# Stored data for newform 546.2.l.l, downloaded from the LMFDB on 25 April 2024. {"label": "546.2.l.l", "space_label": "546.2.l", "level": 546, "weight": 2, "hecke_orbit": 12, "hecke_orbit_code": 49540351848874530, "dim": 4, "is_polredabs": true, "nf_label": "4.0.2601.1", "trace_hash": 623710044443278220, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[5, [-4, 1, 1]], [11, [16, 4, 5, -1, 1]]], "qexp_display": "q+(-1+\\beta _{2})q^{2}+(1-\\beta _{2})q^{3}-\\beta _{2}q^{4}+\\cdots", "char_order": 3, "char_parity": 1, "char_degree": 2, "char_conductor": 13, "char_orbit_label": "l", "char_is_real": false, "Nk2": 2184, "analytic_conductor": 4.359831950361909, "hecke_ring_index": 1, "level_radical": 546, "field_poly_is_cyclotomic": false, "field_poly_root_of_unity": 0, "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": "0.008", "prec": 17}, "analytic_rank_proved": true, "char_values": [546, 3, [365, 157, 379], [3, 3, 1]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 2, "level_primes": [2, 3, 7, 13], "conrey_indexes": [211, 295], "field_disc": 2601, "field_disc_factorization": [[3, 2], [17, 2]], "field_poly": [16, 4, 5, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.023", "prec": 17}, {"__RealLiteral__": 0, "data": "3.905", "prec": 17}, {"__RealLiteral__": 0, "data": "0.970", "prec": 17}, {"__RealLiteral__": 0, "data": "59.375", "prec": 20}, {"__RealLiteral__": 0, "data": "40.134", "prec": 20}, {"__RealLiteral__": 0, "data": "1564.088", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "1.2.3.c3", "trace_display": [-2, 2, -2, -2], "traces": [0, 4, -2, 2, -2, -2, 2, -2, 4, -2, 1, 1, -4, -2, 4, -1, -2, 8, 4, 1, 1, -4, 1, -6, 2, -2, 1, -4, -2, 4, -1, 0, -2, -1, -16, 1, -2, 9, -2, -1, -2, 6, 2, 16, -2, 1, -6, -26, 2, -2, 1, 16, 1, 28, 2, 8, -2, 2, 4, -2, 2, 6, 0, -2, 4, 1, 2, -10, 8, 6, -2, -2, -2, -18, 9, -1, 1, -2, -1, -18, 1, -2, 6, -4, 2, -21, -32, -4, 1, -11, -2, 1, 12, 0, 13, 8, -4, 10, -2, -2, 1, -9, -8, -8, -2, 2, -14, 1, 2, -16, 8, -9, 4, 1, -1, 20, -8, 1, 4, 8, -1, 13, -12, -6, 0, -6, -2, 8, -2, 32, 25, 24, -1, 1, -10, 2, 8, -29, -12, 15, 1, -13, 4, -26, 4, 15, 9, 2, -18, 27, -1, -30, 1, 8, 1, 0, 2, -30, 9, 14, 1, 12, -2, -16, -12, -8, 2, 8, -4, -50, 42, 1, 16, 36, 8, 1, 1, -4, -11, 20, 1, 20, -2, 12, -6, -13, 0, -26, 13, 2, -16, 2, 2, 8, -20, -25, 4, -21, 1, 32, -2, 10, -9, -8, -8, 31, 4, 12, 1, 18, -1, -2, -14, -4, 1, -8, -4, 0, 8, -9, -16, -55, 18, -36, -2, 1, -2, 