# Stored data for newform 720.3.j.e, downloaded from the LMFDB on 28 December 2025. {"Nk2": 6480, "analytic_conductor": 19.618579033941376, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 20, "char_degree": 1, "char_is_minimal": true, "char_is_real": true, "char_orbit_index": 10, "char_orbit_label": "j", "char_order": 2, "char_parity": -1, "char_values": [720, 2, [271, 181, 641, 577], [1, 2, 2, 1]], "cm_discs": [], "conrey_index": 559, "dim": 4, "field_disc": 576, "field_disc_factorization": [[2, 6], [3, 2]], "field_poly": [4, 0, 2, 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": [[7, [-72, 0, 1]], [11, [192, 0, 1]], [29, [-22, 1]]], "hecke_orbit": 5, "hecke_orbit_code": 18015017035104976, "hecke_ring_generator_nbound": 11, "hecke_ring_index": 384, "hecke_ring_index_factorization": [[2, 7], [3, 1]], "hecke_ring_index_proved": true, "inner_twist_count": 4, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 4, 2, -1, 2, 0], [1, 1, 5, 2, 1, 2, 0], [1, 1, 20, 4, -1, 2, 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": "720.3.j.e", "level": 720, "level_is_powerful": false, "level_is_prime": false, "level_is_prime_power": false, "level_is_prime_square": false, "level_is_square": false, "level_is_squarefree": false, "level_primes": [2, 3, 5], "level_radical": 30, "minimal_twist": "80.3.h.b", "nf_label": "4.0.576.2", "prim_orbit_index": 4, "qexp_display": "q+(1+\\beta _{1})q^{5}-\\beta _{2}q^{7}+\\beta _{3}q^{11}-2\\beta _{1}q^{13}+\\cdots", "related_objects": [], "relative_dim": 4, "rm_discs": [], "sato_tate_group": "2.2.3.c2", "self_twist_discs": [], "self_twist_type": 0, "space_label": "720.3.j", "trace_display": [0, 0, 4, 0], "trace_hash": 2110050939912168412, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.675", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "114.638", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "4423.006", "prec": 27}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.759", "prec": 17}, "traces": [0, 4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -92, 0, 0, 0, 88, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -88, 0, 0, 0, 0, 0, 0, 0, 92, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 184, 0, 0, 0, 192, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 384, 0, 0, 0, -584, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 280, 0, 0, 0, 0, 0, 0, 0, -584, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -284, 0, 0, 0, -284, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 88, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 864, 0, 0, 0, 0, 0, 0, 0, 292, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 104, 0, 0, 0, 960, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -88, 0, 0, 0, -768, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -768, 0, 0, 0, 0, 0, 0, 0, -280, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -488, 0, 0, 0, 92, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -576, 0, 0, 0, -568, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1624, 0, 0, 0, 0, 0, 0, 0, -380, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2016, 0, 0, 0, 184, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 384, 0, 0, 0, -288, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3072, 0, 0, 0, 0, 0, 0, 0, -856, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 676, 0, 0, 0, 1536, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2304, 0, 0, 0, -2680, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, -2600, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1928, 0, 0, 0, 768, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -584, 0, 0, 0, 104, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2008, 0, 0, 0, 0, 0, 0, 0, 2016, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1920, 0, 0, 0, -1152, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 280, 0, 0, 0, -680, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2888, 0, 0, 0, 0, 0, 0, 0, 476, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1448, 0, 0, 0, -584, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -768, 0, 0, 0, 3368, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2592, 0, 0, 0, 0, 0, 0, 0, 3072, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2392, 0, 0, 0, -284, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1732, 0, 0, 0, -3840, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -664, 0, 0, 0, 0, 0, 0, 0, -768, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -392, 0, 0, 0, 2304, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4224, 0, 0, 0, 1152, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2872, 0, 0, 0, 0, 0, 0, 0, -3352, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -864, 0, 0, 0, -2024, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 1440, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2120, 0, 0, 0, 0, 0, 0, 0, 1544, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1536, 0, 0, 0, 1344, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 864, 0, 0, 0, 4024, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1928, 0, 0, 0, 0, 0, 0, 0, -4424, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1428, 0, 0, 0, 292, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 960, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2200, 0, 0, 0, 0, 0, 0, 0, 3744, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2304, 0, 0, 0, 104, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1920, 0, 0, 0, -5272, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6616, 0, 0, 0, 0, 0, 0, 0, -3072, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8444, 0, 0, 0, -6528, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2112, 0, 0, 0, 6048, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], "weight": 3, "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], [1, 1, 0, 0], [0, 0, 0, 0], [0, 0, -1, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 1], [0, 0, 0, 0], [0, -2, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -4, 0, 0], [0, 0, 0, 0], [0, 0, 0, 1], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, -3, 0], [0, 0, 0, 0], [-23, 2, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [22, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, -4], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, -1, -3], [0, 0, 0, 0], [0, -10, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-22, 0, 0, 0], [0, 0, 0, 0], [0, 0, -7, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 1, 0], [0, 0, 0, 0], [23, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 6, 0, 0], [0, 0, 0, 0], [0, 0, -8, 1], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 1], [0, 0, 0, 0], [46, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [48, -2, 0, 0], [0, 0, 0, 0], [0, 0, -7, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, -2], [0, 0, 0, 0], [0, -16, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -24, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, -9, 0], [0, 0, 0, 0], [96, -4, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-146, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 6], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, -8, 1], [0, 0, 0, 0], [0, 12, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]]}