# Stored data for newform 306.2.g.c, downloaded from the LMFDB on 22 May 2024. {"Nk2": 1224, "analytic_conductor": 2.4434223018511796, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 17, "char_degree": 2, "char_is_minimal": true, "char_is_real": false, "char_orbit_index": 7, "char_orbit_label": "g", "char_order": 4, "char_parity": 1, "char_values": [306, 4, [137, 37], [4, 3]], "cm_discs": [], "conrey_index": 55, "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": [[5, [8, 4, 1]], [7, [2, -2, 1]]], "hecke_orbit": 3, "hecke_orbit_code": 9007611605156146, "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, 17, 3, 1, 4, 0]], "is_cm": false, "is_polredabs": true, "is_rm": false, "is_self_dual": false, "is_self_twist": false, "is_twist_minimal": true, "label": "306.2.g.c", "level": 306, "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": [2, 3, 17], "level_radical": 102, "minimal_twist": "306.2.g.c", "nf_label": "2.0.4.1", "prim_orbit_index": 3, "qexp_display": "q+iq^{2}-q^{4}+(-2-2i)q^{5}+(1-i)q^{7}+\\cdots", "related_objects": [], "relative_dim": 1, "rm_discs": [], "sato_tate_group": "1.2.3.c4", "self_twist_discs": [], "self_twist_type": 0, "space_label": "306.2.g", "trace_display": [0, 0, -4, 2], "trace_hash": 1624523867764195705, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.992", "prec": 17}, {"__RealLiteral__": 0, "data": "0.035", "prec": 17}, {"__RealLiteral__": 0, "data": "11.736", "prec": 20}, {"__RealLiteral__": 0, "data": "0.050", "prec": 17}, {"__RealLiteral__": 0, "data": "94.098", "prec": 20}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.253", "prec": 17}, "traces": [0, 2, 0, 0, -2, -4, 0, 2, 0, 0, 4, 4, 0, 12, 2, 0, 2, -2, 0, 0, 4, 0, 4, -6, 0, 0, 0, 0, -2, 4, 0, -6, 0, 0, 8, -8, 0, -12, 8, 0, -4, -2, 0, 0, -4, 0, -6, 20, 0, 0, -6, 0, -12, 0, 0, -16, -2, 0, -4, 0, 0, 4, 6, 0, -2, -24, 0, 8, 2, 0, 0, 2, 0, -2, 12, 0, 0, 0, 0, -10, -4, 0, -2, 0, 0, -12, -24, 0, -4, 24, 0, 12, 6, 0, 0, -16, 0, -22, -10, 0, 0, -28, 0, -4, 0, 0, 12, 28, 0, -8, 0, 0, 2, 22, 0, 24, -4, 0, 0, -10, 0, 0, 4, 0, 6, -8, 0, 0, 0, 0, 24, 28, 0, -8, 0, 0, -8, -12, 0, 28, 8, 0, -2, 24, 0, 0, 2, 0, 12, 4, 0, 0, -8, 0, 8, 0, 0, 28, -10, 0, 4, 0, 0, 24, 2, 0, -32, -22, 0, 46, -20, 0, 0, 20, 0, 6, 4, 0, 0, 0, 0, 4, 12, 0, 6, 0, 0, -20, -20, 0, -16, -36, 0, 6, 22, 0, 0, 0, 0, 10, 6, 0, 0, 8, 0, 8, 0, 0, 12, -16, 0, -36, 0, 0, -28, 48, 0, -12, -8, 0, 16, -12, 0, 0, 2, 0, 22, 16, 0, 0, 0, 0, 4, -30, 0, -40, 0, 0, 6, -44, 0, 18, -6, 0, -4, 20, 0, 0, -6, 0, -8, 0, 0, 0, 16, 0, 2, 0, 0, -24, 24, 0, -28, 0, 0, -24, 8, 0, -8, -20, 0, -32, -2, 0, 0, 12, 0, -40, -28, 0, 0, 0, 0, -20, -2, 0, 24, 0, 0, -30, 16, 0, 2, 60, 0, 0, -12, 0, 0, -36, 0, 24, 16, 0, 0, -16, 0, 8, 0, 0, -24, 6, 0, 26, 0, 0, 10, -16, 0, 16, 4, 0, -12, -32, 0, 0, 24, 0, 2, 20, 0, 0, 0, 0, 22, -16, 0, -22, 0, 0, 12, -24, 0, 24, 24, 0, -20, 40, 0, 0, -6, 0, 4, 4, 0, 0, -24, 0, -32, 0, 0, 6, 4, 0, -12, 0, 0, -6, -6, 0, -48, -12, 0, -44, 12, 0, 0, 24, 0, 0, 16, 0, 0, 0, 0, -16, 6, 0, 22, 0, 0, 30, 10, 0, 0, 40, 0, 36, -10, 0, 0, -10, 0, -36, 28, 0, 0, -48, 0, 48, 0, 0, 4, 0, 