# Stored data for newform 2646.2.e.b, downloaded from the LMFDB on 18 April 2024. {"label": "2646.2.e.b", "space_label": "2646.2.e", "level": 2646, "weight": 2, "hecke_orbit": 2, "hecke_orbit_code": 4503874538834518, "dim": 2, "is_polredabs": true, "nf_label": "2.0.3.1", "trace_hash": 1851213395746027631, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[5, [0, 1]], [11, [9, 3, 1]], [13, [4, 2, 1]]], "qexp_display": "q-q^{2}+q^{4}-q^{8}-3\\zeta_{6}q^{11}-2\\zeta_{6}q^{13}+\\cdots", "char_order": 3, "char_parity": 1, "char_degree": 2, "char_conductor": 63, "char_orbit_label": "e", "char_is_real": false, "Nk2": 10584, "analytic_conductor": 21.12841637483079, "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": "0.018", "prec": 17}, "analytic_rank_proved": true, "char_values": [2646, 3, [785, 1081], [1, 1]], "hecke_ring_generator_nbound": 13, "inner_twist_count": 2, "level_primes": [2, 3, 7], "conrey_indexes": [1549, 2125], "field_disc": -3, "field_disc_factorization": [[-1, 1], [3, 1]], "field_poly": [1, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.014", "prec": 17}, {"__RealLiteral__": 0, "data": "2.022", "prec": 17}, {"__RealLiteral__": 0, "data": "0.169", "prec": 17}, {"__RealLiteral__": 0, "data": "12.542", "prec": 20}, {"__RealLiteral__": 0, "data": "1.144", "prec": 17}, {"__RealLiteral__": 0, "data": "117.323", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "1.2.3.c3", "trace_display": [-2, 0, 0, 0], "traces": [0, 2, -2, 0, 2, 0, 0, 0, -2, 0, 0, -3, 0, -2, 0, 0, 2, -3, 0, 1, 0, 0, 3, -6, 0, 5, 2, 0, 0, 6, 0, -8, -2, 0, 3, 0, 0, 4, -1, 0, 0, 9, 0, 1, -3, 0, 6, 12, 0, 0, -5, 0, -2, 12, 0, 0, 0, 0, -6, -6, 0, 16, 8, 0, 2, 0, 0, 10, -3, 0, 0, 24, 0, -11, -4, 0, 1, 0, 0, -8, 0, 0, -9, 12, 0, 0, -1, 0, 3, 6, 0, 0, -6, 0, -12, 0, 0, -5, 0, 0, 5, 0, 0, -14, 2, 0, -12, 3, 0, 16, 0, 0, 0, 6, 0, 0, 6, 0, 6, 0, 0, 2, -16, 0, -8, 0, 0, 4, -2, 0, 0, 0, 0, 0, -10, 0, 3, -3, 0, 19, 0, 0, -24, -6, 0, 0, 11, 0, 4, -6, 0, 10, -1, 0, 0, 0, 0, -8, 8, 0, 0, 0, 0, 4, 9, 0, -12, -12, 0, 9, 0, 0, 1, 12, 0, 0, -3, 0, -6, 12, 0, 28, 0, 0, 6, 0, 0, 18, 12, 0, 0, 36, 0, 10, 5, 0, 0, 24, 0, 10, -5, 0, 0, 0, 0, 0, 14, 0, -2, 3, 0, -20, 12, 0, -3, 0, 0, 0, -16, 0, 0, 12, 0, -26, 0, 0, -6, 21, 0, -14, 0, 0, -6, 3, 0, 0, -6, 0, 0, 6, 0, 7, -2, 0, 16, 0, 0, 2, 8, 0, 0, -42, 0, 36, -4, 0, 2, -21, 0, 0, 0, 0, 0, 18, 0, 0, 0, 0, 10, -24, 0, -20, -3, 0, 3, 15, 0, 10, -19, 0, 0, 6, 