30, -1, -6, 20, -1, 4, -44, -2, 64, -2, -9, 8, 28, -1, 21, -26, 2, 6, 1, 12, 25, 0, -2, 3, -14, 4, -14, 8, -42, -2, 24, -16, -18, -26, -8, -12, -2, -1, -14, 1, 11, 20, -46, -1, -4, -16, 2, 58, -9, 6, 35, -30, 0, 1, -6, -13, 40, -2, 16, 25, -12, -2, -32, 15, 20, 9, -15, -4, -16, 9, -1, -54, -48, 2, 16, 15, 9, -2, 31, 8, 18, 1, -4, 0, 30, -1, -24, 15, 1, 9, 58, 14, -19, -2, -1, -6, 13, 4, 1, 32, -8, 6, 13, 16, -14, 2, -18, 8, -12, 2, 12, 25, 2, -21, 0, 1, 4, 16, -20, -72, 7, -4, 36, -2, 2, -2, 47, 2, 52, 22, -8, 20, -40, 1, 29, -10, 26, 1, 26, -6, 14, -6, -12, -13, -14, 0, 35, 13, -3, -26, -53, -4, -34, 8, -8, -4, 5, 2, -16, 8, 16, 10, -46, 26, -116, -2, 12, -21, -8, 1, -27, -64, -1, 1, -17, -20, 0, 18, 1, 4, 4, 16, 19, 31, -58, 4, -2, -6, -32, 1, 30, -9, -22, -1, 18, -2, 13, 28, 13, 2, 6, -2, -25, 16, -14, 2, 55, 0, -15, 8, 28, -9, 36, 8, 4, 8, -34, -9, 14, -36, 54, -2, 38, -2, -37, 1, -15, -60, -26, 2, -29, 3, -8, -40, 25, -1, 74, 4, 0, 22, -16, 1, 20, -32, -15, -2, 16, -9, -9, -16, -14, -14, -25, 2, 21, -42, 6, 13, -22, -4, -35, 6, -32, 1, 0, -6, -36, 1, -16, 0, -2, -2, 88, 3, -8, 28, 24, -2, 47, 28, -25, -16, 63, 21, 9, 4, -1, 24, 72, -16, 19, 9, 72, 1, 120, 4, 13, -12, 2, -2, 0, 2, -6, 7, -2, -2, -105, -22, -60, -10, -20, 92, 1, -1, -14, -4, 10, 8, -60, -1, -52, -29, 6, -9, 38, 6, 9, -70, 13, 15, -16, 0, -8, -2, -13, 3, 28, 26, -9, 40, 4, -2, 44, -8, -68, 1, 4, 6, -14, -2, -134, -32, -8, -30, 2, -10, 7, -18, -26, 30, 12, 2, 0, 32, 21, 9, -4, -1, -21, 27, 64, 54, -20, -1, -3, 16, 20, 15, -15, -18, 32, 1, -4, -62, 13, -16, -39, -9, -31, -2, -1, -4, 66, 0, 6, -15, 22, -1, -72, 12, 9, 15, 106, 1, 49, -18, 2, -29, -72, -28, 1, 38, -2, 1, -21, 2, -83, -6, -16, 13, 55, -2, -36, -26, 0, -16, -37, -8, 56, 6, 9, -26, -33, -8, 3, 28, -8, -4, 8, 9, -22, -16, 36, -12, 74, 2, 22, -6, 2, 25, 0, -1, 10, -21, 60, 0, -48, -2, 23, -2, -3, -32, -14, 40, 0, 36, 1, -14, -16, -4, -88, 36, -22, 1, -50, -1, -8, 1, 32, 47, 18, 2, 23, -104, 9, -11, 0, 16, -4, -40, 14, 20, 19, -2, 4, 29, 42, -10, -19, -13, 160, 1, 4, -13, -64, -6, 0, 14, -1, 12, 22, 6, -6, 26, -1, 28, -24, 0, -5, -70, 2, 13, -2, -3, 61, 13, -28, 49, -104, 2, -56, -34, -28, 8, -36, 16, 8, 2, -21, -10, -50, -4, -18, 8, -24, -16, 8, 16, 0, 10, -9, 23, 74, -1, 100, 58, -4, -2, 66, 12, -45, 42, 2, 4, 1, -2, 99, 54, -7, 32, -68, 2, -103, 1, 22, -17, 4, 10, -40, 0, -92, -9, 11, 1, 96, 4, 4, -8, -60, -8, -8, -38, 1, -62, -1, 29, 60, -8, 9, -2, 104, -6, -24, 16, 