# Stored data for newform 1690.2.d.d, downloaded from the LMFDB on 06 June 2024. {"Nk2": 6760, "analytic_conductor": 13.494717941596384, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 13, "char_degree": 1, "char_is_minimal": false, "char_is_real": true, "char_orbit_index": 4, "char_orbit_label": "d", "char_order": 2, "char_parity": 1, "char_values": [1690, 2, [677, 171], [2, 1]], "cm_discs": [], "conrey_index": 1351, "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": [[3, [0, 1]], [7, [0, 1]]], "hecke_orbit": 4, "hecke_orbit_code": 13511005074097818, "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, 13, 2, 1, 2, 0]], "is_cm": false, "is_largest": false, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": false, "is_self_twist": false, "is_twist_minimal": false, "label": "1690.2.d.d", "level": 1690, "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, 5, 13], "level_radical": 130, "minimal_twist": "130.2.a.b", "nf_label": "2.0.4.1", "prim_orbit_index": 2, "qexp_display": "q+iq^{2}-q^{4}+iq^{5}-iq^{8}-3q^{9}+\\cdots", "related_objects": [], "relative_dim": 2, "rm_discs": [], "sato_tate_group": "1.2.3.c2", "self_twist_discs": [], "self_twist_type": 0, "space_label": "1690.2.d", "trace_display": [0, 0, 0, 0], "trace_hash": 701664680836098053, "trace_moments": [{"__RealLiteral__": 0, "data": "0.069", "prec": 17}, {"__RealLiteral__": 0, "data": "1.928", "prec": 17}, {"__RealLiteral__": 0, "data": "0.565", "prec": 17}, {"__RealLiteral__": 0, "data": "14.953", "prec": 20}, {"__RealLiteral__": 0, "data": "4.428", "prec": 17}, {"__RealLiteral__": 0, "data": "143.279", "prec": 24}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.520", "prec": 17}, "traces": [0, 2, 0, 0, -2, 0, 0, 0, 0, -6, -2, 0, 0, 0, 0, 0, 2, -4, 0, 0, 0, 0, 0, 8, 0, -2, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 6, 0, 16, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 14, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, -4, 8, 0, -2, 0, 0, 0, 4, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, -16, 0, 18, -20, 0, 0, 0, 0, 0, 0, 0, 6, 0, -8, 0, 16, 16, 0, 0, 0, 0, 2, -12, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, -28, 0, 0, 4, 0, 16, 0, 0, 22, 0, 0, 0, 0, 0, 40, 0, 0, 0, 8, 0, 0, -8, 0, 0, 0, 0, 8, 0, 0, 24, 0, -6, 0, 20, 0, 0, 0, 0, 0, -16, 12, 0, 8, 0, -36, 0, 0, -2, 0, 0, 0, 0, 0, -24, 0, 0, 0, 4, 0, 0, 36, 0, 0, 0, 0, 20, -8, 0, -44, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 28, 0, -14, 0, 0, -48, 0, 0, 0, 0, 0, -20, 0, -24, 0, 0, 0, 