0, -8, 24, 0, 6, 0, 0, 8, 0, 0, -11, 30, 0, 0, -4, 0, 6, 24, 0, 0, -10, 0, 1, 0, 0, -14, 0, 0, 0, 36, 0, 58, 8, 0, -8, 36, 0, -36, 0, 0, 0, -6, 0, 10, -4, 0, -9, 0, 0, -8, 12, 0, 12, 0, 0, 1, -9, 0, 0, 12, 0, 0, -1, 0, -12, -66, 0, 16, 0, 0, 3, -21, 0, 0, 6, 0, -12, -18, 0, 18, -28, 0, 0, 0, 0, 28, -6, 0, 0, 0, 0, 34, -18, 0, -12, -24, 0, 46, 0, 0, -36, 0, 0, 0, -10, 0, -5, 18, 0, -18, 0, 0, -24, 0, 0, -20, -10, 0, 5, -27, 0, 8, 0, 0, 0, 12, 0, 34, 0, 0, -14, 0, 0, 0, 2, 0, -3, -12, 0, -20, 20, 0, -12, -30, 0, 0, 3, 0, 0, -30, 0, -14, 0, 0, 16, -12, 0, 16, 0, 0, -12, -6, 0, 0, 26, 0, 0, -18, 0, 27, 6, 0, -21, 0, 0, 34, 14, 0, 0, -30, 0, -20, 6, 0, -3, -15, 0, 0, 0, 0, 6, -6, 0, -5, 0, 0, -6, -42, 0, 8, -7, 0, 2, 0, 0, -26, -16, 0, 0, -15, 0, 18, -2, 0, -8, 0, 0, 13, 0, 0, 42, 0, 0, 0, -36, 0, 4, 0, 0, 0, -2, 0, 21, 0, 0, -18, 0, 0, 0, -3, 0, -20, 0, 0, -18, 12, 0, -13, 0, 0, 0, 18, 0, 0, -10, 0, 24, 0, 0, 4, 20, 0, 3, 0, 0, 1, -3, 0, -15, 12, 0, 0, -10, 0, 19, -30, 0, -4, 0, 0, -6, 78, 0, 0, 8, 0, -24, -90, 0, -74, -6, 0, 0, -60, 0, -11, -8, 0, 0, 0, 0, -72, 11, 0, -30, -9, 0, -4, 0, 0, 4, 6, 0, 0, -6, 0, -24, -24, 0, 37, 0, 0, 10, 0, 0, 28, -1, 0, 0, -12, 0, 16, 14, 0, 0, 27, 0, -35, 0, 0, -36, 0, 0, -25, -58, 0, -8, -24, 0, -80, 8, 0, -36, 0, 0, 0, 36, 0, 0, -3, 0, -23, 0, 0, 6, 18, 0, 9, -10, 0, 4, -6, 0, 0, 9, 0, 0, -36, 0, -8, 8, 0, -12, 0, 0, 36, -12, 0, 0, -24, 0, 22, -1, 0, 9, -72, 0, 0, 0, 0, -12, -9, 0, 0, 0, 0, 1, -48, 0, 16, 12, 0, 66, 0, 0, -54, -16, 0, 0, -60, 0, -4, -3, 0, 21, 0, 0, -8, 0, 0, -6, 24, 0, 0, 12, 0, 18, -36, 0, 0, -18, 0, 28, 60, 0, -26, 0, 0, 0, 3, 0, -14, -28, 0, 6, -15, 0, -47, 0, 0, 0, 6, 0, 0, -34, 0, 18, 0, 0, -8, 12, 0, 24, 0, 0, 4, -46, 0, 0, 42, 0, 0, 36, 0, 0, 6, 0, -2, 0, 0, 10, 18, 0, -20, 5, 0, -18, -9, 0, -36, 18, 0, 0, 0, 0, -8, 24, 0, 0, 0, 0, -16, 20, 0, 10, -12, 0, -18, -5, 0, 27, 66, 0, 0, -8, 0, 0, 33, 0, -14, 0, 0, -12, 0, 0, 2, -34, 0, 0, 36, 0, -32, 14, 0, 0, 24, 0, 10, 0, 0, -2, 0, 0, 0, 3, 0, 12, 12, 0, -7, 20, 0, -20, 0, 0, 0, 12, 0, 30, -48, 0, -26, 0, 0, -3, -42, 0, -35, 0, 0, 30, 24, 0, 0, 14, 0, 0, 12, 0, -10, -16, 0, 12, 0, 0, -8, -16, 0, 0, 84, 0, -38, 12, 0, 6, 0, 0, 0, 0, 0, -26, 6, 0, 0, 0, 0, 18, -24, 0, 36, -27, 0, -6, 0, 0, 31, 21, 0, 0, 48, 0, -72, -34, 0, -14, 0, 0, -38, 0, 0, 30, -24, 0, -20, 20, 0, -6, 12, 0, 0, 3, 0, 15, 0, 0, 28, 0, 0, 0, 120, 0, -108, -6, 0, 6, -6, 0, 44, 5, 0, 0, -18, 0, 0, 6, 0, 