# Stored data for newform 363.2.a.g, downloaded from the LMFDB on 20 September 2025. {"Nk2": 1452, "analytic_conductor": 2.898569593372478, "analytic_rank": 0, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[3, -1], [11, 1]], "atkin_lehner_string": "-+", "char_conductor": 1, "char_degree": 1, "char_is_minimal": true, "char_is_real": true, "char_orbit_index": 1, "char_orbit_label": "a", "char_order": 1, "char_parity": 1, "char_values": [363, 1, [122, 244], [1, 1]], "cm_discs": [], "conrey_index": 1, "dim": 2, "field_disc": 5, "field_disc_factorization": [[5, 1]], "field_poly": [-1, -1, 1], "field_poly_is_cyclotomic": false, "field_poly_is_real_cyclotomic": true, "field_poly_root_of_unity": 10, "fricke_eigenval": -1, "has_non_self_twist": 1, "hecke_cutters": [[2, [-5, 0, 1]]], "hecke_orbit": 7, "hecke_orbit_code": 27021597797777771, "hecke_ring_generator_nbound": 2, "hecke_ring_index": 2, "hecke_ring_index_factorization": [[2, 1]], "hecke_ring_index_proved": true, "inner_twist_count": 2, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 11, 2, -1, 2, 0]], "is_cm": false, "is_largest": false, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": true, "is_self_twist": false, "is_twist_minimal": true, "label": "363.2.a.g", "level": 363, "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": [3, 11], "level_radical": 33, "minimal_twist": "363.2.a.g", "nf_label": "2.2.5.1", "prim_orbit_index": 1, "qexp_display": "q-\\beta q^{2}+q^{3}+3q^{4}+2q^{5}-\\beta q^{6}+\\cdots", "related_objects": ["EllipticCurve/2.0.11.1/1089.2/c", "ModularForm/GL2/ImaginaryQuadratic/2.0.11.1/1089.2/c"], "relative_dim": 2, "rm_discs": [], "sato_tate_group": "1.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "363.2.a", "trace_display": [0, 2, 4, 0], "trace_hash": 1190271713143038769, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.936", "prec": 17}, {"__RealLiteral__": 0, "data": "0.076", "prec": 17}, {"__RealLiteral__": 0, "data": "15.123", "prec": 20}, {"__RealLiteral__": 0, "data": "1.554", "prec": 17}, {"__RealLiteral__": 0, "data": "148.645", "prec": 24}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.511", "prec": 17}, "traces": [0, 2, 0, 2, 6, 4, 0, 0, 0, 2, 0, 0, 6, 0, -20, 4, -2, 0, 0, 0, 12, 0, 0, -8, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, 