# Stored data for newform 1650.2.c.l, downloaded from the LMFDB on 18 April 2024.
{"label": "1650.2.c.l", "space_label": "1650.2.c", "level": 1650, "weight": 2, "hecke_orbit": 12, "hecke_orbit_code": 49539733373585010, "dim": 2, "is_polredabs": true, "nf_label": "2.0.4.1", "trace_hash": 510160118399185584, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[7, [0, 1]], [13, [4, 0, 1]], [17, [4, 0, 1]], [19, [8, 1]]], "qexp_display": "q+iq^{2}-iq^{3}-q^{4}+q^{6}-iq^{8}-q^{9}+\\cdots", "char_order": 2, "char_parity": 1, "char_degree": 1, "char_conductor": 5, "char_orbit_label": "c", "char_is_real": true, "Nk2": 6600, "analytic_conductor": 13.175316333511264, "hecke_ring_index": 1, "level_radical": 330, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 4, "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": "0.514", "prec": 17}, "analytic_rank_proved": true, "char_values": [1650, 2, [551, 727, 1201], [2, 1, 2]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 2, "level_primes": [2, 3, 5, 11], "conrey_indexes": [199], "field_disc": -4, "field_disc_factorization": [[-1, 1], [2, 2]], "field_poly": [1, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.016", "prec": 17}, {"__RealLiteral__": 0, "data": "1.955", "prec": 17}, {"__RealLiteral__": 0, "data": "0.296", "prec": 17}, {"__RealLiteral__": 0, "data": "15.222", "prec": 20}, {"__RealLiteral__": 0, "data": "3.383", "prec": 17}, {"__RealLiteral__": 0, "data": "147.439", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "1.2.3.c2", "trace_display": [0, 0, 0, 0], "traces": [0, 2, 0, 0, -2, 0, 2, 0, 0, -2, 0, 2, 0, 0, 0, 0, 2, 0, 0, -16, 0, 0, 0, 0, -2, 0, -4, 0, 0, -4, 0, 16, 0, 0, -4, 0, 2, 0, 0, 4, 0, 12, 0, 0, -2, 0, -8, 0, 0, 14, 0, 4, 0, 0, -2, 0, 0, 0, 0, -8, 0, -12, 0, 0, -2, 0, 2, 0, 0, 8, 0, -24, 0, 0, -4, 0, 16, 0, 0, 0, 0, 2, 0, 0, 0, 0, -16, 0, 0, 12, 0, 0, 0, 0, -8, 0, 2, 0, 0, -2, 0, -12, 0, 0, 4, 0, -4, 0, 0, 12, 0, 4, 0, 0, -16, 0, 4, 0, 0, 0, 0, 2, 0, 0, -16, 0, 0, 0, 0, 16, 0, 24, 0, 0, -24, 0, 4, 0, 0, -32, 0, 8, 0, 0, -2, 0, -4, 0, 0, -20, 0, -16, 0, 0, 0, 0, -4, 0, 0, 4, 0, 0, 0, 0, -12, 0, -8, 0, 0, 18, 0, 16, 0, 0, -4, 0, 2, 0, 0, 24, 0, -4, 0, 0, 8, 0, 16, 0, 0, 0, 0, -24, 0, 0, -28, 0, -14, 0, 0, 48, 0, 24, 0, 0, -4, 0, -32, 0, 0, -16, 0, 0, 0, 0, 40, 0, 2, 0, 0, 4, 0, -8, 0, 0, 0, 0, -4, 0, 0, -28, 0, 0, 0, 0, 4, 0, 8, 0, 0, -32, 0, 36, 0, 0, 12, 0, 12, 0, 