# Stored data for newform 390.2.i.b, downloaded from the LMFDB on 25 April 2024.
{"label": "390.2.i.b", "space_label": "390.2.i", "level": 390, "weight": 2, "hecke_orbit": 2, "hecke_orbit_code": 4504149416739206, "dim": 2, "is_polredabs": true, "nf_label": "2.0.3.1", "trace_hash": 1994331636335089494, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[7, [9, -3, 1]], [11, [1, 1, 1]]], "qexp_display": "q+(-1+\\zeta_{6})q^{2}+(1-\\zeta_{6})q^{3}-\\zeta_{6}q^{4}+\\cdots", "char_order": 3, "char_parity": 1, "char_degree": 2, "char_conductor": 13, "char_orbit_label": "i", "char_is_real": false, "Nk2": 1560, "analytic_conductor": 3.114165678829935, "hecke_ring_index": 1, "level_radical": 390, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 6, "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": "0.006", "prec": 17}, "analytic_rank_proved": true, "char_values": [390, 3, [131, 157, 301], [3, 3, 2]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 2, "level_primes": [2, 3, 5, 13], "conrey_indexes": [61, 211], "field_disc": -3, "field_disc_factorization": [[-1, 1], [3, 1]], "field_poly": [1, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.927", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "11.010", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "96.185", "prec": 20}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "1.2.3.c3", "trace_display": [-1, 1, 2, 3], "traces": [0, 2, -1, 1, -1, 2, 1, 3, 2, -1, -1, -1, -2, 5, -6, 1, -1, 0, 2, 5, -1, 6, -1, 4, 1, 2, 2, -2, 3, 0, 1, 20, -1, 1, 0, 3, -1, 1, -10, -2, 2, -6, -3, 2, 2, -1, 4, -18, 1, -2, -1, 0, -7, -26, 1, -1, 3, 10, 0, -4, -2, 2, -10, 3, 2, 5, -2, 12, 0, -4, -6, 2, -1, -32, 1, 1, 5, -6, 7, -20, -1, -1, -6, 24, -3, 0, -4, 0, -1, -1, 2, 21, -8, 10, 9, 5, -2, -12, -2, 2, -1, -4, 0, -18, 5, 6, 13, 6, 1, -20, -1, -1, -6, -16, -5, 4, 0, -7, 8, 0, 1, 10, -4, 6, -10, 2, 3, -5, -1, 4, 2, -30, 1, -15, 12, -2, 0, -16, 8, 9, 3, -9, -4, 2, 2, 0, 16, 2, -2, 6, 1, -12, 5, 0, 3, 20, -5, 2, 10, -13, -1, 24, -1, 20, 12, 1, -12, 13, 6, -1, 0, 5, 2, 9, 0, 3, -1, -8, -1, -12, -1, 12, -15, 4, 4, 1, 10, 0, 9, -3, -10, 18, 1, -16, 24, -2, 4, 15, -1, 2, 2, -12, -4, 0, 0, -6, 9, -8, 2, -10, -3, 15, 13, 4, 6, 2, -2, 30, 10, -16, 2, 0, 2, -11, 3, -1, 32, 20, -5, -20, 4, -3, 0, 20, 5, -18, -4, -10, 0, -4, 1, -15, -20, 1, 2, -2, -12, 35, 20, 12, -1, -11, -6, 4, -5, 0, -1, 24, -2, 6, -7, 0, 15, -3, 1, -26, -15, 1, -24, 20, 1, 24, 0, 15, 32, -1, -4, -23, -18, -10, 3, 20, -9, -2, 2, 10, -7, -36, -1, 17, 0, -24, 16, -13, -4, -4, 1, 1, -12, -8, -2, -6, 6, 4, -10, 2, 0, 36, 3, -9, -10, -24, -2, -68, -1, 3, 10, 38, -13, 0, 2, -6, -12, 0, 2, 5, -40, -10, -6, -27, -2, -28, -12, -2, 13, 12, -3, 4, 23, -32, 0, -10, 5, 30, 2, -4, -18, 28, 0, -36, -6, -5, 2, 36, 4, 2, 2, 0, -12, 68, -1, -6, -6, 20, -6, -32, -2, 0, 4, 12, 1, -39, -20, -10, 0, 1, -18, 0, 6, 1, 5, 5, -36, 28, 1, -6, -16, 2, -12, -32, 7, 0, -2, -15, 15, -20, -1, 33, -4, 15, -1, -25, 24, 50, 8, -1, 0, 1, 0, -17, -6, -32, 9, 12, 4, 24, -7, 18, 5, 28, -3, 40, 15, 9, -26, 0, -2, -6, -12, 7, -4, -36, 1, -16, -60, 0, 10, 40, -16, 10, -1, 4, 0, -36, -1, -1, -11, 12, 3, 15, 2, -6, -16, -6, -40, 21, 10, -22, 10, 0, -8, 12, -3, -32, 0, 10, -10, -72, 2, 72, 9, 1, -4, -4, -10, 5, 0, 13, 2, 8, -2, -2, 30, 12, 10, -12, -2, -35, 2, 40, -2, -25, 