# Stored data for newform 336.2.bl.e, downloaded from the LMFDB on 28 March 2024. {"label": "336.2.bl.e", "space_label": "336.2.bl", "level": 336, "weight": 2, "hecke_orbit": 5, "hecke_orbit_code": 18016941163675984, "dim": 2, "is_polredabs": true, "nf_label": "2.0.3.1", "trace_hash": 2085794849224721543, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[5, [12, 6, 1]], [11, [12, -6, 1]]], "qexp_display": "q+(1-\\zeta_{6})q^{3}+(-4+2\\zeta_{6})q^{5}+(-2+\\cdots)q^{7}+\\cdots", "char_order": 6, "char_parity": 1, "char_degree": 2, "char_conductor": 28, "char_orbit_label": "bl", "char_is_real": false, "Nk2": 1344, "analytic_conductor": 2.6829735079150208, "hecke_ring_index": 1, "level_radical": 42, "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": "0.186", "prec": 17}, "analytic_rank_proved": true, "char_values": [336, 6, [127, 85, 113, 241], [3, 6, 6, 1]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 2, "level_primes": [2, 3, 7], "conrey_indexes": [31, 271], "field_disc": -3, "field_disc_factorization": [[-1, 1], [3, 1]], "field_poly": [1, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.003", "prec": 17}, {"__RealLiteral__": 0, "data": "1.931", "prec": 17}, {"__RealLiteral__": 0, "data": "0.080", "prec": 17}, {"__RealLiteral__": 0, "data": "11.460", "prec": 20}, {"__RealLiteral__": 0, "data": "0.144", "prec": 17}, {"__RealLiteral__": 0, "data": "94.044", "prec": 20}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "1.2.3.c6", "trace_display": [0, 1, -6, -1], "traces": [0, 2, 0, 1, 0, -6, 0, -1, 0, -1, 0, 6, 0, 0, 0, 0, 0, -12, 0, 7, 0, 4, 0, 0, 0, 7, 0, -2, 0, 0, 0, 5, 0, 6, 0, -6, 0, -1, 0, 9, 0, 0, 0, 0, 0, 6, 0, -6, 0, -13, 0, -12, 0, 0, 0, -24, 0, 14, 0, 0, 0, 0, 0, 5, 0, -18, 0, -3, 0, 0, 0, 0, 0, 15, 0, -7, 0, -12, 0, 27, 0, -1, 0, 12, 0, 48, 0, 0, 0, 12, 0, -27, 0, -5, 0, -42, 0, 0, 0, 0, 0, -6, 0, 5, 0, -18, 0, 12, 0, -5, 0, -2, 0, 12, 0, 0, 0, 9, 0, 24, 0, 1, 0, 18, 0, 0, 0, 0, 0, -3, 0, 18, 0, -35, 0, 6, 0, 12, 0, -10, 0, -12, 0, -18, 0, 0, 0, -11, 0, 12, 0, 18, 0, 0, 0, 0, 0, -24, 0, 0, 0, 0, 0, 6, 0, -12, 0, -12, 0, -28, 0, 7, 0, 0, 0, 28, 0, 0, 0, 30, 0, 0, 0, 0, 0, 6, 0, -24, 0, 1, 0, 6, 0, -13, 0, -36, 0, 24, 0, 16, 0, -3, 0, 0, 0, -36, 0, 0, 0, 0, 0, 0, 0, 6, 0, 6, 0, 20, 0, 15, 0, 36, 0, 16, 0, -14, 0, -30, 0, 3, 0, 6, 0, 18, 0, 36, 0, 0, 0, 0, 0, -24, 0, 1, 0, 48, 0, -63, 0, 6, 0, 48, 0, 0, 0, 24, 0, -18, 0, 5, 0, 0, 0, -48, 0, 0, 0, 0, 0, -54, 0, -16, 0, -18, 0, 42, 0, 17, 0, -10, 0, 24, 0, -5, 0, -42, 0, -54, 0, 31, 0, -12, 0, 0, 0, 0, 0, -6, 0, 0, 0, 9, 0, -6, 0, 0, 0, -50, 0, 10, 0, 18, 0, 27, 0, -12, 0, 12, 0, 0, 0, 0, 0, 0, 0, 63, 0, 5, 0, 30, 0, -15, 0, -1, 0, 12, 0, -38, 0, 6, 0, 30, 0, 20, 0, 0, 0, -60, 0, 0, 0, 0, 0, 30, 0, -12, 0, -12, 0, -12, 0, -30, 0, 2, 0, -60, 0, 37, 0, 18, 0, 0, 0, -11, 0, 12, 0, 0, 0, 0, 0, 27, 0, 36, 0, 12, 0, -3, 0, -30, 0, 0, 0, 36, 0, -54, 0, 9, 0, -7, 0, -24, 0, 45, 0, 0, 0, 0, 0, 33, 0, -12, 0, 0, 0, -36, 0, -5, 0, 60, 0, -58, 0, -6, 0, -84, 0, 0, 0, 18, 0, -30, 0, 0, 0, 0, 0, 0, 0, 16, 0, 2, 0, -12, 0, -24, 0, 24, 0, -12, 0, -36, 0, 18, 0, 90, 0, -5, 0, 12, 0, 0, 0, 