8, -12, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, -8, 0, 0, 12, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, -8, 0, 2, 56, 0, 0, 0, 0, 2, -4, 0, 0, 0, 12, 0, -56, 0, 0, 0, 0, 0, -36, 0, 0, -4, 0, -12, 0, 0, -44, 0, 0, 0, 0, 0, -32, 0, 0, 0, 0, 0, -26, 4, 0, 0, 0, 0, 16, -12, 0, -12, 0, 0, 0, -40, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, -18, 0, 40, 0, 20, 0, 0, 0, 0, 0, 32, -8, 0, -36, 0, 0, 0, 0, -48, 0, 0, 0, 0, 64, 0, 0, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, -6, -90, 0, 0, 0, 20, 0, -24, 8, 0, 0, 0, 0, 12, 0, 0, -16, 0, 0, 0, -16, 0, 0, 0, 0, 0, 36, 0, 0, -12, 0, -16, 0, 0, 52, 0, 0, 0, 0, 0, -2, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, -24, 0, 0, 0, -72, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, -68, 0, 0, 0, 0, 0, 48, 0, -42, 0, 48, 0, 20, 16, 0, 0, 0, 0, 0, 28, 0, -40, 0, 0, 0, -20, 0, 0, 0, 0, 0, -4, 0, 0, 32, 0, 0, 0, 0, -16, 0, 0, 0, 0, -36, -40, 0, 0, 0, 4, 0, -22, 28, 0, 0, 0, 0, -14, -40, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 40, 0, 0, 0, 0, -40, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 52, 0, -16, -8, 0, 0, 0, 0, -14, -12, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, -56, 0, 0, 4, 0, -80, 0, 12, 0, 0, 0, 0, 0, 0, -8, 0, -24, 0, 0, 0, -44, -48, 0, 0, 0, 0, -24, -20, 0, 56, 0, 0, 0, -8, 6, 0, 0, 0, 0, 0, 0, 0, -20, 0, 12, 0, 0, -64, 0, 0, 0, 0, 0, 0, 0, 0, 0, 64, 0, 52, 0, 0, 0, 0, 0, 72, 16, 0, 4, 0, -12, 0, 56, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 2, 0, 0, 36, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 2, 60, 0, 0, 0, 0, -32, 56, 0, 0, 0, 0, 0, 92, 0, 0, 0, 0, 0, -72, 0, 0, 16, 0, 24, 0, -36, -16, 0, 0, 0, 0, 0, 28, 0, 0, 0, 44, 0, 0, -4, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, -36, 0, 0, 0, 0, 0, 28, 0, 0, 68, 0, -96, 0, 0, 60, 0, 0, 0, 0, 48, -20, 0, 0, 0, 8, 0, 8, -32, 0, 0, 0, 0, 44, 4, 0, 56, 0, -54, 0, 0, 0, 0, 0, 0, 0, 0, 60, 0, -12, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 80, 0, 0, 0, -40, 0, 44, 0, 0, 0, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, -28, 0, 0, 160, 0, 0, 0, 0, 14, 0, 0, 0, 0, 0, 16, 0, 0, 0, -36, 0, 48, 68, 0, 0, 0, 0, -60, 0, 0, 0, 0, 0, 0, 52, -18, 0, 0, 0, 0, 40, 0, 0, -52, 0, 20, 0, 0, 8, 0, 0, 0, 0, 24, 68, 0, 0, 0, -28, 0, 32, 0, 0, 0, 0, 0, -50, 52, 0, -8, 0, -48, 0, 12, 0, 0, 0, 0, 0, 0, -48, 0, 12, 0, -56, 0, 0, -24, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 64, 0, 0, 0, 0, 0, 0, -4, 0, 16, 0, 0, 0, 88, 0, 0, 0, 0, 0, -128, 0, 0, 0, 0, 36, 0, -6, -24, 0, 0, 0, 0, 0, -16, 0, 36, 0, 96, 0, 0, 76, 0, 0, 0, 0, 