0, 8, 0, -40, 0, 0, -32, 0, 2, 0, 0, 0, 0, 4, 0, 0, -2, 0, 0, 0, 0, 44, 0, 0, 0, 0, 4, 0, -8, 0, 0, -16, 0, -20, 0, 0, 24, 0, -4, 0, 0, 26, 0, 28, 0, 0, 14, 0, 4, 0, 0, -16, 0, 0, 0, 0, -16, 0, 4, 0, 0, 32, 0, -40, 0, 0, -4, 0, 0, 0, 0, -4, 0, -40, 0, 0, -2, 0, -40, 0, 0, 0, 0, -24, 0, 0, 32, 0, 0, 0, 0, 4, 0, 16, 0, 0, 16, 0, -36, 0, 0, 60, 0, -4, 0, 0, -8, 0, -12, 0, 0, 64, 0, 90, 0, 0, 0, 0, -12, 0, 0, -12, 0, 0, 0, 0, -4, 0, 8, 0, 0, -72, 0, 32, 0, 0, -2, 0, 44, 0, 0, 44, 0, -16, 0, 0, 20, 0, 2, 0, 0, 0, 0, 36, 0, 0, 12, 0, 0, 0, 0, -52, 0, -4, 0, 0, 8, 0, -4, 0, 0, -8, 0, 76, 0, 0, 4, 0, -24, 0, 0, 4, 0, -48, 0, 0, 0, 0, -12, 0, 0, 32, 0, -14, 0, 0, -4, 0, 32, 0, 0, -20, 0, 12, 0, 0, 24, 0, 16, 0, 0, -4, 0, 36, 0, 0, -4, 0, 36, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, -48, 0, -8, 0, 0, -2, 0, 2, 0, 0, 40, 0, -24, 0, 0, 32, 0, 16, 0, 0, -8, 0, -32, 0, 0, 0, 0, -8, 0, 0, 44, 0, 0, 0, 0, 52, 0, -16, 0, 0, 36, 0, -76, 0, 0, -24, 0, 48, 0, 0, 14, 0, 8, 0, 0, 12, 0, 24, 0, 0, 14, 0, 52, 0, 0, -4, 0, 0, 0, 0, 12, 0, 32, 0, 0, -28, 0, 32, 0, 0, -32, 0, 4, 0, 0, -8, 0, 16, 0, 0, -28, 0, -80, 0, 0, 0, 0, 2, 0, 0, -44, 0, 0, 0, 0, 4, 0, 12, 0, 0, -128, 0, -20, 0, 0, -2, 0, 20, 0, 0, 72, 0, -44, 0, 0, 16, 0, -12, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 40, 0, -8, 0, 0, 4, 0, 12, 0, 0, -8, 0, 0, 0, 0, -12, 0, -4, 0, 0, 24, 0, 84, 0, 0, 0, 0, 32, 0, 0, -8, 0, 0, 0, 0, 12, 0, 12, 0, 0, -8, 0, 28, 0, 0, 8, 0, 4, 0, 0, -32, 0, -12, 0, 0, 20, 0, -18, 0, 0, 0, 0, -24, 0, 0, -16, 0, 0, 0, 0, -8, 0, 40, 0, 0, -40, 0, 4, 0, 0, -36, 0, -92, 0, 0, -2, 0, -52, 0, 0, -92, 0, 0, 0, 0, 0, 0, -24, 0, 0, 72, 0, 0, 0, 0, 4, 0, 2, 0, 0, -2, 0, -32, 0, 0, 32, 0, -8, 0, 0, -48, 0, -32, 0, 0, -16, 0, -4, 0, 0, 0, 0, -80, 0, 0, 8, 0, 0, 0, 0, 8, 0, 60, 0, 0, 24, 0, -24, 0, 0, -20, 0, -52, 0, 0, 16, 0, 28, 0, 0, -96, 0, -24, 0, 0, 14, 0, 24, 0, 0, -48, 0, 0, 0, 0, -4, 0, -48, 0, 0, -16, 0, -12, 0, 0, -24, 0, -32, 0, 0, -60, 0, -16, 0, 0, -4, 0, 4, 0, 0, 0, 0, 20, 0, 0, 32, 0, 0, 0, 0, 4, 0, 28, 0, 0, -32, 0, 16, 0, 0, 24, 0, -50, 0, 0, 0, 0, 8, 0, 0, -16, 0, -16, 0, 0, 0, 0, -40, 0, 0, -8, 0, 0, 0, 0, -2, 0, -4, 0, 0, 0, 0, -48, 0, 0, 64, 0, -4, 0, 0, -12, 0, 116, 0, 0, 8, 0, 56, 0, 0, 0, 0, 2, 0, 0, -20, 0, 0, 0, 0, -32, 0, -8, 0, 0, 4, 0, -16, 0, 0, 12, 0, -40, 0, 0, -76, 0, 28, 0, 0, -112, 0, 0, 0, 0, 0, 0, -16, 0, 0, -100, 0, -112, 0, 0, 72, 