# Stored data for newform 1350.2.e.c, downloaded from the LMFDB on 23 April 2024.
{"label": "1350.2.e.c", "space_label": "1350.2.e", "level": 1350, "weight": 2, "hecke_orbit": 3, "hecke_orbit_code": 9007474166203718, "dim": 2, "is_polredabs": true, "nf_label": "2.0.3.1", "trace_hash": 963845508207795616, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[7, [4, -2, 1]], [11, [9, 3, 1]], [17, [3, 1]]], "qexp_display": "q+(-1+\\zeta_{6})q^{2}-\\zeta_{6}q^{4}+(2-2\\zeta_{6})q^{7}+\\cdots", "char_order": 3, "char_parity": 1, "char_degree": 2, "char_conductor": 9, "char_orbit_label": "e", "char_is_real": false, "Nk2": 5400, "analytic_conductor": 10.779804272872852, "hecke_ring_index": 1, "level_radical": 30, "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": "0.017", "prec": 17}, "analytic_rank_proved": true, "char_values": [1350, 3, [1001, 1027], [2, 3]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 2, "level_primes": [2, 3, 5], "conrey_indexes": [451, 901], "field_disc": -3, "field_disc_factorization": [[-1, 1], [3, 1]], "field_poly": [1, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.007", "prec": 17}, {"__RealLiteral__": 0, "data": "1.987", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "11.664", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "103.286", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "1.2.3.c3", "trace_display": [-1, 0, 0, 2], "traces": [0, 2, -1, 0, -1, 0, 0, 2, 2, 0, 0, -3, 0, 2, 2, 0, -1, -6, 0, -2, 0, 0, -3, 6, 0, 0, -4, 0, -4, 6, 0, 4, -1, 0, 3, 0, 0, 8, 1, 0, 0, 9, 0, -1, 6, 0, -12, 6, 0, 3, 0, 0, 2, 24, 0, 0, 2, 0, 6, 3, 0, -8, -8, 0, 2, 0, 0, 5, 3, 0, 0, 24, 0, -22, -4, 0, 1, 6, 0, 4, 0, 0, -18, -12, 0, 0, -1, 0, -3, -12, 0, 8, 6, 0, 6, 0, 0, 5, -6, 0, 0, 0, 0, 14, 2, 0, -12, 6, 0, -32, 0, 0, 2, -6, 0, 0, -12, 0, -6, -6, 0, 2, -8, 0, 4, 0, 0, -4, -1, 0, 0, 0, 0, -2, -10, 0, -6, 3, 0, 19, 0, 0, -12, -12, 0, 0, 11, 0, -4, -6, 0, 10, -2, 0, -12, 0, 0, -4, 4, 0, 0, 24, 0, 8, 9, 0, -12, 12, 0, 9, 0, 0, 2, 6, 0, 0, -3, 0, 6, -24, 0, 28, -4, 0, 6, 0, 0, 9, -12, 0, 0, -18, 0, 5, 5, 0, 3, -24, 0, -20, 0, 0, 0, -12, 0, 0, -28, 0, -4, 3, 0, -20, -12, 0, -3, 0, 0, 16, 16, 0, 0, -6, 0, 26, -4, 0, 12, -21, 0, -14, 0, 0, 6, 6, 0, 0, 3, 0, -6, 6, 0, 7, -4, 0, 16, 0, 0, -2, 4, 0, 0, -42, 0, -36, 2, 0, -1, 21, 0, 8, 0, 0, 0, -18, 0, 0, -2, 0, 5, 48, 0, 40, 3, 0, 3, 0, 0, -10, -38, 0, 0, 6, 0, -4, -12, 0, 6, 36, 0, -16, 0, 0, 11, -30, 0, 0, 8, 0, 