# Stored data for newform 684.2.k.c, downloaded from the LMFDB on 24 September 2023. {"label": "684.2.k.c", "space_label": "684.2.k", "level": 684, "weight": 2, "hecke_orbit": 3, "hecke_orbit_code": 9007886483063468, "dim": 2, "is_polredabs": true, "nf_label": "2.0.3.1", "trace_hash": 941074430766697623, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[5, [0, 1]], [7, [1, 1]]], "qexp_display": "q-q^{7}+7\\zeta_{6}q^{13}+(5-2\\zeta_{6})q^{19}+5\\zeta_{6}q^{25}+\\cdots", "char_order": 3, "char_parity": 1, "char_degree": 2, "char_conductor": 19, "char_orbit_label": "k", "char_is_real": false, "Nk2": 2736, "analytic_conductor": 5.461767498255578, "hecke_ring_index": 1, "level_radical": 114, "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": 1, "is_self_dual": false, "is_self_twist": true, "is_cm": true, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.509", "prec": 17}, "analytic_rank_proved": true, "char_values": [684, 3, [343, 533, 325], [3, 3, 2]], "hecke_ring_generator_nbound": 19, "inner_twist_count": 4, "level_primes": [2, 3, 19], "conrey_indexes": [505, 577], "field_disc": -3, "field_disc_factorization": [[-1, 1], [3, 1]], "field_poly": [1, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "2.030", "prec": 17}, {"__RealLiteral__": 0, "data": "0.213", "prec": 17}, {"__RealLiteral__": 0, "data": "18.591", "prec": 20}, {"__RealLiteral__": 0, "data": "4.538", "prec": 17}, {"__RealLiteral__": 0, "data": "228.435", "prec": 24}], "related_objects": ["EllipticCurve/2.0.3.1/51984.3/CMa", "EllipticCurve/2.0.3.1/51984.1/CMa"], "self_twist_discs": [-3], "cm_discs": [-3], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "1.2.1.d3", "trace_display": [0, 0, 0, -2], "traces": [0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 22, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -5, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 13, 0, 0, 0, 0, 0, -5, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 13, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -7, 0, 0, 0, 0, 0, -14, 0, 0, 0, 0, 0, -26, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -22, 0, 0, 0, 0, 0, -20, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, -23, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 25, 0, 0, 0, 0, 0, 34, 0, 0, 0, 0, 0, -36, 0, 0, 0, 0, 0, -5, 0, 0, 0, 0, 0, -26, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -23, 0, 0, 0, 0, 0, -11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 13, 0, 0, 0, 0, 0, -22, 0, 0, 0, 0, 0, -23, 0, 0, 0, 0, 0, 58, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -17, 0, 0, 0, 0, 0, 49, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 28, 0, 0, 0, 0, 0, 52, 0, 0, 0, 0, 0, -32, 0, 0, 0, 0, 0, 17, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 22, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -35, 0, 0, 0, 0, 0, -62, 0, 0, 0, 0, 0, -5, 0, 0, 0, 0, 0, 26, 0, 0, 0, 0, 0, 46, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 26, 0, 0, 0, 0, 0, 31, 0, 0, 0, 0, 0, 76, 0, 0, 0, 0, 0, 58, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 77, 0, 0, 0, 0, 0, -38, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 22, 0, 0, 0, 0, 0, -13, 0, 0, 0, 0, 0, -35, 0, 0, 0, 0, 0, -41, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -62, 0, 0, 0, 0, 0, -86, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 35, 0, 0, 0, 0, 0, -7, 0, 0, 0, 0, 0, 88, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -35, 0, 0, 0, 0, 0, 23, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -17, 0, 0, 0, 0, 0, -41, 0, 0, 0, 0, 0, -13, 0, 0, 0, 0, 0, -70, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 94, 0, 0, 0, 0, 0, -92, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 88, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 46, 0, 0, 0, 0, 0, -98, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, -98, 0, 0, 0, 0, 0, -25, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -42, 0, 0, 0, 0, 0, -47, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -38, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -74, 0, 0, 0, 0, 0, 14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, -53, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 26, 0, 0, 0, 0, 0, 49, 0, 0, 0, 0, 0, 100, 0, 0, 0, 0, 0, -53, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11, 0, 0, 0, 0, 0, 55, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -47, 0, 0, 0, 0, 0, 55, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -50, 0, 0, 0, 0, 0, -91, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -56, 0, 0, 0, 0, 0, -5, 0, 0, 0, 0, 0, 52, 0, 0, 0, 0, 0, -14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 29, 0, 0, 0, 0, 0, 22, 0, 0, 0, 0, 0, -35, 0, 0, 0, 0, 0, 43, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 35, 0, 0, 0, 0, 0, 25, 0, 0, 0, 0, 0, 55, 0, 0, 0, 0, 0, 20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 40, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 106, 0, 0, 0, 0, 0, -5, 0, 0, 0, 0, 0, -48, 0, 0, 0, 0, 0, -35, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 98, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 180, 0, 0, 0, 0, 0, -41, 0, 0, 0, 0, 0, 23, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -17, 0, 0, 0, 0, 0, 49, 0, 0, 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, 3, 2, -1, 2, -3], [1, 1, 19, 3, 1, 3, 0], [1, 1, 57, 8, -1, 6, 0]], "char_orbit_index": 11, "prim_orbit_index": 3, "minimal_twist": "684.2.k.c", "char_is_minimal": true, "conrey_index": 505, "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], [0, 0], [0, 0], [0, 0], [0, 0], [-1, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 7], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [5, -2], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 5], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [11, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [-1, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [-5, 5], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [-6, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 13], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, -5], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [7, -7], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [13, -13], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, -7], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [-14, 14], [0, 0], [0, 0], [0, 0]]}