64, 8, 0, -28, 0, 0, 0, -32, -24, 0, 0, 0, 0, -12, 0, 0, 0, 0, 52, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, -16, 0, 0, -52, 0, 0, 0, 0, -8, 0, 0, 30, 0, 0, 0, 36, 0, 0, 0, 0, 0, -8, 0, 0, 16, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 52, 0, 0, 0, 0, 0, 64, 8, 0, 0, 0, 0, 44, -16, 0, -2, 0, 0, 0, -56, 0, 0, 0, 0, 0, 12, 0, 0, -12, 0, 0, 0, 84, 36, 0, 0, 0, 0, 0, -2, 0, 0, 0, 4, 0, -8, 0, 0, 0, 0, 0, 0, 8, 0, -64, 0, 0, 0, 0, -12, 0, 0, 0, 0, -12, 0, 0, 56, 0, -16, 0, 0, 0, 0, 0, 0, 0, -48, 8, 0, 0, 0, 0, 0, -36, 0, 0, 0, 0, 0, 0, 36, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 4, -66, 0, 72, 0, -20, 0, 0, 12, 0, 0, 0, 0, 0, -32, 0, 0, 0, 0, 0, 44, -44, 0, 0, 0, 0, 28, 16, 0, -28, 0, 0, 0, -128, 0, 0, 0, 0, 0, 56, 0, 0, 28, 0, 32, 0, 0, -40, 0, 0, 0, 0, 0, 0, 0, -120, 0, -20, 0, -48, 0, 0, 0, 0, 0, -60, -4, 0, 26, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -24, 0, 0, 40, 0, 0, 0, 0, -24, -16, 0, 0, 0, 12, 0, 4, 128, 0, 0, 0, 0, 12, 76, 0, -40, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 24, 0, 40, 0, -22, 0, 0, 4, 0, 0, 0, 0, 0, 48, 0, 0, 0, 72, 0, -14, -76, 0, 0, 0, 0, -32, 0, 0, -52, 0, 0, 0, -48, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 100, 0, -24, 12, 0, 0, 0, 0, 0, -24, 0, 0, 0, 24, 0, -16, 0, 0, 0, 0, 0, -40, 80, 0, 64, 0, 0, 0, -68, -72, 0, 0, 0, 0, 96, 0, 0, -56, 0, 0, 0, 0, -104, 0, 0, 0, 0, 18, -68, 0, 0, 0, -84, 0, -120, -40, 0, 0, 0, 0, 0, -8, 0, -20, 0, -60, 0, 0, 0, 0, 0, 0, 0, 44, 0, 0, -12, 0, 104, 0, 0, 0, 0, 0, 0, 0, 0, -32, 0, 0, 0, 8, 0, 0, 32, 0, 0, 0, 0, 36, -192, 0, 0, 0, 0, 0, -56, 0, 0, 0, 0, 0, 36, 0, 0, 0, 0, 56, 0, 48, 2, 0, 0, 0, 0, 0, 0, 0, -36, 0, 0, 0, -116, -64, 0, 0, 0, 0, -160, -64, 0, -8, 0, 0, 0, 40, -24, 0, 0, 0, 0, 0, 0, 0, -16, 0, -44, 0, 0, 0, 0, 0, 0, 0, 108, 0, 0, 0, 0, -20, 0, -24, -28, 0, 0, 0, 0, 32, -64, 0, -108, 0, 0, 0, 84, 0, 0, 0, 0, 0, -48, 6, 0, 0, 0, 90, 0, 0, 56, 0, 0, 0, 0, 0, -28, 0, 0, 0, -64, 0, -40, -20, 0, 0, 0, 0, 12, 68, 0, 24, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, -84, 0, -16, 0, 0, -32, 0, 0, 0, 0, 0, -12, 0, 72, 0, 0, 0, 0, 40, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 120, 0, 0, 16, 0, -12, 0, 0, 4, 0, 0, 0, 0, -12, -8, 0, 0, 0, 56, 0, -24, 28, 0, 0, 0, 0, -88, -36, 0, 52, 0, 0, 0, -8, 0, 0, 0, 0, 0, 12, -108, 0, -112, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 36, 0, 0, 0, -8, 0, -52, 192, 0, 0, 0, 0, 0, -72, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -32, 0, 2, 0, -60, 0, 0, 0, 0, 0, 0, 108, 0, 24, 0, 60, 0, -32, -12, 0, 0, 0, 