, 0, 0, 0, 0, 0, 0, 0, -666, 0, 0, 0, 0, 0, -280, 0, 0, 0, 40, 0, 1084, 0, 0, 0, 240, 0, 0, 0, 0, 0, -2256, 0, 0, 0, 0, 0, 0, 0, -1440, 0, 0, 0, 0, 0, -1280, 0, 0, 0, -980, 0, -624, 0, 0, 0, -600, 0, 0, 0, 0, 0, 1156, 0, 0, 0, 0, 0, 0, 0, -740, 0, 0, 0, 0, 0, -1160, 0, 0, 0, 3328, 0, -1094, 0, 0, 0, -2750, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, 6200, 0, 0, 0, 0, 0, 900, 0, 0, 0, 500, 0, -4304, 0, 0, 0, 1280, 0, 0, 0, 0, 0, 3016, 0, 0, 0, 0, 0, 0, 0, 4106, 0, 0, 0, 0, 0, 5200, 0, 0, 0, -5000, 0, -5156, 0, 0, 0, -4720, 0, 0, 0, 0, 0, -1536, 0, 0, 0, 0, 0, 0, 0, -6960, 0, 0, 0, 0, 0, -2420, 0, 0, 0, 3360, 0, -6264, 0, 0, 0, -7240, 0, 0, 0, 0, 0, 1536, 0, 0, 0, 0, 0, 0, 0, 380, 0, 0, 0, 0, 0, -4520, 0, 0, 0, 11360, 0, -556, 0, 0, 0, -3330, 0, 0, 0, 0, 0, 6504, 0, 0, 0, 0, 0, 0, 0, 12272, 0, 0, 0, 0, 0, 2160, 0, 0, 0, 5220, 0, 10336, 0, 0, 0, 4200, 0, 0, 0, 0, 0, -6084, 0, 0, 0, 0, 0, 0, 0, 1634, 0, 0, 0, 0, 0, 200, 0, 0, 0, 1392, 0, 18824, 0, 0, 0, 5420, 0, 0, 0, 0, 0, -11376, 0, 0, 0, 0, 0, 0, 0, -5040, 0, 0, 0, 0, 0, 2400, 0, 0, 0, 11752, 0, 15736, 0, 0, 0, -8680, 0, 0, 0, 0, 0, -7168, 0, 0, 0, 0, 0, 0, 0, 6220, 0, 0, 0, 0, 0, -11280, 0, 0, 0, 18480, 0, -6518, 0, 0, 0, 12640, 0, 0, 0, 0, 0, -5616, 0, 0, 0, 0, 0, 0, 0, 9880, 0, 0, 0, 0, 0, -14560, 0, 0, 0, 6100, 0, -7424, 0, 0, 0, -7200, 0, 0, 0, 0, 0, -28964, 0, 0, 0, 0, 0, 0, 0, 2180, 0, 0, 0, 0, 0, -9560, 0, 0, 0, 14360, 0, -16276, 0, 0, 0, -12800, 0, 0, 0, 0, 0, -416, 0, 0, 0, 0, 0, 0, 0, 2160, 0, 0, 0, 0, 0, -4900, 0, 0, 0, 28620, 0, 13552, 0, 0, 0, -3120, 0, 0, 0, 0, 0, -22764, 0, 0, 0, 0, 0, 0, 0, 22568, 0, 0, 0, 0, 0, 9000, 0, 0, 0, -15040, 0, 5664, 0, 0, 0, -29120, 0, 0, 0, 0, 0, 28104, 0, 0, 0, 0, 0, 0, 0, 15240, 0, 0, 0, 0, 0, 5780, 0, 0, 0, 35700, 0, -32864, 0, 0, 0, -29240, 0, 0, 0, 0, 0, 38476, 0, 0, 0, 0, 0, 0, 0, 17606, 0, 0, 0, 0, 0, -19320, 0, 0, 0, 18648, 0, -19636, 0, 0, 0, -3700, 0, 0, 0, 0, 0, -10800, 0, 0, 0, 0, 0, 0, 0, 8688, 0, 0, 0, 0, 0, 10560, 0, 0, 0, -14660, 0, -11624, 0, 0, 0, -11600, 0, 0, 0, 0, 0, 24856, 0, 0, 0, 0, 0, 0, 0, -15360, 0, 0, 0, 0, 0, 16640, 0, 0, 0, 7440, 0, -25916, 0, 0, 0, -5470, 0, 0, 0, 0, 0, 5424, 0, 0, 0, 0, 0, 0, 0, -42440, 0, 0, 0, 0, 0, -8750, 0, 0, 0, -30208, 0, -35344, 0, 0, 0, -30680, 0, 0, 0, 0, 0, -14644, 0, 0, 0, 0, 0, 0, 0, -1120, 0, 0, 0, 0, 0, 120, 0, 0, 0, 53560, 0, -49076, 0, 0, 0, -31200, 0, 0, 0, 0, 0, -30352, 0, 