0, 0, 30, 0, -6, 0, 6, 0, -24, 0, 6, 0, 98, 0, 0, 0, 24, 0, 9, 0, 0, 0, 24, 0, -21, 0, 0, 0, 0, 0, 0, 0, 12, 0, -18, 0, 21, 0, -6, 0, 60, 0, 24, 0, -14, 0, -6, 0, -30, 0, -7, 0, -30, 0, 0, 0, 0, 0, -24, 0, -1, 0, 35, 0, -60, 0, -23, 0, 0, 0, -108, 0, -24, 0, 30, 0, -30, 0, 41, 0, 27, 0, 0, 0, 0, 0, 0, 0, 0, 0, 27, 0, 6, 0, -18, 0, 18, 0, -48, 0, 18, 0, -36, 0, -4, 0, 6, 0, 45, 0, 0, 0, 0, 0, -3, 0, 13, 0, -6, 0, 0, 0, -18, 0, -24, 0, 70, 0, 12, 0, -66, 0, -24, 0, -16, 0, -12, 0, 0, 0, 0, 0, -6, 0, 37, 0, 0, 0, 54, 0, 22, 0, -72, 0, -84, 0, 35, 0, 0, 0, 12, 0, 11, 0, 42, 0, 0, 0, 0, 0, -30, 0, -54, 0, 27, 0, 6, 0, 36, 0, -86, 0, 12, 0, -18, 0, 0, 0, 25, 0, 18, 0, -108, 0, 0, 0, 0, 0, 33, 0, -36, 0, 84, 0, 0, 0, 8, 0, 0, 0, 2, 0, -7, 0, 60, 0, 36, 0, 30, 0, 72, 0, 0, 0, 0, 0, 0, 0, -13, 0, 18, 0, 30, 0, 72, 0, 36, 0, 0, 0, 7, 0, 36, 0, 12, 0, 10, 0, -27, 0, 0, 0, 0, 0, 30, 0, -18, 0, -25, 0, -24, 0, 0, 0, 2, 0, 2, 0, -12, 0, -63, 0, 18, 0, -6, 0, -63, 0, 0, 0, 0, 0, -72, 0, -6, 0, 12, 0, 81, 0, 24, 0, -72, 0, -44, 0, 0, 0, 60, 0, -20, 0, -24, 0, 0, 0, 0, 0, 0, 0, -54, 0, -35, 0, 1, 0, -126, 0, -12, 0, 0, 0, 96, 0, 8, 0, -48, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, 0, 30, 0, 0, 0, -54, 0, -54, 0, 32, 0, -32, 0, -12, 0, 21, 0, 9, 0, 6, 0, 30, 0, 0, 0, 0, 0, -39, 0, -17, 0, 60, 0, 36, 0, -5, 0, 48, 0, -58, 0, 12, 0, 84, 0, -5, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 40, 0, -36, 0, 54, 0, 0, 0, 62, 0, 108, 0, 9, 0, -12, 0, -36, 0, 22, 0, -36, 0, 0, 0, 0, 0, 0, 0, -30, 0, -81, 0, -6, 0, 42, 0, -120, 0, 0, 0, 0, 0, 0, 0, 6, 0, -54, 0, 27, 0, 0, 0, 0, 0, 36, 0, 0, 0, -90, 0, -3, 0, -25, 0, -36, 0, -14, 0, 5, 0, 6, 0, -14, 0, -18, 0, 144, 0, 0, 0, 0, 0, 84, 0, 0, 0, 6, 0, 30, 0, -45, 0, 24, 0, 72, 0, -12, 0, 0, 0, 48, 0, 6, 0, -12, 0, 0, 0, 0, 0, -84, 0, 12, 0, 5, 0, 63, 0, -54, 0, 48, 0, 10, 0, 0, 0, -72, 0, 6, 0, 0, 0, -21, 0, 0, 0, 0, 0, 75, 0, 1, 0], "weight_parity": 1, "has_non_self_twist": 1, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": false, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 28, 6, 1, 6, 0]], "char_orbit_index": 38, "prim_orbit_index": 6, "minimal_twist": "336.2.bl.a", "char_is_minimal": true, "conrey_index": 31, "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, 0], [1, -1], [0, 0], [-4, 2], [0, 0], [-2, 3], [0, 0], [0, -1], [0, 0], [2, 2], [0, 0], [-3, 6], [0, 0], [-2, 4], [0, 0], [-4, -4], [0, 0], [0, 7], [0, 0], [1, 2], [0, 0], [0, 0], [0, 0], [7, -7], [0, 0], [-1, 0], [0, 0], [0, 0], [0, 0], [5, -5], [0, 0], [4, -2], [0, 0], [2, -10], [0, 0], [0, -1], [0, 0], [3, 3], [0, 0], [-6, 12], [0, 0], [1, -2], [0, 0], [2, 2], [0, 0], [0, -6], [0, 0], [-5, -3], [0, 0], [-8, 4], [0, 0], [0, 0], [0, 0], [-12, 0], [0, 0], [7, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [3, -1], [0, 0], [0, -18], [0, 0], [-1, -1], [0, 0], [0, 0], [0, 0], [-2, 4], [0, 0], [5, 5], [0, 0], [0, -7], [0, 0], [-10, 8], [0, 0], [18, -9], [0, 0], [-1, 1], [0, 0], [6, 0], [0, 0], [24, 0], [0, 0], [0, 0], [0, 0], [8, -4], [0, 0], [-12, -3], [0, 0], [0, -5], [0, 0], [-14, -14], [0, 0], [4, -8], [0, 0], [2, -4], [0, 0]]}