6, 0, -25, 2, -10, -6, 12, 40, -1, -13, 22, 1, 3, -4, -8, -23, 10, -18, 0, -48, 2, -5, 24, -18, -2, 9, -3, 18, 5, 66, 0, -6, 15, 6, -3, 0, -2, 7, 13, -4, 30, 12, -2, 6, 12, 12, -40, -2, 1, -4, 24, 6, 0, -20, 6, 68, -16, 2, -1, 0, -4, -30, 46, -1, 9, 3, 20, 14, -6, 0, -10, -24, 18, -16, -2, -6, 2, 11, -5, 14, 5, 36, 18, 4, -1, 36, 17, 16, 0, 36, 12, 13, -32, -7, 26, 18, 2, 50, 8, -15, 1, 56, 1, 0, 6, 4, 28, -60, 1, 27, -6, -24, 6, 10, -8, -37, 5, 0, -4, -45, 0, -23, -18, 6, -6, 6, -9, -62, -10, -4, 12, -6, 7, 2, 34, -5, -1, 0, 3, 4, -20, -15, -19, -5, 26, 4, 0, 2, -1, 9, 12, 44, -12, 4, 0, -9, -1, 8, 2, 60, 20, -41, -10, -30, -6, 16, 54, -4, 1, -14, 56, 0, 24, -15, 1, 0, -26, 11, 12, -4, -3, 32, -2, -2, -22, -52, 16, 36, 0, 40, -10, 26, -10, -16, -15, -10, -4, -65, 8, -33, 9, 3, -56, 9, 0, 0, -36, 10, 3, 8, -2, 10, -1, -9, 36, -24, 4, -4, -4, 10, -1, 40, 0, 2, 24, -2, -34, -36, 2, -27, -6, -30, -6, 0, -10, -74, 21, 2, 16, 0, -2, -10, 0, 2, -8, 12, -6, -35, -2, 25, 78, -24, 10, 6, 20, -12, 0, 36, 1, -44, 9, -22, 0, -12, -3, -39, 1, 8, 5, -45, -10, -30, 18, 0, -56, -28, -2, 26, 3, -24, 32, 37, 2, 20, -12, 3, 16, -60, -5, -4, 0, 0, -2, 2, -15, -16, -30, 3, 10, 48, 2, 14, -66, -13, 2, 14, -30, 0, -1, 2, -25, 16, -12, 24, 20, 40, -4, 18, -1, 66, 0, -24, -2, 20, 0, -10, 34, -6, 12, -18, 16, 5, -18, 1, 12, -60, 4, 44, -12, -46, 5, 0, -9, 13, 5, -20, 28, 54, 6, 29, -20, 10, -30, -1, -18, -30, 13, 2, 0, -4, -2, -28, -6, 5, 6, -36, -5, 38, 2, -18, -36, -96, 1, 9, 32, -17, 30, 10, 0, -24, -20, -12, -20, 3, 32, -38, 10, -26, -1, -5, -2, 84, 0, -8, 18, 13, -1, -30, -1, -1, 22, -45, -6, -12, -6, -28, -30, 0, -1, 0, 12, 6, -16, 12, -6, -42, 20, 8, -15, 24, -5, -12, -22, 4, 10, -45, 0, -34, 4, 18, -24, 14, 6, 1, 16, 9, 0, -34, 10, -20, -10, -12, 36, 0, -7, -20, -36, -34, 9, 48, 1, 24, 8, -3, 2, 38, 20, -80, -10, 19, 0, -22, -26, 18, 2, 0, 8, 48, 1, 138, 7, -12, -15, -16, 12, 14, 10, 0, 24, -27, 1, -27, 70, -2, -4, -48, -20, -1, 4, 10, -25, 106, 6, 15, 0, -54, -10, 16, -1, -38, -10, -56, -6, 2, -24, 7, -20, -1, 2], "weight_parity": 1, "has_non_self_twist": 1, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": false, "level_is_squarefree": true, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 13, 3, 1, 3, 0]], "char_orbit_index": 9, "prim_orbit_index": 3, "minimal_twist": "390.2.i.b", "char_is_minimal": true, "conrey_index": 61, "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], [-1, 1], [1, -1], [0, -1], [1, 0], [0, 1], [0, 3], [1, 0], [0, -1], [-1, 1], [-1, 1], [-1, 0], [4, -3], [-3, 0], [1, -1], [-1, 1], [0, 0], [1, 0], [0, 5], [0, -1], [3, 0], [0, -1], [4, -4], [1, -1], [1, 0], [-1, 4], [-1, 0], [3, -3], [0, 0], [0, 1], [10, 0], [0, -1], [0, 1], [0, 0], [0, 3], [-1, 1], [1, -1], [-5, 0], [1, -4], [1, 0], [-6, 6], [-3, 3], [0, 2], [1, 0], [0, -1], [0, 4], [-9, 0], [0, 1], [-2, 2], [-1, 1], [0, 0], [-3, -1], [-13, 0], [1, -1], [-1, 1], [0, 3], [5, 0], [0, 0], [0, -4], [-1, 0], [0, 2], [-10, 10], [3, -3], [1, 0], [4, -3], [-1, 0], [12, -12], [0, 0], [0, -4], [-3, 0], [0, 2], [0, -1], [-16, 0], [0, 1], [1, -1], [5, -5], [-3, 0], [3, 1], [-10, 0], [-1, 1], [-1, 1], [0, -6], [12, 0], [0, -3], [0, 0], [-2, 0], [0, 0], [-1, 1], [-1, 1], [1, 0], [9, 3], [-4, 0], [10, -10], [9, -9], [0, 5], [-1, 0], [0, -12], [0, -2], [1, 0], [0, -1]]}