# Stored data for newform 363.2.a.f, downloaded from the LMFDB on 20 April 2024. {"label": "363.2.a.f", "space_label": "363.2.a", "level": 363, "weight": 2, "hecke_orbit": 6, "hecke_orbit_code": 22517998170407275, "dim": 2, "is_polredabs": true, "nf_label": "2.2.12.1", "trace_hash": 1059301991538034721, "analytic_rank": 1, "is_twist_minimal": true, "hecke_cutters": [[2, [-3, 0, 1]]], "qexp_display": "q+\\beta q^{2}-q^{3}+q^{4}-3q^{5}-\\beta q^{6}-2\\beta q^{7}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 1452, "fricke_eigenval": 1, "atkin_lehner_string": "++", "analytic_conductor": 2.898569593372478, "hecke_ring_index": 1, "level_radical": 33, "field_poly_is_cyclotomic": false, "field_poly_root_of_unity": 12, "field_poly_is_real_cyclotomic": true, "hecke_ring_index_proved": true, "self_twist_type": 0, "is_self_dual": true, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.508", "prec": 17}, "analytic_rank_proved": true, "char_values": [363, 1, [122, 244], [1, 1]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 2, "level_primes": [3, 11], "conrey_indexes": [1], "field_disc": 12, "field_disc_factorization": [[2, 2], [3, 1]], "field_poly": [-3, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.912", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "15.032", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "148.757", "prec": 24}], "related_objects": ["ModularForm/GL2/ImaginaryQuadratic/2.0.11.1/1089.2/a", "EllipticCurve/2.0.11.1/1089.2/a"], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[3, 1], [11, 1]], "trace_display": [0, -2, -6, 0], "traces": [0, 2, 0, -2, 2, -6, 0, 0, 0, 2, 0, 0, -2, 0, -12, 6, -10, 0, 0, 0, -6, 0, 0, -12, 0, 8, -6, -2, 0, 0, 0, 8, 0, 0, 6, 0, 2, -22, 24, 0, 0, 0, 12, 0, 0, -6, 0, 0, 10, 10, 0, 0, 0, -18, 0, 0, 12, 0, -6, -12, 6, 0, 0, 0, 2, 0, 0, -4, 0, 12, 36, -12, 0, 0, 0, -8, 0, 0, 6, 0, 30, 2, -6, 0, 0, 0, 12, 0, 0, 18, 0, 12, -12, -8, 0, 0, 0, -14, 0, 0, 8, 0, -6, 28, 6, 0, 0, 0, -2, 0, 0, 22, 0, -42, -24, 36, 0, 0, 0, -12, 0, 0, 0, 0, 8, 6, -12, 0, 0, 0, 18, 0, 0, -48, 0, 6, -6, -12, 0, 0, 0, 0, 0, 0, -10, 0, 24, -10, -22, 0, 0, 0, -24, 0, 0, -24, 0, -28, 0, 18, 0, 0, 0, 4, 0, 0, 0, 0, -12, -20, -18, 0, 0, 0, 6, 0, 0, 12, 0, 24, -6, -14, 0, 0, 0, 66, 0, 0, 0, 0, -72, 24, -2, 0, 0, 0, 10, 0, 0, 20, 0, 4, -48, 12, 0, 0, 0, -12, 0, 0, -36, 0, -18, 12, 12, 0, 0, 0, 54, 0, 0, -6, 0, 40, 36, 8, 0, 0, 0, -46, 0, 0, 6, 0, -6, 0, -12, 0, 0, 0, -30, 0, 0, -2, 0, -30, 6, -24, 0, 0, 0, -12, 0, 0, 0, 0, 38, 18, -12, 0, 0, 0, -60, 0, 0, 54, 0, -18, -4, -42, 0, 0, 0, -12, 0, 0, 12, 0, 36, 8, -36, 0, 0, 0, -12, 0, 0, 12, 0, -28, 18, 14, 0, 0, 0, 36, 0, 0, -42, 0, -8, -24, 48, 0, 0, 0, 6, 0, 0, -28, 0, 24, -6, 14, 0, 0, 0, 12, 0, 0, -6, 0, 72, 24, 2, 0, 0, 0, 6, 0, 0, 40, 0, -22, -12, 12, 0, 0, 0, 42, 0, 0, 24, 0, -12, -36, 72, 0, 0, 0, -48, 0, 0, 42, 0, 36, 18, 12, 0, 0, 0, 58, 0, 0, 12, 0, 0, 52, 60, 0, 0, 0, -8, 0, 0, -6, 0, 6, 12, 28, 0, 0, 0, 12, 0, 0, -18, 0, -14, -54, -18, 0, 0, 0, -66, 0, 0, 22, 0, 48, -40, 6, 0, 0, 0, -6, 0, 0, 6, 0, 18, 12, 28, 0, 0, 0, 18, 0, 0, -60, 0, 14, -60, 0, 0, 0, 0, 0, 0, 0, -36, 0, 10, -38, -48, 0, 0, 