# Stored data for newform 1305.2.c.b, downloaded from the LMFDB on 09 November 2024. {"Nk2": 5220, "analytic_conductor": 10.42047746377709, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 5, "char_degree": 1, "char_is_minimal": true, "char_is_real": true, "char_orbit_index": 3, "char_orbit_label": "c", "char_order": 2, "char_parity": 1, "char_values": [1305, 2, [146, 262, 901], [2, 1, 2]], "cm_discs": [], "conrey_index": 784, "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": [[2, [1, 0, 1]], [7, [4, 0, 1]], [11, [0, 1]]], "hecke_orbit": 2, "hecke_orbit_code": 4503737099879705, "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, 5, 2, 1, 2, 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": false, "label": "1305.2.c.b", "level": 1305, "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": [3, 5, 29], "level_radical": 435, "minimal_twist": "435.2.c.b", "nf_label": "2.0.4.1", "prim_orbit_index": 2, "qexp_display": "q+iq^{2}+q^{4}+(-1-2i)q^{5}+2iq^{7}+\\cdots", "related_objects": [], "relative_dim": 2, "rm_discs": [], "sato_tate_group": "1.2.3.c2", "self_twist_discs": [], "self_twist_type": 0, "space_label": "1305.2.c", "trace_display": [0, 0, -2, 0], "trace_hash": 1143595836905310340, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "2.026", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "16.633", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "168.473", "prec": 24}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.516", "prec": 17}, "traces": [0, 2, 0, 0, 2, -2, 0, 0, 0, 0, 4, 0, 0, 0, -4, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, -6, -8, 0, 0, 2, 0, 8, 0, 0, -4, 8, 0, 0, 0, 0, 12, -20, 0, 0, 0, 0, 4, 0, 0, 6, -8, 0, 0, 0, 0, 0, -12, 0, 0, 8, 0, 4, 0, 0, -14, 16, 0, 0, 0, 0, 4, 16, 0, 0, 4, 0, 0, 0, 0, -16, 2, 0, 0, 0, 0, 8, 0, 0, 0, 20, 0, -16, 0, 0, -24, 0, 0, 0, 0, 0, -6, -4, 0, 0, -24, 0, -24, 0, 0, 28, 0, 0, 0, 0, 0, -8, 2, 0, 0, -8, 0, -22, 0, 0, 8, 22, 0, 0, 0, 0, 8, 24, 0, 0, 4, 0, -12, 0, 0, 8, 8, 0, 0, 0, 0, -2, -28, 0, 0, -12, 0, -48, 0, 0, 0, -8, 0, 0, 0, 0, 20, 8, 0, 0, -20, 0, -12, 0, 0, -6, 4, 0, 0, 0, 0, -16, 0, 0, 0, -40, 0, 4, 0, 0, 12, -8, 0, 0, 0, 0, 0, -24, 0, 0, 20, 0, 6, 0, 0, 32, -24, 0, 0, 0, 0, 20, 4, 0, 0, 0, 0, -24, 0, 0, -12, 0, 0, 0, 0, 0, 0, -16, 0, 0, -20, 0, 28, 0, 0, 44, -4, 0, 0, 0, 0, 48, 8, 0, 0, 48, 0, 60, 0, 0, 4, -6, 0, 0, 0, 0, -4, 