0, -20, -48, 0, 0, 0, 0, 0, 0, 132, 0, 0, 0, 0, 0, 0, 0, -108, 0, 0, 0, 0, 84, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 72, 16, 0, 0, 0, 0, 24, 0, 0, -8, 0, -36, 0, 48, 0, 0, 0, 0, 0, 0, 0, 0, 72, 0, 8, 0, 0, -118, 0, 0, 0, 0, 0, 0, 0, 0, 0, -160, 0, -4, 0, 0, 0, 0, 0, 88, -4, 0, 48, 0, 0, 0, 44, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, 0, -80, 0, 0, 0, -36, 0, 68, -12, 0, 0, 0, 0, 0, -96, 0, -156, 0, 0, 0, 28, -84, 0, 0, 0, 0, -16, 0, 0, -28, 0, -48, 0, 0, 128, 0, 0, 0, 0, 42, 60, 0, 0, 0, 8, 0, 0, -48, 0, 0, 0, 0, 100, 0, 0, -20, 0, 0, 0, -16, 0, 0, 0, 0, 0, 8, 144, 0, 0, 0, 8, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, -28, 0, 44, -88, 0, 0, 0, 0, 40, -64, 0, 0, 0, 0, 0, -104, 0, 0, 0, 0, 0, -64, 0, 0, 20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -224, 0, 60, 0, 24, 0, -86, -12, 0, 0, 0, 0, 0, 4, 0, 28, 0, 0, 0, 112, 72, 0, 0, 0, 0, -32, 0, 0, -80, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, -60, 0, 0, 0, -80, 0, 16, -36, 0, 0, 0, 0, -8, 0, 0, 0, 0, -24, 0, -36, 0, 0, 0, 0, 0, -144, 36, 0, 0, 0, 40, 0, 0, -16, 0, 0, 0, 0, 0, 56, 0, 0, 0, 0, 0, 160, -4, 0, 0, 0, 0, -68, -48, 0, 22, 0, 0, 0, -28, 0, 0, 0, 0, 0, 0, 0, 0, 132, 0, -32, 0, 0, -36, 0, 0, 0, 0, 0, 14, 0, -12, 0, 40, 0, -48, 0, 0, 0, 0, 0, -8, 116, 0, 16, 0, 0, 0, 72, 0, 0, 0, 0, 0, -36, 0, 0, 0, 0, 48, 0, 0, 172, 0, 0, 0, 0, 0, 128, 0], "weight": 2, "weight_parity": 1, "id": null, "artin_degree": null, "artin_field": null, "artin_field_label": null, "artin_image": null, "atkin_lehner_eigenvals": null, "atkin_lehner_string": null, "embedded_related_objects": null, "fricke_eigenval": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp": [[0, 0], [1, 0], [0, 1], [0, 0], [-1, 0], [0, 1], [0, 0], [0, 0], [0, -1], [-3, 0], [-1, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [1, 0], [-2, 0], [0, -3], [0, -8], [0, -1], [0, 0], [0, 0], [4, 0], [0, 0], [-1, 0], [0, 0], [0, 0], [0, 0], [-2, 0], [0, 0], [0, -4], [0, 1], [0, 0], [0, -2], [0, 0], [3, 0], [0, -6], [8, 0], [0, 0], [1, 0], [0, 10], [0, 0], [0, 0], [0, 0], [0, -3], [0, 4], [0, -8], [0, 0], [7, 0], [0, -1], [0, 0], [0, 0], [6, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, -2], [0, -8], [0, 0], [-2, 0], [4, 0], [0, 0], [-1, 0], [0, 0], [0, 0], [0, 4], [2, 0], [0, 0], [0, 0], [0, -12], [0, 3], [0, -10], [6, 0], [0, 0], [0, 8], [0, 0], [0, 0], [-8, 0], [0, 1], [9, 0], [-10, 0], [0, 12], [0, 0], [0, -2], [0, 0], [0, 0], [0, 0], [0, -10], [3, 0], [0, 0], [-4, 0], [0, 0], [8, 0], [8, 0], [0, 0], [0, -14], [0, 7], [0, 0], [1, 0]]}