# Stored data for newform 130.2.e.b, downloaded from the LMFDB on 25 April 2024.
{"label": "130.2.e.b", "space_label": "130.2.e", "level": 130, "weight": 2, "hecke_orbit": 2, "hecke_orbit_code": 4503874538832002, "dim": 2, "is_polredabs": true, "nf_label": "2.0.3.1", "trace_hash": 965608495006878214, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[3, [4, -2, 1]]], "qexp_display": "q+(1-\\zeta_{6})q^{2}+(2-2\\zeta_{6})q^{3}-\\zeta_{6}q^{4}+\\cdots", "char_order": 3, "char_parity": 1, "char_degree": 2, "char_conductor": 13, "char_orbit_label": "e", "char_is_real": false, "Nk2": 520, "analytic_conductor": 1.038055226276645, "hecke_ring_index": 1, "level_radical": 130, "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": "0.020", "prec": 17}, "analytic_rank_proved": true, "char_values": [130, 3, [27, 41], [3, 2]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 2, "level_primes": [2, 5, 13], "conrey_indexes": [61, 81], "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": "1.915", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "11.455", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "105.027", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "1.2.3.c3", "trace_display": [1, 2, -2, 1], "traces": [0, 2, 1, 2, -1, -2, -2, 1, -2, -1, -1, -3, -4, 5, 2, -2, -1, 6, -2, -5, 1, 4, 3, 0, -2, 2, -2, 8, 1, 0, 2, -8, 1, 6, 12, -1, -1, -11, -10, -4, 2, -6, 2, -2, 6, 1, 0, -6, 2, 6, 1, 24, -7, -18, 4, 3, -1, -20, 0, 0, 4, -8, -4, 1, 2, -5, 12, 16, 6, 0, -2, -6, 1, 28, 11, 2, -5, -6, -14, -32, 1, 11, 6, -12, -2, -6, -4, 0, 3, -9, 2, 7, 0, -8, -3, 5, 4, 10, -6, 6, -1, 6, 12, 10, -5, -4, -9, 12, -4, 4, -3, 22, -2, 12, -10, 0, 0, -7, 0, -6, 2, 2, -16, 12, 4, -2, -1, 1, 1, -8, 2, -18, 6, 5, -16, -8, -6, -6, 0, 19, -1, -6, -12, 6, 2, 0, 14, -12, 22, 18, -2, -32, 5, 6, -3, 8, -10, 34, -16, -18, -1, 0, -11, -2, 12, -6, -6, 15, -4, -1, -12, -5, -2, -15, 0, 1, -3, 0, 9, 24, 1, 16, 5, -32, 0, 11, 8, -36, 3, 4, 10, 0, 2, 4, 20, 4, -12, 27, 3, 10, -2, -32, -6, 0, -12, 6, 5, 0, 2, 30, -2, -23, 9, -24, -12, 2, -8, -4, 2, 28, -6, 42, 44, 19, -1, -1, 24, 24, 10, -8, 0, -6, 0, -48, -5, 6, 0, -32, 6, 0, -2, -23, 4, -10, -8, -6, 24, -35, 8, -12, -1, 15, -2, 0, -1, -24, -1, -12, -4, -22, 7, 0, -9, -9, -6, 18, -5, 18, -32, -6, -4, -20, -12, 10, -12, -3, 0, 1, 38, 4, 1, -12, 6, -14, -6, 20, 21, -12, 1, -19, 0, 40, -14, -9, -24, 0, 11, -12, 36, 0, -4, 2, -16, -12, 10, 8, -6, 4, 3, 10, 4, 60, 4, 28, 17, -1, 16, 30, 18, 0, -2, -24, 0, 30, -22, 5, -4, 4, 6, -3, -12, -20, 6, 22, -15, -16, -2, -32, -23, 48, -6, 12, 5, 26, 2, 0, -30, -6, 0, -2, 2, 20, -6, -6, 0, 6, 18, 12, -24, -12, -1, -6, 8, 8, -2, -28, -16, -32, 0, 12, -11, -9, 16, -14, -18, -2, 6, 0, 8, 19, 5, -2, 0, 0, -2, 6, -4, -2, 10, -60, 14, 0, -6, -18, -27, 32, -3, 13, 20, -10, -1, 15, -64, -20, -12, -11, 0, -33, -24, -5, -6, -24, -5, 0, 0, 12, 7, 76, 15, 36, 2, -20, 23, 3, 18, 6, -12, 8, -24, 42, 4, -30, -4, 16, -8, 0, -2, 0, -28, -20, -3, -12, 30, -36, 22, 9, -19, 72, 1, -9, -2, -18, 12, -32, 48, -7, 20, 4, -4, 24, 0, 42, 6, 16, 0, 8, -24, -24, 2, 32, 3, 34, 0, 12, 32, -5, 12, 9, 0, 30, -4, 22, -46, 0, 