0, 0, 0, 24, 0, -34, 0, 0, 8, 16, 0, 0, 0, 0, 48, 0, 0, 0, 52, 0, -48, 0, 0, 28, 0, 0, 0, 0, 0, 12, 12, 0, 0, 16, 0, 0, 0, 0, 26, 4, 0, 0, 0, 0, -8, 12, 0, 0, 16, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 16, -16, 0, 0, 44, 0, -16, 0, 0, 0, 14, 0, 0, 0, 0, -32, 8, 0, 0, -48, 0, 16, 0, 0, -4, -8, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 4, 12, 0, 0, 0, 0, -16, 20, 0, 0, 0, 0, -38, 0, 0, -16, 56, 0, 0, 0, 0, -4, -48, 0, 0, 0, 0, -72, 0, 0, -40, 0, 0, 0, 0, 0, 0, -12, 0, 0, 4, 0, 8, 0, 0, 16, 16, 0, 0, 0, 0, 6, 68, 0, 0, -4, 0, -4, 0, 0, 44, -40, 0, 0, 0, 0, 24, -40, 0, 0, 24, 0, -44, 0, 0, -72, -16, 0, 0, 0, 0, 0, 0, 0, 0, -16, 0, 28, 0, 0, 32, 0, 0, 0, 0, 0, -20, 36, 0, 0, -68, 0, 0, 0, 0, 12, 16, 0, 0, 0, 0, -8, -52, 0, 0, -2, 0, 40, 0, 0, 8, 24, 0, 0, 0, 0, 0, -8, 0, 0, 72, 0, 16, 0, 0, -22, -40, 0, 0, 0, 0, 12, 8, 0, 0, 0, 0, -8, 0, 0, 8, 22, 0, 0, 0, 0, 4, 0, 0, 0, 52, 0, -56, 0, 0, -16, -8, 0, 0, 0, 0, 24, -20, 0, 0, 24, 0, 32, 0, 0, 38, 24, 0, 0, 0, 0, 24, 12, 0, 0, 0, 0, -4, 0, 0, -20, -28, 0, 0, 0, 0, 0, 0, 0, 0, -16, 0, 8, 0, 0, 0, -8, 0, 0, 0, 0, -56, 20, 0, 0, 28, 0, 8, 0, 0, 40, 16, 0, 0, 0, 0, -2, -24, 0, 0, -84, 0, 12, 0, 0, 0, 16, 0, 0, 0, 0, 8, -12, 0, 0, -72, 0, -4, 0, 0, -48, 22, 0, 0, 0, 0, 8, -96, 0, 0, -16, 0, 0, 0, 0, -72, -8, 0, 0, 0, 0, -14, -56, 0, 0, 8, 0, -16, 0, 0, 12, -48, 0, 0, 0, 0, 12, -100, 0, 0, 8, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, -24, 20, 0, 0, 56, 0, 52, 0, 0, -36, 0, 0, 0, 0, 0, -4, 0, 0, 0, 4, 0, -6, 0, 0, 40, 12, 0, 0, 0, 0, -56, -40, 0, 0, -96, 0, -88, 0, 0, 12, -8, 0, 0, 0, 0, -16, 60, 0, 0, 0, 0, 56, 0, 0, 12, 32, 0, 0, 0, 0, 0, -40, 0, 0, 0, 0, 8, 0, 0, 4, -6, 0, 0, 0, 0, 28, 0, 0, 0, -48, 0, 20, 0, 0, 80, -8, 0, 0, 0, 0, 12, -8, 0, 0, -24, 0, -40, 0, 0, -8, 48, 0, 0, 0, 0, 0, 84, 0, 0, -24, 0, 36, 0, 0, -76, 0, 0, 0, 0, 0, -24, 60, 0, 0, 0, 0, 0, 0, 0, -6, -88, 0, 0, 0, 0, -32, 56, 0, 0, 40, 0, 32, 0, 0, -48, -40, 0, 0, 0, 0, -8, -32, 0, 0, -60, 0, 88, 0, 0, 0, -16, 0, 0, 0, 0, 20, 84, 0, 0, 12, 0, -16, 0, 0, 68, 12, 0, 0, 0, 0, 8, 0, 0, 0, 40, 0, 2, 0, 0, -24, 6, 0, 0, 0, 0, 12, -8, 0, 0, -8, 0, -36, 0, 0, -72, 0, 0, 0, 0, 0, 0, 28, 0, 0, 0, 0, 16, 0, 0, 0, -8, 0, 0, 0, 0, 0, -84, 0, 0, -16, 0, -48, 0, 0, 48, 40, 0, 0, 0, 0, 40, -12, 0, 0, 8, 0, -48, 0, 0, 84, -4, 0, 0, 0, 0, -32, 96, 0, 0, -16, 0, 44, 0, 0, -48, -12, 0, 0, 0, 0, 16, 