# Stored data for newform 720.2.x.a, downloaded from the LMFDB on 07 September 2024. {"Nk2": 2880, "analytic_conductor": 5.749228945532187, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 20, "char_degree": 2, "char_is_minimal": true, "char_is_real": false, "char_orbit_index": 24, "char_orbit_label": "x", "char_order": 4, "char_parity": 1, "char_values": [720, 4, [271, 181, 641, 577], [2, 4, 4, 1]], "cm_discs": [-4], "conrey_index": 127, "dim": 2, "field_disc": -4, "field_disc_factorization": [[-1, 1], [2, 2]], "field_poly": [1, 0, 1], "field_poly_is_cyclotomic": true, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 4, "has_non_self_twist": 1, "hecke_cutters": [[7, [0, 1]], [11, [0, 1]], [13, [50, 10, 1]], [17, [50, -10, 1]]], "hecke_orbit": 1, "hecke_orbit_code": 1580581520080, "hecke_ring_generator_nbound": 5, "hecke_ring_index": 1, "hecke_ring_index_factorization": [], "hecke_ring_index_proved": true, "inner_twist_count": 4, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 4, 2, -1, 2, -4], [1, 1, 5, 3, -1, 4, 0], [1, 1, 20, 5, 1, 4, 0]], "is_cm": true, "is_largest": false, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": false, "is_self_twist": true, "is_twist_minimal": false, "label": "720.2.x.a", "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": "80.2.n.a", "nf_label": "2.0.4.1", "prim_orbit_index": 5, "qexp_display": "q+(-2-i)q^{5}+(-5+5i)q^{13}+(5+\\cdots)q^{17}+\\cdots", "related_objects": ["EllipticCurve/2.0.4.1/32400.1/CMb", "EllipticCurve/2.0.4.1/32400.3/CMb"], "relative_dim": 1, "rm_discs": [], "sato_tate_group": "1.2.1.d4", "self_twist_discs": [-4], "self_twist_type": 1, "space_label": "720.2.x", "trace_display": [0, 0, -4, 0], "trace_hash": 432563129689362571, "trace_moments": [{"__RealLiteral__": 0, "data": "0.035", "prec": 17}, {"__RealLiteral__": 0, "data": "1.917", "prec": 17}, {"__RealLiteral__": 0, "data": "0.501", "prec": 17}, {"__RealLiteral__": 0, "data": "16.724", "prec": 20}, {"__RealLiteral__": 0, "data": "6.070", "prec": 17}, {"__RealLiteral__": 0, "data": "180.911", "prec": 24}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.625", "prec": 17}, "traces": [0, 2, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, -10, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10, 0, 0, 0, 0, 0, 0, 0, -24, 0, 0, 0, 30, 0, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -30, 0, 0, 0, 0, 0, 0, 0, 22, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 30, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 30, 0, 0, 0, 0, 0, 0, 0, -36, 0, 0, 0, -10, 0, 0, 0, 0, 0, 0, 0, -10, 0, 0, 0, 30, 0, 0, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -100, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -30, 0, 0, 0, 0, 0, 0, 0, 30, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10, 0, 0, 0, 64, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -30, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 48, 0, 0, 0, 0, 0, 0, 0, -50, 0, 0, 0, 50, 0, 0, 0, 0, 0, 0, 0, -70, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 50, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -50, 0, 0, 0, 0, 0, 0, 0, -38, 0, 0, 0, -30, 0, 0, 0, 0, 0, 0, 0, 50, 0, 0, 0, -40, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 50, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 56, 0, 0, 0, -10, 0, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -50, 0, 0, 0, 76, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -100, 0, 0, 0, -10, 0, 0, 0, 0, 0, 0, 0, -40, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -44, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 80, 0, 0, 0, 0, 0, 0, 0, 84, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10, 0, 0, 0, 0, 0, 0, 0, 90, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -50, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 30, 0, 0, 0, 0, 0, 0, 0, 96, 0, 0, 0, -44, 0, 0, 0, 0, 0, 0, 0, 70, 0, 0, 0, -70, 0, 0, 0, 0, 0, 0, 0, -14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -70, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 70, 0, 0, 0, 0, 0, 0, 0, -24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -70, 0, 0, 0, -50, 0, 0, 0, 0, 0, 0, 0, -30, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -80, 0, 0, 0, 104, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -32, 0, 0, 0, 0, 0, 0, 0, 50, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -28, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 70, 0, 0, 0, 76, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, 120, 0, 0, 0, -30, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -56, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -70, 0, 0, 0, 0, 0, 0, 0, 26, 0, 0, 0, -74, 0, 0, 0, 0, 0, 0, 0, -10, 0, 0, 0, -50, 0, 0, 0, 0, 0, 0, 0, -90, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 70, 0, 0, 0, 64, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -100, 0, 0, 0, 72, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10, 0, 0, 0, 116, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -30, 0, 0, 0, 0, 0, 0, 0, 62, 0, 0, 0, 30, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 70, 0, 0, 0, 0, 0, 0, 0, -30, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -50, 0, 0, 0], "weight": 2, "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], [1, 0], [0, 0], [0, 0], [0, 0], [-2, -1], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [-5, 5], [0, 0], [0, 0], [0, 0], [5, 5], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [3, 4], [0, 0], [0, 0], [0, 0], [0, 4], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [5, 5], [0, 0], [0, 0], [0, 0], [-8, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 7], [0, 0], [0, 0], [0, 0], [-5, 5], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [-12, 0], [0, 0], [0, 0], [0, 0], [15, -5], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [5, -5], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [-5, -15], [0, 0], [0, 0], [0, 0], [0, -16], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [5, 5], [0, 0], [0, 0], [0, 0]]}