42, 0, 0, -30, -8, 0, 7, 0, 0, 22, -2, 0, 0, -36, 0, 0, 26, 0, 16, 102, 0, 18, 0, 0, 15, 0, 0, 0, -18, 0, 2, 6, 0, 16, 8, 0, 0, 0, 0, 28, -13, 0, 0, 0, 0, 9, -42, 0, 0, 24, 0, 4, 0, 0, 36, 0, 0, 0, -4, 0, 0, -3, 0, 40, 0, 0, 2, -45, 0, 8, -21, 0, 0, 36, 0, -11, 18, 0, 0, -24, 0, 76, 0, 0, 3, 0, 0, 0, 20, 0, 0, 30, 0, 1, 18, 0, -12, 0, 0, 0, 13, 0, 0, 54, 0, -56, 0, 0, -18, 30, 0, 16, 0, 0, 10, 48, 0, 10, -24, 0, 0, -48, 0, -36, -4, 0, -20, 0, 0, 76, -3, 0, 0, -9, 0, 22, -1, 0, 3, 27, 0, 0, 15, 0, -12, -108, 0, 0, 0, 0, 10, 0, 0, 0, -19, 0, 30, 0, 0, 16, 4, 0, 0, -3, 0, -56, 6, 0, -78, 0, 0, -29, 0, 0, -8, 84, 0, 0, 24, 0, 90, -15, 0, 0, 74, 0, 6, 0, 0, -16, 0, 0, 60, 60, 0, 1, 11, 0, 8, 12, 0, 8, 0, 0, 0, -15, 0, 0, 72, 0, -11, 0, 0, -59, 30, 0, 9, 30, 0, 9, 4, 0, 0, -72, 0, 0, -4, 0, -6, 33, 0, 108, 0, 0, 6, -6, 0, 0, 24, 0, 24, -96, 0, 94, -37, 0, 0, 0, 0, -36, -10, 0, 0, 0, 0, -8, -28, 0, 1, -9, 0, 72, 0, 0, 12, 6, 0, 0, -16, 0, -14, 60, 0, 58, 0, 0, -27, 0, 0, -56, 35, 0, 0, -33, 0, 18, 36, 0, 0, -6, 0, -35, 25, 0, 58, 0, 0, 0, 8, 0, 24, -42, 0, 20, 80, 0, -8, 0, 0, 0, 36, 0, 0, -36, 0, 5, 0, 0, -36, -66, 0, 64, 0, 0, 3, -27, 0, 0, 23, 0, 0, 27, 0, 34, -6, 0, -18, 0, 0, 67, -9, 0, 10, 30, 0, -62, -4, 0, 6, -72, 0, 0, 0, 0, -9, 0, 0, 0, 0, 0, 36, -48, 0, -110, 8, 0, -8, 120, 0, 136, 12, 0, 0, -78, 0, -4, -36, 0, 12, 0, 0, 56, 0, 0, 24, 12, 0, 0, -22, 0, 1, 12, 0, 0, -9, 0, 72, 0, 0, 18, 0, 0, 0, 21, 0, 36, 12, 0, 9, 66, 0, 21, 0, 0, 0, 48, 0, 0, -1, 0, 48, 0, 0, 34, -16, 0, -12, 0, 0, -22, -66, 0, 0, 6, 0, 0, 54, 0, 16, -6, 0, 40, 0, 0, 60, -48, 0, 0, 4, 0, 3, -27, 0, 36, -21, 0, 0, 0, 0, -64, 8, 0, 0, 0, 0, -38, 6, 0, -24, 51, 0, 22, 0, 0, -12, 12, 0, 0, -18, 0, 36, 12, 0, 0, 0, 0, 18, 0, 0, -68, -28, 0, -60, -48, 0, 52, 26, 0, 0, -48, 0, 52, 0, 0, -3, 0, 0, 0, 14, 0, 28, 12, 0, 22, -6, 0, 15, -15, 0, 0, 47, 0, 0, 18, 0, 16, 0, 0, -6, 42, 0, 70, 0, 0, 34, -18, 0, 0, -18, 0, 0, -57, 0, -4, 8, 0, -12, 0, 0, -9, -24, 0, 0, 84, 0, -36, -4, 0, 46, -36, 0, 0, 0, 0, -42, -45, 0, 40, 0, 0, -36, 57, 0, -20, 0, 0, -6, 0, 0, -72, 2, 0, 0, -30, 0, -8, -10, 0, -18, 0, 0, -38, 20, 0, -5, -33, 0, 0, 18, 0, 9, 96, 0, 0, 36, 0, -18, 0, 0, -56, 0, 0, 0, -90, 0, -8, 8, 0, -24, 24, 0, 136, 0, 0, 0, 108, 0, 0, 16, 0, -20, 0, 0, 8, -10, 0, 12, 0, 0, 22, 18, 0, 5, 27, 0, 0, -27, 0, -66, -24, 0, -26, 0, 0, 8, -42, 0, 0, 0, 0, -33, -39, 0, 16, 14, 0, 0, 0, 0, 28, 12, 0, 0, 0, 0, -72, -2, 0, 