70, -2, -16, -15, -72, -9, 0, -22, -20, 2, 16, -9, -3, 4, 25, -26, 13, -14, -40, -26, 44, 2, 72, 6, 8, 1, 74, -1, 14, -8, -6, -14, 148, 2, -18, -110, 32, 0, -13, 30, 56, -16, 10, -14, 3, 18, -13, 36, -30, 8, -77, -2, -80, 47, -32, 17, 55, -9, -16, 14, 1, 72, 19, -27, -44, 4, -54, -76, 0, 1, 56, 74, -16, 1, 58, -15, -6, 30, 18, 1, -28, -1, -18, -29, 62, 3, -12, 16, 63, 20, 9, -50, 154, 2, 4, -37, 4, -8, 22, 0, -2, 22, 15, 8, 64, 1, -146, -10, -12, -32, -92, -15, -50, 4, -1, -8, -113, 18, 9, 18, 29, 8, -34, 28, 16, -14, -38, -25, -29, -1, -124, -30, -2, 21, -21, 6, -48, 13, -13, 44, -42, 2, 15, 70, 26, -12, 37, 16, -3, -2, 8, 0, -24, -6, 2, 18, 26, -26, -96, 8, -21, 0, -28, -2, -16, 4, 18, -44, -9, -6], "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": 12, "prim_orbit_index": 3, "minimal_twist": "546.2.l.l", "char_is_minimal": true, "conrey_index": 211, "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, 0, 0], [1, 0, 0, 0], [-1, 0, 1, 0], [1, 0, -1, 0], [0, 0, -1, 0], [0, 0, 0, 1], [0, 0, 1, 0], [0, 0, -1, 0], [1, 0, 0, 0], [0, 0, -1, 0], [0, -1, 0, -1], [1, 1, -1, 1], [-1, 0, 0, 0], [0, 2, -1, 1], [1, 0, 0, 0], [0, 1, 0, 1], [-1, 0, 1, 0], [0, 2, 3, 0], [1, 0, 0, 0], [0, -1, 1, 0], [0, 1, 0, 0], [-1, 0, 0, 0], [0, -1, 1, 0], [-2, 2, 2, 2], [1, 0, -1, 0], [-1, 0, 0, -1], [1, -1, 0, 1], [-1, 0, 0, 0], [-1, 0, 1, 0], [3, 2, -3, 2], [0, -1, 0, 0], [0, 0, 0, 0], [0, 0, -1, 0], [0, 1, -1, 0], [-3, 0, 0, 2], [0, 1, 0, 0], [-1, 0, 1, 0], [4, -1, -4, -1], [-1, 0, 0, -1], [-1, 1, 0, -1], [0, 0, 0, 1], [5, 4, -5, 4], [1, 0, -1, 0], [0, 0, 8, 0], [-1, 0, 0, -1], [0, 1, 0, 0], [0, -2, -2, 0], [-5, 0, 0, 3], [0, 0, 1, 0], [-1, 0, 1, 0], [1, 1, -1, 1], [3, 0, 0, -2], [-1, -1, 1, -2], [7, 0, 0, 0], [1, 0, -1, 0], [4, 0, -4, 0], [0, 0, -1, 0], [1, 0, 0, 1], [0, -2, 3, 0], [0, 2, -2, 0], [0, 0, 0, -1], [0, -4, 5, 0], [0, 0, 0, 0], [-1, 0, 1, 0], [1, 0, 0, 0], [4, -1, -8, -1], [1, 0, 0, 1], [-6, -2, 6, -2], [3, -2, -3, -2], [0, 2, 2, 0], [0, 0, 0, 1], [0, -6, 2, 0], [0, 0, -1, 0], [-4, 0, 0, 1], [0, 1, 4, 0], [-1, -1, 1, -1], [1, 1, -1, 1], [-1, 0, 0, -1], [1, 1, -1, 2], [-5, 0, 0, -1], [0, -1, 0, -1], [-1, 0, 1, 0], [0, -4, 5, 0], [-2, 0, 0, -2], [0, 0, 1, 0], [0, -5, -8, 0], [-8, 0, 0, 0], [0, 2, -3, 0], [1, 1, -1, 1], [-5, 1, 5, 1], [0, 0, 0, 1], [-1, -1, 1, -2], [2, 0, 0, -2], [0, 0, 0, 0], [5, -3, -5, -3], [0, 0, 4, 0], [-1, 0, 0, 0], [0, 2, 4, 0], [0, 0, -1, 0], [-1, 0, 0, -1], [0, -1, 1, 0]]}