60, 0, 0, 28, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 48, 84, 0, 0, -8, 0, 0, 0, 0, -112, 0, 0, 0, 0, 0, 24, 48, 0, 0, 56, 0, -30, 0, 0, 60, 24, 0, 0, 0, 0, -20, -120, 0, 0, 28, 0, -4, 0, 0, 0, -6, 0, 0, 0, 0, -32, -4, 0, 0, 0, 0, 0, 0, 0, -32, -32, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 8, 0, 0, -68, -8, 0, 0, 0, 0, 8, 72, 0, 0, 40, 0, -4, 0, 0, -46, 60, 0, 0, 0, 0, -4, -48, 0, 0, 0, 0, 8, 0, 0, 96, -16, 0, 0, 0, 0, 0, -68, 0, 0, 76, 0, -56, 0, 0, -16, 24, 0, 0, 0, 0, 48, 108, 0, 0, 0, 0, 80, 0, 0, -92, 12, 0, 0, 0, 0, 0, 52, 0, 0, -48, 0, 48, 0, 0, -48, 32, 0, 0, 0, 0, 56, 40, 0, 0, -92, 0, 84, 0, 0, 88, 0, 0, 0, 0, 0, 16, 32, 0, 0, 52, 0, 0, 0, 0, 40, -72, 0, 0, 0, 0, 20, 0, 0, 0, 12, 0, -56, 0, 0, 60, -28, 0, 0, 0, 0, -24, -16, 0, 0, 8, 0, 16, 0, 0, 0, -44, 0, 0, 0, 0, -12, 16, 0, 0, 12, 0, 26, 0, 0, 0, 12, 0, 0, 0, 0, -80, 0, 0, 0, -8, 0, 112, 0, 0, -84, -96, 0, 0, 0, 0, -8, 52, 0, 0, 20, 0, 72, 0, 0, -20, -16, 0, 0, 0, 0, -48, 16, 0, 0, 0, 0, 12, 0, 0, 0, -60, 0, 0, 0, 0, -44, 0, 0, 0, -56, 0, 0, 0, 0, 48, -4, 0, 0, 0, 0, -18, -80, 0, 0, 12, 0, 96, 0, 0, -36, 0, 0, 0, 0, 0, 48, -56, 0, 0, -16, 0, -40, 0, 0, 4, 48, 0, 0, 0, 0, 0, 132, 0, 0, -72, 0, 80, 0, 0, 16, 0, 0, 0, 0, 0, -24, -80, 0, 0, -24, 0, 0, 0, 0, -120, 34, 0, 0, 0, 0, 32, 20, 0, 0, 108, 0, 120, 0, 0, 36, -8, 0, 0, 0, 0, -32, 20, 0, 0, 24, 0, -12, 0, 0, 0, 48, 0, 0, 0, 0, -64, -48, 0, 0, -120, 0, 20, 0, 0, 16, -96, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, -12, 0, 0, 16, -8, 0, 0, 0, 0, -52, 24, 0, 0, 0, 0, -24, 0, 0, -28, 48, 0, 0, 0, 0, -8, 36, 0, 0, 0, 0, -36, 0, 0, 66, -28, 0, 0, 0, 0, 0, 0, 0, 0, 32, 0, -44, 0, 0, 0, 32, 0, 0, 0, 0, 16, -48, 0, 0, 40, 0, 4, 0, 0, 128, 36, 0, 0, 0, 0, -12, 0, 0, 0, 68, 0, -24, 0, 0, 8, -40, 0, 0, 0, 0, -16, 6, 0, 0, -20, 0, 16, 0, 0, -44, 0, 0, 0, 0, 0, -80, 0, 0, 0, -120, 0, 0, 0, 0, -38, -26, 0, 0, 0, 0, -8, -56, 0, 0, -80, 0, 16, 0, 0, 120, 56, 0, 0, 0, 0, -24, 100, 0, 0, 112, 0, -16, 0, 0, 0, -24, 0, 0, 0, 0, -12, -20, 0, 0, -48, 0, 40, 0, 0, 108, -24, 0, 0, 0, 0, -16, 0, 0, 0, 40, 0, 0, 0, 0, -120, 0, 0, 0, 0, 0, -96, -48, 0, 0, 84, 0, -40, 0, 0, 24, 0, 0, 0, 0, 0, -12, -56, 0, 0, 0, 0, -104, 0, 0, -32, 32, 0, 0, 0, 0, 0, -8, 0, 0, -36, 0, -60, 0, 0, -100, -32, 0, 0, 0, 0, 16, 4, 0, 0, -128, 0, 72, 0, 0, 8, 112, 0, 0, 0, 0, -44, 24, 0, 0, -68, 0, 48, 0, 0, 40, 16, 0, 0, 0, 