# Stored data for newform 390.2.i.c, downloaded from the LMFDB on 12 November 2025. {"Nk2": 1560, "analytic_conductor": 3.114165678829935, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 13, "char_degree": 2, "char_is_minimal": true, "char_is_real": false, "char_orbit_index": 9, "char_orbit_label": "i", "char_order": 3, "char_parity": 1, "char_values": [390, 3, [131, 157, 301], [3, 3, 2]], "cm_discs": [], "conrey_index": 61, "dim": 2, "field_disc": -3, "field_disc_factorization": [[-1, 1], [3, 1]], "field_poly": [1, -1, 1], "field_poly_is_cyclotomic": true, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 6, "has_non_self_twist": 1, "hecke_cutters": [[7, [4, 2, 1]], [11, [9, -3, 1]]], "hecke_orbit": 3, "hecke_orbit_code": 9007749044109702, "hecke_ring_generator_nbound": 2, "hecke_ring_index": 1, "hecke_ring_index_factorization": [], "hecke_ring_index_proved": true, "inner_twist_count": 2, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 13, 3, 1, 3, 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": true, "label": "390.2.i.c", "level": 390, "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": true, "level_primes": [2, 3, 5, 13], "level_radical": 390, "minimal_twist": "390.2.i.c", "nf_label": "2.0.3.1", "prim_orbit_index": 3, "qexp_display": "q+(1-\\zeta_{6})q^{2}+(-1+\\zeta_{6})q^{3}-\\zeta_{6}q^{4}+\\cdots", "related_objects": [], "relative_dim": 1, "rm_discs": [], "sato_tate_group": "1.2.3.c3", "self_twist_discs": [], "self_twist_type": 0, "space_label": "390.2.i", "trace_display": [1, -1, -2, -2], "trace_hash": 1153429512592830292, "trace_moments": [{"__RealLiteral__": 0, "data": "0.006", "prec": 17}, {"__RealLiteral__": 0, "data": "1.912", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "10.623", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "90.156", "prec": 20}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.010", "prec": 17}, "traces": [0, 2, 1, -1, -1, -2, 1, -2, -2, -1, -1, 3, 2, 2, -4, 1, -1, -6, -2, -2, 1, 4, -3, -3, 1, 2, -5, 2, -2, -3, -1, 10, 1, 3, -12, 2, -1, 7, -4, 5, 2, -6, 2, 1, -6, 1, 3, -6, -1, 3, 1, 12, -7, -12, 1, -3, 2, 4, 3, 9, -2, -2, 5, -2, 2, -2, 6, -8, -6, -3, 4, 12, 1, 28, -7, -1, -2, -12, 7, 10, 1, -1, 6, -12, -2, 6, 2, -3, -3, 18, 2, -14, 6, -5, -3, 2, -2, -14, -3, -6, -1, -6, 6, 28, -2, -4, -6, 6, -1, 28, 3, 7, 4, -15, 2, 3, 6, -7, 18, -12, -1, 2, -4, -6, -5, -2, 2, -14, 1, -2, 5, 18, 3, -4, 8, -2, 6, -9, -6, -14, 2, 3, 24, -15, 2, 3, 14, 3, -14, 9, 1, 16, 2, -6, -6, -10, 2, -26, 5, 6, -1, 12, 1, 13, 12, -3, -6, 9, -4, -22, 12, -2, 1, -12, -6, -2, 3, -18, -18, 3, 1, -32, -4, 4, 3, -7, 5, -36, 3, -2, 4, 12, -1, 4, -28, -5, -6, -24, -3, -8, -2, -8, 6, 12, -6, 6, 14, 6, 5, -12, -2, -20, 6, -24, -6, -1, -2, -10, 14, -14, 6, -42, 14, 10, 2, -1, -30, 0, -2, 28, -3, 6, 3, 42, -2, 6, 9, -5, 12, 48, 1, -17, 4, -1, -2, -3, -12, -14, -10, 6, -1, -15, 4, 9, 14, -12, -1, 21, -1, -28, 7, 6, 9, 15, -3, 12, 4, 18, 16, -18, -1, -11, 12, 4, -18, 3, -3, 1, -28, -5, -2, 36, -3, 31, 12, -4, -21, 24, 1, -19, -3, 28, -14, 30, 6, -9, -7, 3, 18, 15, 2, 2, 8, -6, 4, 2, 6, 16, 6, -14, -5, -24, -5, 16, -13, 2, -5, 24, -6, 9, -2, 6, 6, -12, 2, 2, 26, -14, 6, 6, -6, -32, 6, -14, -9, 8, -2, 28, -23, 30, 6, 15, 2, -40, -1, 3, -24, 30, -3, -8, -4, 2, 6, -30, -9, -12, -36, -12, -3, 48, -1, 15, -16, -4, 10, -28, 2, -20, -3, 12, 7, 12, 10, 25, -18, 1, 6, 15, -4, -38, 2, -14, 24, 21, 1, 12, -4, 1, -14, 