12, -12, 0, 2, 10, 0, 1, 0, 0, 14, 6, 0, 0, -18, 0, 29, 8, 0, -8, 18, 0, 18, 0, 0, -12, 6, 0, 0, -4, 0, 9, -12, 0, 4, 24, 0, -24, 0, 0, -1, 9, 0, 0, -24, 0, 40, -1, 0, 6, -33, 0, 16, 0, 0, 6, 21, 0, 0, 6, 0, 12, 36, 0, -36, -14, 0, -4, 0, 0, -28, -12, 0, 0, 24, 0, -34, 9, 0, 6, 24, 0, 46, 0, 0, -18, 0, 0, 0, -10, 0, -10, 18, 0, -18, 3, 0, 12, 0, 0, -40, 10, 0, 0, -27, 0, -8, 0, 0, 24, -12, 0, -17, 0, 0, 14, 12, 0, 0, 2, 0, 3, -12, 0, -20, 40, 0, 24, 0, 0, 16, -3, 0, 0, 60, 0, 14, -8, 0, 16, -6, 0, -8, 0, 0, 12, -3, 0, 0, 26, 0, 2, -18, 0, -54, -6, 0, -21, 0, 0, 17, 28, 0, 0, -30, 0, 20, 6, 0, -3, -30, 0, 20, 0, 0, 3, -3, 0, 0, 12, 0, -12, -42, 0, 8, 7, 0, 2, 0, 0, -52, -8, 0, 0, -15, 0, -18, 4, 0, -8, 24, 0, 13, 0, 0, 21, 0, 0, 0, 18, 0, 2, 0, 0, -22, 2, 0, -42, 0, 0, 18, 8, 0, 0, 6, 0, -40, 0, 0, -18, -12, 0, -13, 0, 0, 4, -18, 0, 0, 5, 0, -24, -18, 0, -8, -20, 0, 3, 0, 0, -1, -6, 0, 0, -6, 0, -8, -10, 0, 19, -60, 0, -4, 0, 0, 6, 39, 0, 0, 8, 0, 24, 45, 0, 37, 6, 0, -18, 0, 0, -22, 8, 0, 0, 24, 0, -36, -22, 0, 60, 9, 0, -4, 0, 0, -4, 12, 0, 0, -6, 0, -12, 12, 0, 37, -4, 0, -20, 0, 0, -28, 1, 0, 0, 24, 0, 32, -7, 0, 6, -27, 0, -35, 0, 0, 36, -12, 0, 0, 29, 0, -4, -24, 0, -80, 4, 0, 18, 0, 0, -6, -36, 0, 0, -3, 0, 23, -12, 0, -3, 36, 0, -18, 0, 0, -4, 6, 0, 0, -18, 0, 24, -36, 0, 4, 4, 0, -12, 0, 0, 72, 12, 0, 0, -24, 0, -22, 2, 0, -18, -36, 0, -10, 0, 0, 12, -18, 0, 0, -20, 0, -1, 24, 0, -8, -12, 0, 66, 0, 0, -27, 16, 0, 0, -60, 0, -8, -3, 0, 21, 0, 0, 4, 0, 0, -12, -24, 0, 0, 12, 0, -18, 72, 0, 56, 18, 0, -14, 0, 0, 26, 8, 0, 0, 3, 0, 14, -28, 0, 6, -30, 0, 94, 0, 0, 24, -6, 0, 0, 68, 0, -18, 6, 0, -8, 6, 0, -12, 0, 0, -4, -23, 0, 0, 42, 0, -32, 36, 0, 0, -6, 0, -2, 0, 0, 5, 36, 0, 0, 5, 0, 18, -9, 0, -36, 36, 0, -6, 0, 0, -4, 12, 0, 0, -24, 0, -32, 20, 0, 10, 12, 0, -18, 0, 0, 54, 33, 0, 0, -8, 0, 0, -66, 0, -14, -12, 0, -12, 0, 0, 1, 34, 0, 0, -18, 0, -16, 14, 0, -6, -24, 0, -20, 0, 0, 2, -9, 0, 0, -6, 0, 24, 12, 0, -7, -20, 0, -20, 0, 0, 8, -12, 0, 0, 24, 0, 26, -32, 0, 6, 42, 0, -35, 0, 0, -30, 48, 0, 0, -7, 0, -8, 12, 0, -10, -32, 0, 12, 0, 0, 8, -8, 0, 0, 84, 0, 38, -6, 0, -3, 0, 0, -4, 0, 0, -52, -6, 0, 0, 2, 0, 9, 48, 0, -72, 27, 0, -6, 0, 0, -31, 42, 0, 0, 48, 0, -36, 17, 0, -14, 0, 0, 76, 0, 0, -30, 24, 0, 0, -40, 0, -12, -6, 0, -3, -3, 0, 15, 0, 0, -28, -10, 0, 0, -60, 0, -54, -6, 0, 6, -3, 0, -22, 0, 0, -6, 18, 0, 0, 6, 0, -42, -6, 0, 15, -16, 0, -14, 0, 0, -22, 2, 0, 0, 