20, 0, 6, 4, -20, 0, 0, 0, -20, 0, 0, 4, 0, 16, -2, 26, 0, 0, 0, 12, 0, 0, -20, 0, 20, 0, 12, 0, 0, 0, -26, 0, 0, -24, 0, -8, -40, -16, 0, 0, 0, -2, 0, 0, 0, 0, -4, 2, -20, 0, 0, 0, 20, 0, 0, -28, 0, 0, -24, 0, 0, 0, 0, 4, 0, 0, -6, 0, 20, 32, 0, 0, 0, 0, 6, 0, 0, 4, 0, 12, -20, -16, 0, 0, 0, -40, 0, 0, 40, 0, 0, -24, -20, 0, 0, 0, 0, 0, 0, 40, 0, 4, 20, 44, 0, 0, 0, 16, 0, 0, -2, 0, -40, 26, 12, 0, 0, 0, -20, 0, 0, 0, 0, 4, 60, 12, 0, 0, 0, 8, 0, 0, -40, 0, -20, -26, 40, 0, 0, 0, 20, 0, 0, 0, 0, -8, 12, -20, 0, 0, 0, 8, 0, 0, 48, 0, -40, 0, -26, 0, 0, 0, 78, 0, 0, 0, 0, -24, 20, -40, 0, 0, 0, -8, 0, 0, -40, 0, 36, -16, 40, 0, 0, 0, 0, 0, 0, 0, 0, -32, 60, -2, 0, 0, 0, 20, 0, 0, 20, 0, 0, 32, 0, 0, 0, 0, -4, 0, 0, 2, 0, 52, -20, 0, 0, 0, 0, -24, 0, 0, 60, 0, -18, -44, 20, 0, 0, 0, -80, 0, 0, 24, 0, -28, -72, -20, 0, 0, 0, 0, 0, 0, -24, 0, 60, 0, -40, 0, 0, 0, -48, 0, 0, 40, 0, 6, 40, 4, 0, 0, 0, 0, 0, 0, -100, 0, -6, -40, 60, 0, 0, 0, 20, 0, 0, 32, 0, -24, 0, 28, 0, 0, 0, 36, 0, 0, -52, 0, 80, -40, 6, 0, 0, 0, -20, 0, 0, -40, 0, 4, 40, -48, 0, 0, 0, 12, 0, 0, -20, 0, 20, -16, -60, 0, 0, 0, 20, 0, 0, -28, 0, -32, -84, -40, 0, 0, 0, 2, 0, 0, 0, 0, 40, 16, 8, 0, 0, 0, 0, 0, 0, -24, 0, 0, -20, -40, 0, 0, 0, -72, 0, 0, -80, 0, 12, 20, 0, 0, 0, 0, 100, 0, 0, 44, 0, 40, 2, 60, 0, 0, 0, 4, 0, 0, 20, 0, -40, 44, 96, 0, 0, 0, 0, 0, 0, 8, 0, 20, -20, 16, 0, 0, 0, -80, 0, 0, 40, 0, -2, -12, 0, 0, 0, 0, -40, 0, 0, 26, 0, -48, 12, -56, 0, 0, 0, -12, 0, 0, 36, 0, 40, 0, -20, 0, 0, 0, -48, 0, 0, 48, 0, 0, -20, -16, 0, 0, 0, 4, 0, 0, 60, 0, -120, 12, 40, 0, 0, 0, 40, 0, 0, 8, 0, 16, 40, 8, 0, 0, 0, 40, 0, 0, 0, 0, -40, -40, -72, 0, 0, 0, -20, 0, 0, -26, 0, 60, 40, 80, 0, 0, 0, 64, 0, 0, -40, 0, 0, 60, 20, 0, 0, 0, 40, 0, 0, -14, 0, 0, 120, 0, 0, 0, 0, -8, 0, 0, 12, 0, -60, -20, -60, 0, 0, 0, 132, 0, 0, -40, 0, -120, 0, 8, 0, 0, 0, 0, 0, 0, 140, 0, 48, 24, -60, 0, 0, 0, -40, 0, 0, 0, 0, 8, -26, -4, 0, 0, 0, 80, 0, 0, -40, 0, -100, -16, 78, 0, 0, 0, -4, 0, 0, -80, 0, 0, 0, -72, 0, 0, 0, -24, 0, 0, 20, 0, 60, -40, 80, 0, 0, 0, -20, 0, 0, -4, 0, 88, 0, -8, 0, 0, 0, -38, 0, 0, 12, 0, -40, 64, 60, 0, 0, 0, 36, 0, 0, -16, 0, -60, 40, 72, 0, 0, 0, -24, 0, 0, 0, 0, 24, 92, 0, 0, 0, 0, -160, 0, 0, -44, 0, 0, -40, 80, 0, 0, 0, -32, 0, 