0, -24, -16, 0, 0, 24, 0, 0, 0, 0, 44, 0, 0, 0, 0, 0, 42, -28, 0, 0, 68, 0, 0, 0, 0, -20, 16, 0, 0, 0, 0, 0, 4, 0, 0, -72, 0, 28, 0, 0, -12, -16, 0, 0, 0, 0, -8, 80, 0, 0, 0, 0, 44, 0, 0, 0, -120, 0, 0, 0, 0, 48, 80, 0, 0, 40, 0, 96, 0, 0, -16, -16, 0, 0, 0, 0, 24, 0, 0, 0, -24, 0, -12, 0, 0, -116, 4, 0, 0, 0, 0, 16, 24, 0, 0, 56, 0, 118, 0, 0, -44, -8, 0, 0, 0, 0, -12, 0, 0, 0, 44, 0, -120, 0, 0, -40, -16, 0, 0, 0, 0, 0, 52, 0, 0, 108, 0, 8, 0, 0, -64, 80, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 100, 0, 0, 0, 0, 0, 0, 0, 0, -24, -48, 0, 0, 48, 0, -28, 0, 0, -28, -4, 0, 0, 0, 0, -44, 8, 0, 0, 16, 0, 32, 0, 0, -80, 0, 0, 0, 0, 0, -112, 76, 0, 0, 4, 0, 0, 0, 0, -88, -48, 0, 0, 0, 0, -20, 112, 0, 0, 108, 0, 0, 0, 0, 84, -80, 0, 0, 0, 0, 0, -68, 0, 0, -32, 0, 76, 0, 0, 0, 38, 0, 0, 0, 0, 8, -104, 0, 0, 16, 0, 36, 0, 0, -24, 16, 0, 0, 0, 0, -112, 0, 0, 0, 32, 0, -16, 0, 0, -48, 96, 0, 0, 0, 0, 8, 64, 0, 0, -52, 0, -64, 0, 0, 86, -12, 0, 0, 0, 0, 48, -14, 0, 0, 0, 0, -52, 0, 0, 120, 16, 0, 0, 0, 0, 0, -144, 0, 0, -32, 0, 8, 0, 0, 112, 72, 0, 0, 0, 0, 16, -40, 0, 0, -108, 0, 16, 0, 0, -96, 40, 0, 0, 0, 0, 0, -36, 0, 0, 8, 0, 24, 0, 0, 24, -48, 0, 0, 0, 0, -72, 72, 0, 0, 0, 0, 56, 0, 0, 16, 0, 0, 0, 0, 0, 12, -80, 0, 0, -96, 0, 22, 0, 0, -32, -40, 0, 0, 0, 0, -4, -16, 0, 0, -132, 0, 8, 0, 0, 64, -8, 0, 0, 0, 0, 36, 48, 0, 0, 8, 0, -24, 0, 0, 0, -16, 0, 0, 0, 0, 48, 0, 0, 0, -152, 0, 40, 0, 0, -56, -80, 0, 0, 0, 0, 64, 0, 0, 0, 52, 0, 8, 0, 0, -8, -22], "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, 1], [0, 0], [1, 0], [-1, -2], [0, 0], [0, 2], [0, 3], [0, 0], [2, -1], [0, 0], [0, 0], [0, 4], [-2, 0], [0, 0], [-1, 0], [0, 2], [0, 0], [0, 0], [-1, -2], [0, 0], [0, 0], [0, -2], [0, 0], [-3, 4], [-4, 0], [0, 0], [0, 2], [1, 0], [0, 0], [4, 0], [0, 5], [0, 0], [-2, 0], [4, -2], [0, 0], [0, -2], [0, 0], [0, 0], [6, -3], [-10, 0], [0, 0], [0, 0], [0, 0], [0, 0], [2, 0], [0, 12], [0, 0], [3, 0], [-4, -3], [0, 0], [0, 4], [0, 12], [0, 0], [0, 0], [-6, 0], [0, 0], [0, 1], [4, 0], [0, 0], [2, 0], [0, 4], [0, 0], [-7, 0], [8, -4], [0, 0], [0, -2], [0, 2], [0, 0], [2, 4], [8, 0], [0, 0], [0, 14], [2, 0], [0, 0], [0, 0], [0, 0], [0, 0], [-8, 0], [1, 2], [0, 0], [0, -10], [0, 6], [0, 0], [4, -2], [0, 0], [0, 0], [0, 0], [10, 0], [0, 0], [-8, 0], [0, -2], [0, 0], [-12, 0], [0, 0], [0, 0], [0, -10], [0, 3], [0, 0], [-3, 4]]}