6, -7, 36, -3, -9, 24, -10, 3, 31, -16, -4, -1, 12, -16, 10, 12, 1, 6, -21, -12, 10, -6, 18, -14, 18, 3, 12, 7, 28, -6, 12, 2, -32, 20, 3, 12, -6, -12, -4, -12, 21, -2, -12, -1, 40, -20, 3, -14, 12, 14, 4, 3, -6, -12, -72, 7, -18, -10, -18, -2, -36, -2, 18, -15, -8, 0, 14, -4, -2, 14, -6, -6, -15, -6, -68, -3, 5, 21, 36, 5, 32, 3, 13, -9, 6, 5, -2, 24, 6, 24, 0, 2, -35, -34, -6, 2, 14, -2, -2, 2, -26, 3, 0, -6, 36, -4, 6, -5, 24, -6, 64, 1, 9, -30, -24, 2, 6, 18, 23, 28, -3, -6, -28, -2, -2, -21, -28, 1, -9, -14, 24, 2, -60, 3, -11, -9, 4, -15, -30, -6, 14, 6, 9, 8, 30, 36, -6, 8, 3, -36, -9, 1, 40, 11, 16, 6, -28, -10, 40, -9, -2, -3, 12, 3, -10, 2, -7, -14, 6, -10, 7, -4, 18, 18, -36, -6, 15, -31, 4, -12, -6, -2, -80, -6, -24, 12, -3, -1, 4, 19, 4, -6, 12, 14, -18, -28, 7, 60, -18, 3, -10, -18, -24, 7, 54, -3, 12, 9, 16, 21, 12, 1, 19, -2, 16, -8, -2, -12, 22, 2, -6, 4, -6, 12, 31, 8, 6, 12, -21, 14, -92, 5, -3, -12, -72, -7, 2, 8, 6, 13, -84, -2, 16, -10, -20, 12, 14, -12, -15, 18, 12, -1, -6, 12, 16, -6, 2, 12, -24, 1, 54, -5, 20, 13, -6, 14, -18, -6, -14, 12, -15, -3, -32, -64, 12, 12, 4, -7, -9, -18, 10, -8, -12, 2, 4, 14, 2, -1, -72, 15, -28, -6, 0, -15, 12, 4, 9, -20, -14, -2, -12, 6, 46, -12, 6, 60, 14, 3, 72, 8, -21, -2, -42, -5, -28, 3, -3, 30, 24, 9, -32, -24, -5, -18, -15, -24, 15, -6, -24, 24, -36, -2, -28, -15, 34, 16, -3, -2, -8, 14, 2, -14, 6, -2, -44, 20, -3, -6, 24, 6, 16, 14, 4, 24, 9, 5, -9, 50, 6, 18, -24, -1, -41, 3, 30, 21, -16, -2, -38, 38, -18, -2, 12, -28, -28, 12, 6, 42, 63, 2, 13, 6, 21, -8, 48, -1, 10, 14, 14, 3, 24, -2, 72, 18, -3, 3, 26, 9, -35, 48, 15, -5, -30, 6, -14, 62, -6, -8, 24, -8, 18, 1, -36, -12, 42, -8, -12, -25, 36, 6, -30, -1, 64, -6, -11, -42, -13, -6, 2, 20, 10, -12, -27, 9, -14, -28, 3, -18, 12, -3, -26, 6, -2, 2, -36, 14, -9, 6, 10, -12, -42, 4, 20, -16, -18, 40, 22, 6, 4, 6, 31, -12, 21, 12, -38, 4, 2, -6, 6, 6, -92, -1, -12, 12, -90, 1, 12, 80, -19, -10, 15, 6, 40, -28, -14, 6, 2, 28, -23, -4, -60, -3, -6, -3, -38, 30, 18, -36, 57, -7, 56, 18, 3, -20, 6, -9, -3, -4, -21, -72, -15, -1, 36, 36, 2, 15, 32, 8, -17, 0, 12, 4, -12, -2, -18, 2, -4, -14, -18, -12, 16, -3, -8, -30, 84, -12, 7, -34, -14, -6, 12, -5, -12, -21, 12, 18, 36, 7, 4, 16, -8, -3, 84, -13, -18, -18, 2, 3, 12, 10, 28, -4, -12, 12, -9, 12, -12, -24, -18, 0, -18, 1, -12, -49, -12, -17, -4, 6, 64, -2, -12, 28, 48, -1, -28, -4, 5, 4, 57, -13, -54, 6, -14, 0, 18, 6, 24, 18, -12, 10, -6, 3, 25, 5, 64, -24, 8, -12, 22, 32, 7, 2], "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], [1, -1], [-1, 1], [0, -1], [-1, 0], [0, 1], [0, -2], [-1, 0], [0, -1], [-1, 1], [3, -3], [1, 0], [3, -4], [-2, 0], [1, -1], [-1, 1], [0, -6], [-1, 0], [0, -2], [0, 1], [2, 0], [0, -3], [-3, 3], [1, -1], [1, 0], [-1, -3], [1, 0], [-2, 2], [-3, 3], [0, -1], [5, 0], [0, 1], [0, 3], [-6, 0], [0, 2], [-1, 1], [7, -7], [-2, 0], [1, 3], [1, 0], [-6, 6], [2, -2], [0, 1], [-3, 0], [0, 1], [0, 3], [-3, 0], [0, -1], [3, -3], [1, -1], [6, 0], [-4, 1], [-6, 0], [1, -1], [-3, 3], [0, 2], [2, 0], [0, 3], [0, 9], [-1, 0], [0, -2], [5, -5], [-2, 2], [1, 0], [-3, 4], [3, 0], [-8, 8], [-6, 6], [0, -3], [2, 0], [0, 12], [0, 1], [14, 0], [0, -7], [-1, 1], [-2, 2], [-6, 0], [4, -1], [5, 0], [1, -1], [-1, 1], [0, 6], [-6, 0], [0, -2], [0, 6], [1, 0], [0, -3], [-3, 3], [18, -18], [1, 0], [-8, 2], [3, 0], [-5, 5], [-3, 3], [0, 2], [-1, 0], [0, -14], [0, -3], [-3, 0], [0, -1]]}