0, 60, 0, 40, -2, -78, 0, 0, 0, 40, 0, 0, 88, 0, 88, -120, 20, 0, 0, 0, 24, 0, 0, 40, 0, 20, -40, -120, 0, 0, 0, 0, 0, 0, 32, 0, -40, 0, -12, 0, 0, 0, 0, 0, 0, -24, 0, 0, -48, -4, 0, 0, 0, -60, 0, 0, -16, 0, 2, -80, 40, 0, 0, 0, 52, 0, 0, -20, 0, 24, 0, -120, 0, 0, 0, -120, 0, 0, -80, 0, 64, -16, -24, 0, 0, 0, 84, 0, 0, -40, 0, 60, 0, 0, 0, 0, 0, -18, 0, 0, -44, 0, 28, 20, 0, 0, 0, 0, 40, 0, 0, -80, 0, -26, 8, -80, 0, 0, 0, 120, 0, 0, 0, 0, 24, 0, 84, 0, 0, 0, -28, 0, 0, -72, 0, 0, -20, 20, 0, 0, 0, -120, 0, 0, 16, 0, -40, -120, 0, 0, 0, 0, 32, 0, 0, 0, 0, -24, 28, -80, 0, 0, 0, 60, 0, 0, 0, 0, -40, -40, -18, 0, 0, 0, -52, 0, 0, -12, 0, -20, -16, -48, 0, 0, 0, 40, 0, 0, 8, 0, 40, -40, 8, 0, 0, 0, 6, 0, 0, 40, 0, 0, 4, 80, 0, 0, 0, -60, 0, 0, -36, 0, 88, 0, 0, 0, 0, 0, -120, 0, 0, -96, 0, -100, -16, 140, 0, 0, 0, -6, 0, 0, -40, 0, -40, 60, -24, 0, 0, 0, 0, 0, 0, 120, 0, 60, 160, 20, 0, 0, 0, 60, 0, 0, -4, 0, 32, -60, 60, 0, 0, 0, -24, 0, 0, 0, 0, 240, 28, 96, 0, 0, 0, 0, 0, 0, 104, 0, 0, 20, 36, 0, 0, 0, 0, 0, 0, -40, 0, -52, -62, 0, 0, 0, 0, 80, 0, 0, -40, 0, 0, 6, -120, 0, 0, 0, -84, 0, 0, 156, 0, -120, 72, -20, 0, 0, 0, 0, 0, 0, 80, 0, -40, 160, 0, 0, 0, 0, 4, 0], "weight": 2, "weight_parity": 1, "id": null, "artin_degree": null, "artin_field": null, "artin_field_label": null, "artin_image": null, "embedded_related_objects": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp": [[0, 0], [1, 0], [0, -1], [1, 0], [3, 0], [2, 0], [0, -1], [0, 2], [0, -1], [1, 0], [0, -2], [0, 0], [3, 0], [0, 0], [-10, 0], [2, 0], [-1, 0], [0, -2], [0, -1], [0, 2], [6, 0], [0, 2], [0, 0], [-4, 0], [0, -1], [-1, 0], [0, 0], [1, 0], [0, 6], [0, -2], [0, -2], [0, 0], [0, 3], [0, 0], [10, 0], [0, 4], [3, 0], [2, 0], [-10, 0], [0, 0], [0, -2], [0, 2], [-10, 0], [0, -2], [0, 0], [2, 0], [0, 4], [8, 0], [-1, 0], [13, 0], [0, 1], [0, -2], [0, 0], [6, 0], [0, -1], [0, 0], [-10, 0], [0, 2], [10, 0], [0, 0], [6, 0], [0, -4], [0, 0], [0, 2], [-13, 0], [0, 0], [0, 0], [-12, 0], [0, -6], [-4, 0], [-20, 0], [-8, 0], [0, -1], [0, 4], [0, -2], [-1, 0], [0, 6], [0, 0], [0, 0], [0, -6], [-2, 0], [1, 0], [-10, 0], [0, 4], [0, 6], [0, -4], [10, 0], [0, -2], [0, 0], [-14, 0], [0, -2], [0, 0], [-12, 0], [0, 0], [0, -8], [0, 4], [0, 3], [2, 0], [0, -13], [0, 0], [-3, 0]]}