72, 0, 76, 26, 0, -8, 51, 0, 18, 0, 0, 30, 0, 0, 0, -18, 0, -2, -12, 0, -32, 4, 0, 24, 0, 0, -28, -26, 0, 0, -12, 0, -9, 21, 0, 0, -24, 0, 4, 0, 0, 18, 0, 0, 0, -4, 0, 0, -3, 0, 40, -22, 0, -1, 0, 0, 16, 21, 0, 0, 36, 0, 11, -36, 0, -16, 24, 0, -38, 0, 0, -3, -24, 0, 0, 20, 0, 0, 30, 0, 1, 36, 0, 24, 0, 0, -20, -13, 0, 0, -108, 0, 56, -2, 0, -18, 15, 0, -8, 0, 0, -10, 24, 0, 0, -24, 0, 9, -48, 0, 72, 4, 0, -20, 0, 0, 38, -6, 0, 0, -9, 0, -22, -1, 0, 3, 54, 0, -16, 0, 0, -6, -54, 0, 0, 16, 0, 20, 0, 0, 0, 19, 0, 30, 0, 0, 32, 2, 0, 0, -3, 0, 56, -12, 0, -78, -18, 0, -29, 0, 0, -4, -84, 0, 0, -12, 0, 45, -15, 0, 8, -74, 0, -12, 0, 0, 16, -18, 0, 0, -120, 0, 2, 11, 0, 8, -12, 0, 8, 0, 0, -48, 15, 0, 0, -36, 0, 11, 48, 0, 118, -30, 0, 9, 0, 0, -9, 8, 0, 0, 36, 0, -18, -4, 0, -6, 66, 0, 108, 0, 0, -6, -3, 0, 0, 24, 0, -24, 48, 0, -47, 37, 0, 2, 0, 0, -72, 10, 0, 0, -12, 0, -4, 56, 0, -2, 9, 0, 72, 0, 0, -12, 12, 0, 0, -16, 0, -7, -30, 0, 58, -12, 0, 54, 0, 0, 56, -35, 0, 0, 66, 0, 36, -18, 0, -12, 6, 0, -35, 0, 0, -58, -24, 0, 0, -4, 0, 12, -42, 0, 20, 40, 0, 4, 0, 0, 28, -36, 0, 0, -36, 0, -5, -6, 0, 18, -132, 0, -128, 0, 0, -3, 27, 0, 0, -46, 0, 24, 27, 0, -17, -3, 0, -18, 0, 0, 134, 9, 0, 0, 30, 0, 62, 8, 0, -12, -36, 0, -18, 0, 0, 9, 0, 0, 0, -12, 0, -36, 24, 0, 55, -8, 0, -8, 0, 0, 68, -12, 0, 0, -78, 0, -8, -36, 0, 12, 36, 0, -28, 0, 0, 48, -12, 0, 0, -22, 0, -1, -24, 0, 20, 9, 0, -36, 0, 0, -18, 20, 0, 0, 21, 0, -36, 12, 0, 9, 132, 0, -42, 0, 0, -20, -48, 0, 0, 2, 0, -48, -24, 0, 34, -8, 0, 6, 0, 0, 22, -33, 0, 0, 6, 0, -20, 54, 0, -32, 6, 0, 40, 0, 0, 30, -96, 0, 0, 4, 0, -3, -27, 0, 36, -42, 0, 0, 0, 0, -32, 4, 0, 0, 36, 0, -76, 6, 0, -24, -51, 0, 22, 0, 0, -24, 6, 0, 0, -18, 0, -36, -24, 0, 0, -28, 0, 18, 0, 0, -34, 28, 0, 0, 24, 0, 26, 26, 0, -4, 48, 0, -104, 0, 0, 3, -6, 0, 0, -28, 0, 56, 12, 0, 22, 6, 0, 15, 0, 0, -80, -47, 0, 0, -9, 0, -16, -48, 0, 12, -42, 0, 70, 0, 0, -34, -36, 0, 0, 9, 0, 6, -57, 0, -4, 16, 0, -12, 0, 0, 9, -12, 0, 0, 84, 0, 36, 2, 0, -23, 36, 0, -12, 0, 0, -84, 45, 0, 0, -32, 0, -18, -114, 0, 40, 0, 0, -6, 0, 0, 72, 4, 0, 0, -30, 0, -4, 5, 0, -18, -24, 0, 76, 0, 0, 5, 33, 0, 0, -36, 0, 18, -48, 0, -52, -36, 0, -18, 0, 0, 56, 3, 0, 0, 45, 0, -4, 8, 0, -24, 12, 0, -68, 0, 0, 12, -108, 0, 0, 16, 0, 20, 42, 0, -4, -20, 0, -24, 0, 0, -22, -18, 0, 0, -54, 0, -56, -27, 0, 33, -12, 0, -26, 0, 0, 16, 42, 0, 0, 0, 0, 33, 78, 0, -32, 7, 0, -12, 0, 0, -28, 24, 0, 0, 