2, -10, -20, 19, 8, -8, 6, -27, 12, 0, -25, -6, 4, 6, 12, -8, 1, -30, 30, -9, -1, -6, 0, -46, -2, -6, -12, 14, -2, -20, 12, -10, 4, 9, -11, -60, 5, -54, 0, -14, 9, 4, 9, -24, -12, 23, 9, 0, -10, 12, 36, -12, -16, -48, -12, 18, 4, 40, 20, 16, -6, -4, -4, -68, -6, -8, 3, 0, 0, -16, 2, -22, 19, -21, 8, -14, 2, -36, -6, 36, 12, -12, 14, 22, 6, -9, 10, 34, 15, 0, -6, 0, -1, 64, 19, -8, 0, -6, 20, 27, -28, 7, -18, 6, -12, 20, 0, -54, -11, 48, 12, 6, 18, 40, 0, -36, -2, 19, -2, -32, 16, -2, -24, 13, 5, 0, 16, -15, -12, 13, 2, -12, 6, -18, -10, -2, -4, 0, 30, -18, 14, 2, 14, 30, -17, -132, 1, 28, 32, 46, 15, -1, 36, -12, 0, -6, -1, 9, -48, -2, 0, 8, -30, 9, -11, 0, -2, -16, -2, 27, -4, 18, -6, -14, -6, -12, -6, 4, -40, 60, 12, -5, 11, 0, -30, -38, 16, 48, 2, -20, -16, 8, -22, -36, 24, -10, 6, 96, -12, 6, 10, 6, 13, -8, 4, -45, 0, 13, -15, 3, -12, -19, 0, -72, 2, -48, 1, 12, -8, 110, -3, 6, 6, 12, 0, 10, 12, 16, 9, 0, 24, -6, -48, 0, -6, 0, -2, 5, 6, -92, -8, 0, 4, 58, -7, 26, -14, 12, 16, -50, 32, 12, 0, 48, 6, 7, -22, -50, -18, -12, 8, -18, -28, 6, 18, 24, 2, 40, 3, 60, 0, 32, 4, -23, -19, 0, -5, 3, -4, 2, 0, -6, 0, 0, -4, 34, 3, 24, -8, -39, 2, -8, -10, -22, -30, 60, 10, 36, 0, 0, 6, -34, 18, 22, -54, 18, 16, -12, -6, -56, 26, 18, 10, -42, -20, -18, 1, 18, -15, -42, -32, 0, 8, -24, -6, 18, 11, -98, 0, 40, -66, 2, -12, -10, -10, -2, -12, -36, -12, 43, -10, 6, 0, 72, 0, 40, 6, 4, 5, 72, 38, -15, -15, -32, -36, 24, 4, 29, -10, -12, 46, 1, 6, -2, 9, 28, 12, 0, 12, -92, -8, 5, -12, -24, 30, -62, 2, -12, 30, 72, 4, 15, 32, 38, -4, 48, 0, -32, -4, 10, 0, -1, -56, 10, 20, -36, 3, 15, -6, -104, -12, 0, -18, 27, -22, 2, -9, 33, -38, 15, 36, -24, 2, 0, -18, 0, -1, -54, -36, -4, -12, -16, 32, -8, 24, -12, -5, 0, 10, 18, -4, 32, 4, -9, 48, 34, 0, 4, 84, -42, 12, -11, 8, -5, 0, -42, -8, -60, 24, 60, -12, 36, 7, 100, 16, 28, -3, 0, -34, 0, 0, -4, 6, -48, 64, 70, -10, 30, 6, -24, 18, 0, 0, 0, -30, 6, -2, -30, 77, -24, -23, -4, 0, 10, -2, -60, -20, -33, -10, -19, 38, -4, 16, 0, -4, -27, 12, -2, 27, 78, -12, -27, 0, -12, 10, 0, -3, 22, -4, -80, -6, -10, 24, -41, -4, -44, 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": 5, "prim_orbit_index": 3, "minimal_twist": "130.2.e.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], [2, -2], [0, -1], [-1, 0], [0, -2], [0, 1], [-1, 0], [0, -1], [-1, 1], [-3, 3], [-2, 0], [4, -3], [1, 0], [-2, 2], [-1, 1], [0, 6], [-1, 0], [0, -5], [0, 1], [2, 0], [0, 3], [0, 0], [-2, 2], [1, 0], [1, -4], [4, 0], [1, -1], [0, 0], [0, 2], [-4, 0], [0, 1], [0, 6], [6, 0], [0, -1], [-1, 1], [-11, 11], [-5, 0], [2, -8], [1, 0], [-6, 6], [2, -2], [0, -2], [3, 0], [0, 1], [0, 0], [-3, 0], [0, 2], [6, -6], [1, -1], [12, 0], [-3, -1], [-9, 0], [4, -4], [3, -3], [0, -1], [-10, 0], [0, 0], [0, 0], [2, 0], [0, -8], [-4, 4], [1, -1], [1, 0], [-4, 3], [6, 0], [16, -16], [6, -6], [0, 0], [-1, 0], [0, -6], [0, 1], [14, 0], [0, 11], [2, -2], [-5, 5], [-3, 0], [-6, -2], [-16, 0], [1, -1], [11, -11], [0, 6], [-6, 0], [0, -2], [0, -6], [-2, 0], [0, 0], [3, -3], [-9, 9], [1, 0], [3, 1], [0, 0], [-8, 8], [-3, 3], [0, 5], [2, 0], [0, 10], [0, -6], [3, 0], [0, -1]]}