0, -4, 0, 0, -12, 0, 100, 0, 0, -8, 0, -16, 0, 0, -8, 0, 12, 0, 0, 4, 0, 32, 0, 0, 0, 0, 66, 0, 0, -36, 0, 0, 0, 0, -32, 0, 72, 0, 0, 16, 0, -12, 0, 0, 12, 0, -12, 0, 0, -12, 0, 8, 0, 0, -64, 0, 80, 0, 0, 0, 0, -8, 0, 0, -4, 0, 0, 0, 0, 40, 0, 0, 0, 0, 92, 0, -20, 0, 0, 18, 0, 32, 0, 0, -72, 0, 44, 0, 0, -2, 0, 16, 0, 0, 0, 0, 64, 0, 0, -8, 0, 0, 0, 0, -32, 0, 40, 0, 0, -4, 0, -48, 0, 0, 28, 0, -80, 0, 0, -32, 0, 2, 0, 0, 52, 0, -12, 0, 0, 0, 0, -24, 0, 0, 92, 0, 0, 0, 0, 24, 0, -44, 0, 0, -16, 0, -32, 0, 0, 0, 0, -4, 0, 0, -2, 0, 120, 0, 0, 16, 0, -4, 0, 0, 0, 0, -32, 0, 0, 8, 0, 0, 0, 0, 12, 0, -12, 0, 0, -92, 0, 16, 0, 0, 4, 0, 64, 0, 0, 20, 0, -8, 0, 0, 12, 0, -8, 0, 0, 0, 0, -24, 0, 0, -48, 0, 0, 0, 0, 4, 0, -24, 0, 0, 24, 0, 112, 0, 0, 36, 0, -26, 0, 0, 96, 0, -16, 0, 0, -28, 0, -4, 0, 0, 0, 0, -88, 0, 0, -24, 0, -14, 0, 0, -24, 0, -60, 0, 0, -4, 0, 52, 0, 0, -24, 0, 4, 0, 0, 48, 0, 16, 0, 0, 12, 0, 100, 0, 0, 0, 0, 24, 0, 0, 32, 0, 0, 0, 0, 32, 0, 16, 0, 0, -16, 0, 4, 0, 0, -4, 0, 76, 0, 0, 92, 0, -112, 0, 0, 84, 0, -32, 0, 0, 0, 0, -8, 0, 0, 40, 0, 0, 0, 0, 76, 0, 32, 0, 0, -16, 0, 4, 0, 0, 40, 0, -56, 0, 0, 0, 0, 0, 0, 0, -8, 0, 96, 0, 0, -28, 0, 4, 0, 0, 112, 0, 0, 0, 0, 40, 0, 40, 0, 0, 68, 0, 104, 0, 0, -88, 0, 2, 0, 0, 4, 0, -108, 0, 0, 40, 0, 60, 0, 0, 0, 0, -64, 0, 0, 4, 0, 0, 0, 0, 0, 0, 20, 0, 0, 24, 0, -8, 0, 0, -56, 0, 2, 0, 0, 16, 0, -32, 0, 0, -64, 0, 20, 0, 0, 0, 0, 12, 0, 0, 192, 0, 0, 0, 0, -76, 0, -4, 0, 0, 16, 0, -4, 0, 0, -16, 0, 8, 0, 0, 66, 0, 76, 0, 0, -28, 0, -16, 0, 0, 0, 0, -44, 0, 0, 36, 0, 0, 0, 0, 16, 0, 80, 0, 0, -24, 0, -60, 0, 0, 80, 0, -72, 0, 0, 4, 0, 32, 0, 0, 92, 0, -16, 0, 0, 0, 0, 8, 0, 0, 16, 0, -28, 0, 0, 12, 0, -64, 0, 0, -116, 0, -4, 0, 0, -32, 0, -64, 0, 0, -24, 0, 24, 0, 0, -90, 0, 36, 0, 0, 0, 0, -56, 0, 0, -80, 0, 0, 0, 0, -32, 0, -16, 0, 0, 12, 0, 28, 0, 0, -8, 0, 16, 0, 0, -24, 0, 12, 0, 0, -8, 0, 60, 0, 0, 0, 0, 16, 0, 0, -68, 0, 0, 0, 0, 8, 0, 4, 0, 0, 72, 0, 0, 0, 0, -8, 0, -40, 0, 0, 0, 0, 136, 0, 0, -68, 0, 72, 0, 0, 112, 0, -18, 0, 0, -32, 0, 0, 0, 0, -32, 0, 64, 0, 0, 16, 0, 2, 0, 0, -16, 0, -96, 0, 0, -44, 0, -68, 0, 0, 20, 0, 8, 0, 0, 0, 0, -44, 0, 0, 128, 0, 0, 0, 0, 16, 0, 4, 0, 0, 48, 0, -136, 0, 0, -64, 0, -20, 0, 0, -80, 0, 32, 0, 0, -2, 0, 24, 0, 0, 0, 0, -32, 0, 0, -60, 0, 0, 0, 0, 24, 0, -100, 0, 0, -36, 0, -4, 0, 0, 108, 0, -24, 0, 0, 44, 0, -12, 0, 0, -40, 0, 44, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 128, 0, 52, 0, 0, -20, 0, -16, 0, 0, 4, 0, 48, 0, 0, -56, 0, -64, 0, 0, 24, 0, -8, 0, 0, 0, 0, -16, 0, 0, 4, 0, -28, 0, 0, -68, 0, 92, 0, 0, -16, 0, 8, 0, 0, -16, 0, -10, 0, 0, -76, 0, -20, 0, 0, 8, 0, -96, 0, 0, 0, 0, -4, 0, 0, 72, 0, 0, 0, 0, 24, 0, -52, 0, 0, -4, 0, 16, 0, 0, -84, 0, -4, 0, 0, 24, 0, -60, 0, 0, 48, 0, -8, 0, 0, 0, 0, -36, 0, 0, 26, 0, 0, 0, 0, -16, 0, -20, 0, 0, 12, 0, 28, 0, 0, 4, 0, -64, 0, 0, -44, 0, -32, 0, 0, 16, 0, 24, 0, 0, 14, 0, -8, 0, 0, 24, 0, 0, 0, 0, 80, 0, 4, 0, 0, -52, 0, 8, 0, 0, -32, 0, 64, 0, 0, 108, 0, -48, 0, 0, -16, 0, 20, 0, 0, 0, 0, -44, 0, 0, -12, 0, 0, 0, 0, -24, 0, 136, 0, 0, 104, 0, -24, 0, 0, 80, 0, -32, 0, 0, -16, 0, -8, 0, 0, -64, 0, -48, 0, 0, 0, 0, 4, 0, 0, -76, 0, 0, 0, 0, -36, 0, 48, 0, 0, -42, 0, -84, 0, 0, 32, 0, 4, 0, 0, 18, 0, 116, 0, 0, -36, 0, -40, 0, 0, 0, 0, 104, 0, 0, -108, 0, 0, 0, 0, 112, 0, 16, 0, 0, -4, 0, -48, 0, 0, 68, 0, -96, 0, 0, 56, 0, 0, 0, 0, 0, 0, -60, 0, 0, 0, 0, -76, 0, 0, -32, 0, 28, 0, 0, -4, 0, 48, 0, 0, 96, 0, -8, 0, 0, 8, 0, -40, 0, 0, -40, 0, 56, 0, 0, -16, 0, 2, 0, 0, 0, 0, 88, 0, 0, -2, 0, 0, 0, 0, 60, 0, 160, 0, 0, -76, 0, -40, 0, 0, -60, 0, -8, 0, 0, 24, 0, -8, 0, 0, 24, 0, -4, 0, 0, 0, 0, -32, 0, 0, -120, 0, 0, 0, 0, -16, 0, -24, 0, 0, 8, 0, -4, 0, 0, 4, 0, 8, 0, 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, 5, 2, 1, 2, 0]], "char_orbit_index": 3, "prim_orbit_index": 2, "minimal_twist": "330.2.a.a", "char_is_minimal": false, "conrey_index": 199, "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, -1], [-1, 0], [0, 0], [1, 0], [0, 0], [0, -1], [-1, 0], [0, 0], [1, 0], [0, 1], [0, 2], [0, 0], [0, 0], [1, 0], [0, 2], [0, -1], [-8, 0], [0, 0], [0, 0], [0, 1], [0, 4], [-1, 0], [0, 0], [-2, 0], [0, 1], [0, 0], [-2, 0], [0, 0], [8, 0], [0, 1], [0, -1], [-2, 0], [0, 0], [1, 0], [0, 2], [0, -8], [2, 0], [0, 0], [6, 0], [0, 0], [0, 8], [-1, 0], [0, 0], [-4, 0], [0, 4], [0, -1], [7, 0], [0, 0], [2, 0], [0, -2], [0, 2], [-1, 0], [0, 0], [0, 0], [0, 8], [0, -2], [-4, 0], [0, 0], [-6, 0], [0, 8], [0, 0], [-1, 0], [0, 0], [1, 0], [0, 12], [0, -2], [4, 0], [0, 0], [-12, 0], [0, 1], [0, 2], [-2, 0], [0, 0], [8, 0], [0, 0], [0, 2], [0, 0], [0, 0], [1, 0], [0, 6], [0, 4], [0, 0], [0, 0], [-8, 0], [0, 2], [0, -1], [6, 0], [0, 0], [0, 0], [0, -4], [0, -8], [-4, 0], [0, 0], [1, 0], [0, 14], [0, 7], [-1, 0], [0, 0]]}