6, 0, 72, 1, 0, -17, 0, 0, 36, 0, 0, -18, 48, 0, 0, 32, 0, -28, -15, 0, -4, -6, 0, 12, 0, 0, 86, 10, 0, 0, 30, 0, 32, -4, 0, 18, 15, 0, 4, 0, 0, 3, 24, 0, 0, -12, 0, 12, -66, 0, -40, 14, 0, 40, 0, 0, -14, -20, 0, 0, 12, 0, -28, -4, 0, -12, 18, 0, 55, 0, 0, -48, 0, 0, 0, 26, 0, 16, 24, 0, 36, -3, 0, 42, 0, 0, 0, 70, 0, 0, 75, 0, 41, -30, 0, -24, 24, 0, -8, 0, 0, -7, 30, 0, 0, 16, 0, -24, 24, 0, 28, -10, 0, 16, 0, 0, -136, -6, 0, 0, -42, 0, 35, -16, 0, 16, -42, 0, -50, 0, 0, -42, -18, 0, 0, -19, 0, -6, 48, 0, -36, 6, 0, 0, 0, 0, 23, -4, 0, 0, 12, 0, -40, 26, 0, -6, -36, 0, 10, 0, 0, -4, -12, 0, 0, 9, 0, -24, 84, 0, -50, 36, 0, 27, 0, 0, -38, 12, 0, 0, -27, 0, 12, -31, 0, -21, 48, 0, -18, 0, 0, 48, 18, 0, 0, 72, 0, -34, -12, 0, 58, -14, 0, 0, 0, 0, -72, -38, 0, 0, 36, 0, -5, 60, 0, -48, 30, 0, 42, 0, 0, 20, 96, 0, 0, 6, 0, -6, 27, 0, -26, 6, 0, 6, 0, 0, -49, 15, 0, 0, 36, 0, -52, 14, 0, -10, -48, 0, 28, 0, 0, 120, 48, 0, 0, -54, 0, 3, -126, 0, -64, -3, 0, -3, 0, 0, 40, 44, 0, 0, -24, 0, 18, -6, 0, -9, 78, 0, -144, 0, 0, 6, 69, 0, 0, 84, 0, 12, 0, 0, 18, 15, 0, 8, 0, 0, 108, 7, 0, 0, 51, 0, -64, 44, 0, -4, 12, 0, 20, 0, 0, -36, 60, 0, 0, -38, 0, 26, 66, 0, -50, 16, 0, -102, 0, 0, -14, 18, 0, 0, 96, 0, 40, -15, 0, 0, -12, 0, 36, 0, 0, 36, -54, 0, 0, -2, 0, 6, 72, 0, -16, 16, 0, 4, 0, 0, 68, -48, 0, 0, -42, 0, -7, -28, 0, 13, -36, 0, -32, 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, 9, 3, 1, 3, 0]], "char_orbit_index": 5, "prim_orbit_index": 3, "minimal_twist": "18.2.c.a", "char_is_minimal": false, "conrey_index": 451, "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], [0, 0], [0, -1], [0, 0], [0, 0], [2, -2], [1, 0], [0, 0], [0, 0], [-3, 3], [0, 0], [0, 2], [0, 2], [0, 0], [-1, 1], [-3, 0], [0, 0], [-1, 0], [0, 0], [0, 0], [0, -3], [0, 6], [0, 0], [0, 0], [-2, 0], [0, 0], [-2, 0], [6, -6], [0, 0], [0, 4], [0, -1], [0, 0], [3, -3], [0, 0], [0, 0], [4, 0], [1, -1], [0, 0], [0, 0], [0, 9], [0, 0], [-1, 1], [3, 0], [0, 0], [-6, 0], [6, -6], [0, 0], [0, 3], [0, 0], [0, 0], [2, -2], [12, 0], [0, 0], [0, 0], [2, -2], [0, 0], [0, 6], [0, 3], [0, 0], [-8, 8], [-4, 0], [0, 0], [1, 0], [0, 0], [0, 0], [0, 5], [0, 3], [0, 0], [0, 0], [12, 0], [0, 0], [-11, 0], [-4, 4], [0, 0], [0, 1], [0, 6], [0, 0], [4, -4], [0, 0], [0, 0], [-9, 0], [-12, 12], [0, 0], [0, 0], [0, -1], [0, 0], [-3, 3], [-6, 0], [0, 0], [4, 0], [6, -6], [0, 0], [0, 6], [0, 0], [0, 0], [5, -5], [-3, 0], [0, 0], [0, 0]]}