0, -24, 0, 0, 10, 0, -36, 22, -54, 0, 0, 0, 42, 0, 0, -42, 0, -84, -36, 24, 0, 0, 0, 36, 0, 0, -68, 0, 24, 102, -36, 0, 0, 0, 28, 0, 0, 0, 0, -12, -18, -24, 0, 0, 0, -72, 0, 0, 42, 0, -76, 0, -4, 0, 0, 0, -6, 0, 0, -40, 0, 0, 44, 6, 0, 0, 0, 12, 0, 0, 20, 0, 36, 18, -48, 0, 0, 0, -84, 0, 0, 132, 0, -18, 12, -6, 0, 0, 0, 48, 0, 0, 26, 0, -12, -48, 6, 0, 0, 0, -24, 0, 0, 6, 0, -12, 14, -18, 0, 0, 0, -12, 0, 0, -24, 0, 0, -18, -66, 0, 0, 0, -12, 0, 0, -24, 0, 0, 126, -108, 0, 0, 0, 72, 0, 0, -24, 0, -48, 2, 26, 0, 0, 0, 0, 0, 0, -24, 0, 66, -24, -10, 0, 0, 0, 110, 0, 0, 36, 0, -20, 36, 48, 0, 0, 0, -4, 0, 0, 48, 0, -72, -12, 0, 0, 0, 0, 12, 0, 0, -18, 0, -20, -24, 12, 0, 0, 0, -58, 0, 0, -28, 0, 36, -28, 0, 0, 0, 0, 18, 0, 0, -12, 0, -30, -12, -32, 0, 0, 0, -24, 0, 0, -24, 0, 4, -60, -54, 0, 0, 0, 0, 0, 0, -82, 0, 6, 0, 144, 0, 0, 0, -40, 0, 0, -36, 0, -42, -8, -20, 0, 0, 0, 18, 0, 0, -12, 0, 36, 24, 46, 0, 0, 0, -20, 0, 0, 96, 0, -6, -6, -6, 0, 0, 0, 6, 0, 0, 0, 0, 96, 12, 44, 0, 0, 0, -48, 0, 0, 24, 0, 108, -60, 30, 0, 0, 0, -14, 0, 0, -4, 0, 2, -72, 12, 0, 0, 0, 30, 0, 0, -6, 0, 66, 24, 108, 0, 0, 0, 72, 0, 0, -24, 0, -4, 0, 12, 0, 0, 0, -34, 0, 0, 72, 0, 0, -108, 24, 0, 0, 0, -38, 0, 0, -18, 0, 36, 12, 32, 0, 0, 0, -24, 0, 0, -36, 0, -50, 84, 60, 0, 0, 0, 0, 0, 0, 0, 0, -54, 20, -84, 0, 0, 0, 18, 0, 0, 4, 0, -24, 42, 48, 0, 0, 0, 12, 0, 0, -12, 0, 48, 6, 12, 0, 0, 0, 28, 0, 0, 72, 0, -12, 22, 0, 0, 0, 0, -36, 0, 0, -8, 0, 48, 36, -52, 0, 0, 0, 60, 0, 0, 90, 0, 24, 132, 12, 0, 0, 0, -12, 0, 0, 28, 0, -12, -60, 12, 0, 0, 0, 28, 0, 0, -18, 0, -54, -14, -144, 0, 0, 0, -24, 0, 0, -18, 0, 8, -6, -36, 0, 0, 0, 0, 0, 0, 40, 0, 42, -72, -84, 0, 0, 0, 8, 0, 0, 24, 0, 42, -48, -44, 0, 0, 0, -60, 0, 0, -102, 0, -46, 120, -6, 0, 0, 0, -54, 0, 0, -88, 0, 28, 18, 78, 0, 0, 0, -24, 0, 0, 6, 0, 24, -14, 0, 0, 0, 0, 60, 0, 0, 108, 0, -24, 96, -12, 0, 0, 0, -72, 0, 0, 84, 0, 6, -30, 66, 0, 0, 0, -72, 0, 0, -24, 0, -84, -2, -72, 0, 0, 0, -18, 0, 0, -30, 0, -72, -72, -6, 0, 0, 0, -24, 0, 0, 32, 0, -40, 72, -60, 0, 0, 0, 22, 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, 11, 2, -1, 2, 0]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "363.2.a.f", "char_is_minimal": true, "conrey_index": 1, "id": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0, 0], [1, 0], [0, 1], [-1, 0], [1, 0], [-3, 0], [0, -1], [0, -2], [0, -1], [1, 0], [0, -3], [0, 0], [-1, 0], [0, -1], [-6, 0], [3, 0], [-5, 0], [0, 1], [0, 1], [0, 4], [-3, 0], [0, 2], [0, 0], [-6, 0], [0, 1], [4, 0], [-3, 0], [-1, 0], [0, -2], [0, -1], [0, 3], [4, 0], [0, -3], [0, 0], [3, 0], [0, 6], [1, 0], [-11, 0], [12, 0], [0, 1], [0, 3], [0, -1], [6, 0], [0, 2], [0, 0], [-3, 0], [0, -6], [0, 0], [5, 0], [5, 0], [0, 4], [0, -1], [0, -1], [-9, 0], [0, -1], [0, 0], [6, 0], [0, -4], [-3, 0], [-6, 0], [3, 0], [0, 0], [0, 4], [0, -2], [1, 0], [0, 3], [0, 0], [-2, 0], [0, 1], [6, 0], [18, 0], [-6, 0], [0, -1], [0, 4], [0, -11], [-4, 0], [0, 4], [0, 0], [3, 0], [0, 0], [15, 0], [1, 0], [-3, 0], [0, 0], [0, 2], [0, -3], [6, 0], [0, 1], [0, 0], [9, 0], [0, -3], [6, 0], [-6, 0], [-4, 0], [0, 0], [0, -12], [0, 3], [-7, 0], [0, 5], [0, 0], [4, 0]]}