34, 0, 0, 36, 0, 0, -36, -48, 0, 0, 32, 0, -14, -15, 0, -4, 0, 0, -24, 0, 0, 43, -10, 0, 0, 30, 0, -32, 2, 0, 0, -15, 0, -8, 0, 0, -3, 0, 0, 25, -12, 0, -12, -66, 0, -40, 7, 0, -20, 0, 0, 0, 20, 0, 0, -6, 0, 28, 0, 0, -12, 36, 0, -110, -30, 0, 48, 0, 0, 0, 26, 0, 0, 24, 0, -18, 3, 0, 42, 0, 0, 0, 35, 0, 0, 75, 0, -41, -30, 0, -24, 12, 0, 0, 0, 0, -14, 60, 0, 0, 0, 0, -12, 24, 0, 28, 10, 0, 16, 0, 0, -68, -12, 0, 0, -42, 0, -35, 8, 0, 16, 0, 0, -50, 0, 0, -84, 18, 0, 0, 38, 0, -12, 48, 0, 0, -6, 0, 0, 60, 0, -23, 0, 0, 0, -6, 0, -20, 26, 0, -6, 36, 0, 10, 0, 0, 0, 12, 0, 0, -18, 0, 24, 0, 0, 25, -36, 0, 27, 0, 0, 38, 6, 0, 0, 54, 0, 0, -31, 0, -21, 24, 0, -18, 0, 0, -48, 36, 0, -110, 72, 0, 34, 24, 0, -116, 14, 0, 0, 0, 0, -36, 38, 0, 0, 0, 0, -10, -30, 0, 24, -30, 0, 42, 20, 0, -20, 48, 0, 0, 6, 0, -12, -54, 0, -26, 0, 0, -3, 0, 0, 49, -15, 0, 0, -18, 0, -26, -28, 0, 0, 48, 0, 28, 0, 0, -120, 0, 0, 0, 108, 0, 6, -126, 0, -64, -6, 0, 6, 0, 0, 0, -44, 0, -5, -24, 0, -18, 0, 0, 18, 39, 0, 72, 0, 0, -6, -69, 0, 0, -42, 0, 0, 0, 0, -36, 30, 0, 8, 0, 0, 54, -7, 0, 0, 51, 0, 64, -22, 0, 2, 24, 0, 0, 0, 0, 36, 30, 0, 0, 0, 0, -26, -132, 0, 100, -16, 0, -102, 0, 0, -28, -18, 0, 0, 96, 0, 20, -15, 0, 0, 0, 0, -72, 0, 0, 18, 54, 0, -20, -2, 0, -6, -36, 0, 0, -16, 0, -8, 0, 0, -68, 0, 0, 0, -42, 0, 7, -28, 0, 13, -18, 0, 16, 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, 63, 8, 1, 3, 0]], "char_orbit_index": 5, "prim_orbit_index": 8, "minimal_twist": "18.2.c.a", "char_is_minimal": false, "conrey_index": 1549, "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, 0], [0, 0], [1, 0], [0, 0], [0, 0], [0, 0], [-1, 0], [0, 0], [0, 0], [0, -3], [0, 0], [0, -2], [0, 0], [0, 0], [1, 0], [-3, 3], [0, 0], [0, 1], [0, 0], [0, 0], [0, 3], [-6, 6], [0, 0], [0, 5], [0, 2], [0, 0], [0, 0], [6, -6], [0, 0], [-4, 0], [-1, 0], [0, 0], [3, -3], [0, 0], [0, 0], [0, 4], [0, -1], [0, 0], [0, 0], [0, 9], [0, 0], [1, -1], [0, -3], [0, 0], [6, -6], [6, 0], [0, 0], [0, 0], [0, -5], [0, 0], [0, -2], [12, -12], [0, 0], [0, 0], [0, 0], [0, 0], [-6, 6], [-3, 0], [0, 0], [8, 0], [4, 0], [0, 0], [1, 0], [0, 0], [0, 0], [5, 0], [-3, 3], [0, 0], [0, 0], [12, 0], [0, 0], [-11, 11], [0, -4], [0, 0], [0, 1], [0, 0], [0, 0], [-4, 0], [0, 0], [0, 0], [0, -9], [12, -12], [0, 0], [0, 0], [-1, 1], [0, 0], [0, 3], [0, 6], [0, 0], [0, 0], [-6, 6], [0, 0], [-6, 0], [0, 0], [0, 0], [-5, 5], [0, 0], [0, 0], [0, 5]]}