0, 0, 0, 0, 0, 0, 75712, 0, 0, 0, 0, 0, -24480, 0, 0, 0, -2592, 0, 6856, 0, 0, 0, 31000, 0, 0, 0, 0, 0, -53884, 0, 0, 0, 0, 0, 0, 0, 3900, 0, 0, 0, 0, 0, -6720, 0, 0, 0, -24160, 0, 76024, 0, 0, 0, -13500, 0, 0, 0, 0, 0, -46336, 0, 0, 0, 0, 0, 0, 0, -4120, 0, 0, 0, 0, 0, 2500, 0, 0, 0, 50232, 0, 9056, 0, 0, 0, -21520, 0, 0, 0, 0, 0, 37356, 0, 0, 0, 0, 0, 0, 0, -54780, 0, 0, 0, 0, 0, -19200, 0, 0, 0, 29040, 0, 63168, 0, 0, 0, 10480, 0, 0, 0, 0, 0, -27456, 0, 0, 0, 0, 0, 0, 0, -28928, 0, 0, 0, 0, 0, 15080, 0, 0, 0, 21900, 0, 17656, 0, 0, 0, 70360, 0, 0, 0, 0, 0, 32116, 0, 0, 0, 0, 0, 0, 0, 30780, 0, 0, 0, 0, 0, 10680, 0, 0, 0, 8560, 0, -32578, 0, 0, 0, 20530, 0, 0, 0, 0, 0, -27376, 0, 0, 0, 0, 0, 0, 0, -53480, 0, 0, 0, 0, 0, -85040, 0, 0, 0, 40320, 0, 10416, 0, 0, 0, -13000, 0, 0, 0, 0, 0, -81684, 0, 0, 0, 0, 0, 0, 0, 79768, 0, 0, 0, 0, 0, -25000, 0, 0, 0, 23040, 0, 13824, 0, 0, 0, -25780, 0, 0, 0, 0, 0, -13536, 0, 0, 0, 0, 0, 0, 0, 44400, 0, 0, 0, 0, 0, -47200, 0, 0, 0, -12660, 0, 39960, 0, 0, 0, 35840, 0, 0, 0, 0, 0, 19796, 0, 0, 0, 0, 0, 0, 0, -15168, 0, 0, 0, 0, 0, -7680, 0, 0, 0, 63648, 0, -26814, 0, 0, 0, -52160, 0, 0, 0, 0, 0, 15624, 0, 0, 0, 0, 0, 0, 0, 27440, 0, 0, 0, 0, 0, 102320, 0, 0, 0, -41992, 0, -52544, 0, 0, 0, -34800, 0, 0, 0, 0, 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, 5, 2, 1, 2, 0]], "char_orbit_index": 6, "prim_orbit_index": 2, "minimal_twist": "10.4.b.a", "char_is_minimal": false, "conrey_index": 289, "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, 0], [0, 0], [0, 0], [5, -5], [0, 0], [0, 13], [0, 0], [0, 0], [0, 0], [-28, 0], [0, 0], [0, 6], [0, 0], [0, 0], [0, 0], [0, -32], [0, 0], [-60, 0], [0, 0], [0, 0], [0, 0], [0, -29], [0, 0], [-75, -50], [0, 0], [0, 0], [0, 0], [90, 0], [0, 0], [128, 0], [0, 0], [0, 0], [0, 0], [260, 65], [0, 0], [0, -118], [0, 0], [0, 0], [0, 0], [-242, 0], [0, 0], [0, -181], [0, 0], [0, 0], [0, 0], [0, -113], [0, 0], [-333, 0], [0, 0], [0, 0], [0, 0], [0, 54], [0, 0], [-140, 140], [0, 0], [0, 0], [0, 0], [20, 0], [0, 0], [542, 0], [0, 0], [0, 0], [0, 0], [120, 30], [0, 0], [0, -217], [0, 0], [0, 0], [0, 0], [-1128, 0], [0, 0], [0, 316], [0, 0], [0, 0], [0, 0], [0, -364], [0, 0], [-720, 0], [0, 0], [0, 0], [0, 0], [0, -239], [0, 0], [-640, -160], [0, 0], [0, 0], [0, 0], [-490, 0], [0, 0], [-312, 0], [0, 0], [0, 0], [0, 0], [-300, 300], [0, 0], [0, -728], [0, 0], [0, 0], [0, 0]]}