0, 64, 0, 0, 16, -8, 0, 44, -36, 0, -12, 24, 0, 0, -28, 0, 48, 22, 0, 0, 0, 0, 8, 24, 0, 58, 0, 0, 48, -48, 0, -48, -44, 0, -2, -30, 0, 0, -22, 0, 16, -48, 0, 0, 4, 0, -24, 0, 0, 36, 4, 0, 30, 0, 0, 8, 40, 0, 0, 48, 0, 24, 10, 0, 0, -10, 0, -72, -18, 0, 0, 0, 0, -42, -4, 0, 20, 0, 0, 12, 48, 0, -6, 4, 0, -12, 8, 0, 0, 54, 0, 56, -24, 0, 0, -28, 0, -4, 0, 0, 16, 8, 0, 40, 0, 0, -24, -2, 0, 24, -28, 0, 4, -18, 0, 0, -24, 0, 8, -12, 0, 0, 0, 0, 20, 20, 0, 12, 0, 0, 8, 32, 0, -4, 12, 0, -12, 16, 0, 0, 40, 0, -28, 36, 0, 0, -8, 0, -40, 0, 0, -88, -20, 0, 2, 0, 0, 32, -24, 0, -4, -18, 0, -64, -16, 0, 0, 32, 0, -24, -2, 0, 0, 0, 0, -24, 0, 0, -12, 0, 0, 8, -4, 0, -36, -48, 0, -10, -24, 0, 0, 12, 0, -30, 8, 0, 0, 120, 0, 36, 0, 0, -8, -34, 0, 0, 0, 0, -6, 24, 0, 62, 26, 0, -28, -36, 0, 0, 10, 0, -16, -32, 0, 0, 0, 0, -4, 38, 0, -16, 0, 0, -8, -36, 0, 0, -36, 0, -24, -28, 0, 0, -2, 0, 20, -8, 0, 0, 0, 0, 32, 0, 0, -24, 22, 0, 16, 0, 0, -42, 22, 0, -46, 48, 0, -44, 20, 0, 0, -40, 0, 24, -24, 0, 0, 0, 0, -28, -20, 0, 40, 0, 0, 10, -20, 0, -6, -12, 0, -48, -4, 0, 0, -28, 0, -8, 8, 0, 0, 36, 0, -96, 0, 0, 32, -38, 0, -4, 0, 0, -4, -12, 0, -16, -12, 0, -8, 96, 0, 0, -6, 0, -6, 16, 0, 0, 0, 0, 12, -18, 0, -8, 0, 0, 20, 56, 0, 18, 20, 0, -24, -32, 0, 0, 0, 0, 16, -20, 0, 0, 36, 0, 68, 0, 0, -8, -16, 0, -6, 0, 0, 18, -22, 0, -36, 8, 0, 8, -18, 0, 0, -56, 0, 36, 0, 0, 0, 0, 0, 24, 36, 0, -10, 0, 0, -20, -6, 0, -10, -8, 0, 24, 36, 0, 0, -34, 0, -8, -8, 0, 0, -96, 0, 96, 0, 0, -8, 56, 0, -42, 0, 0, 0, -76, 0, -20, 64, 0, -12, 40, 0, 0, 16, 0, -8, -14, 0, 0, 0, 0, 36, -92, 0, 6, 0, 0, 6, 72, 0, 56, 8, 0, 28, -18, 0, 0, -48, 0, 22, 80, 0, 0, -16, 0, 12, 0, 0, 48, 8, 0, -24, 0, 0, -40, -58, 0, -16, -22, 0, 96, 12, 0, 0, 14, 0, -16, 48, 0, 0, 0, 0, 64, -2, 0, -30, 0, 0, -48, -8, 0, -22, -16, 0, 76, -16, 0, 0, 38, 0, 64, 16, 0, 0, 56, 0, -32, 0, 0, 60, 12, 0, 36, 0, 0, -4, -26, 0, 40, 30, 0, 40, 16, 0, 0, 8, 0, 40, -24, 0, 0, 0, 0, -48, -12, 0, -12, 0, 0, -6, 32, 0, 72, 44, 0, 10, -12, 0, 0, 72, 0, -18, -24, 0, 0, 6, 0, -88, 0, 0, 56, -42, 0, 4, 0, 0, 48, -20, 0, 16, 50, 0, 0, 20, 0, 0, -72, 0, -22, 6, 0, 0, 0, 0, -60, -12, 0, 8], "weight": 2, "weight_parity": 1, "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], [0, 1], [0, 0], [-1, 0], [-2, -2], [0, 0], [1, -1], [0, -1], [0, 0], [2, -2], [2, -2], [0, 0], [6, 0], [1, 1], [0, 0], [1, 0], [-1, -4], [0, 0], [0, -4], [2, 2], [0, 0], [2, 2], [-3, 3], [0, 0], [0, 3], [0, 6], [0, 0], [-1, 1], [2, 2], [0, 0], [-3, -3], [0, 1], [0, 0], [4, -1], [-4, 0], [0, 0], [-6, -6], [4, 0], [0, 0], [-2, 2], [-1, 1], [0, 0], [0, 12], [-2, 2], [0, 0], [-3, -3], [10, 0], [0, 0], [0, 5], [-3, 0], [0, 0], [-6, 0], [0, -6], [0, 0], [-8, 0], [-1, -1], [0, 0], [-2, 2], [0, 0], [0, 0], [2, -2], [3, -3], [0, 0], [-1, 0], [-12, -12], [0, 0], [4, 0], [1, 4], [0, 0], [0, -4], [1, 1], [0, 0], [-1, -1], [6, -6], [0, 0], [0, 4], [0, -4], [0, 0], [-5, 5], [-2, -2], [0, 0], [-1, -1], [0, 16], [0, 0], [-6, 10], [-12, 0], [0, 0], [-2, -2], [12, 0], [0, 0], [6, -6], [3, -3], [0, 0], [0, 10], [-8, 8], [0, 0], [-11, -11], [-5, 0], [0, 0], [0, -3]]}