# Stored data for newform 38.2.a.b, downloaded from the LMFDB on 23 April 2024.
{"label": "38.2.a.b", "space_label": "38.2.a", "level": 38, "weight": 2, "hecke_orbit": 2, "hecke_orbit_code": 4503599660924966, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 51301870551309226, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[3, [1, 1]]], "qexp_display": "q+q^{2}-q^{3}+q^{4}-4q^{5}-q^{6}+3q^{7}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 152, "fricke_eigenval": -1, "atkin_lehner_string": "-+", "analytic_conductor": 0.30343152768086545, "hecke_ring_index": 1, "level_radical": 38, "field_poly_is_cyclotomic": false, "field_poly_root_of_unity": 0, "field_poly_is_real_cyclotomic": false, "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": "0.015", "prec": 17}, "analytic_rank_proved": true, "char_values": [38, 1, [21], [1]], "hecke_ring_generator_nbound": 1, "inner_twist_count": 1, "level_primes": [2, 19], "conrey_indexes": [1], "field_disc": 1, "field_disc_factorization": [], "field_poly": [0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.026", "prec": 17}, {"__RealLiteral__": 0, "data": "0.978", "prec": 17}, {"__RealLiteral__": 0, "data": "0.086", "prec": 17}, {"__RealLiteral__": 0, "data": "1.919", "prec": 17}, {"__RealLiteral__": 0, "data": "0.256", "prec": 17}, {"__RealLiteral__": 0, "data": "4.703", "prec": 17}], "related_objects": ["EllipticCurve/Q/38/b"], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[2, -1], [19, 1]], "trace_display": [1, -1, -4, 3], "traces": [0, 1, 1, -1, 1, -4, -1, 3, 1, -2, -4, 2, -1, -1, 3, 4, 1, 3, -2, -1, -4, -3, 2, -1, -1, 11, -1, 5, 3, -5, 4, -8, 1, -2, 3, -12, -2, -2, -1, 1, -4, -8, -3, 4, 2, 8, -1, 8, -1, 2, 11, -3, -1, -1, 5, -8, 3, 1, -5, 15, 4, 2, -8, -6, 1, 4, -2, 3, 3, 1, -12, 2, -2, 9, -2, -11, -1, 6, 1, -10, -4, 1, -8, -6, -3, -12, 4, 5, 2, 0, 8, -3, -1, 8, 8, 4, -1, -2, 2, -4, 11, 2, -3, -6, -1, 12, -1, -7, 5, -15, -8, 2, 3, 14, 1, 4, -5, 2, 15, 9, 4, -7, 2, 8, -8, -24, -6, 18, 1, -4, 4, 12, -2, -3, 3, -20, 3, -17, 1, 0, -12, -8, 2, -2, -2, 20, 9, -2, -2, 0, -11, 2, -1, -6, 6, 32, 1, -2, -10, 1, -4, -3, 1, -16, -8, 8, -6, -12, -3, -12, -12, 2, 4, -6, 5, 33, 2, -15, 0, 0, 8, 22, -3, -2, -1, 8, 8, 6, 8, 15, 4, 7, -1, -6, -2, -4, 2, 8, -4, -25, 11, -3, 2, -15, -3, 32, -6, 2, -1, -2, 12, 27, -1, -2, -7, -16, 5, -24, -15, -9, -8, -3, 2, 14, 3, -22, 14, -17, 1, -10, 4, -6, -5, -6, 2, -32, 15, 10, 9, 15, 4, -8, -7, -16, 2, -8, 8, 1, -8, 6, -24, 2, -6, -2, 18, 12, 1, 8, -4, -6, 4, 10, 12, 24, -2, 4, -3, 0, 3, 30, -20, 7, 3, 3, -17, 22, 1, 28, 0, 16, -12, -8, -8, -6, 2, -4, -2, -24, -2, -8, 20, 2, 9, 9, -2, -60, -2, 10, 0, 1, -11, 12, 2, -2, -1, -8, -6, -12, 6, 6, 32, 7, 1, 29, -2, 24, -10, -27, 1, -10, -4, 7, -3, -3, 1, -11, -16, 15, -8, 24, 8, 17, -6, 4, -12, -12, -3, -32, -12, -14, -12, -16, 2, -15, 4, -4, -6, -2, 5, 10, 33, -5, 2, 9, -15, -8, 0, -9, 0, -15, 8, 1, 22, 7, -3, -36, -2, 28, -1, 16, 8, -3, 8, 29, 6, 24, 8, 5, 15, 15, 4, -18, 7, -26, -1, -24, -6, -8, -2, -30, -4, -3, 2, -12, 8, 40, -4, 8, -25, 3, 11, -8, -3, 8, 2, -4, -15, -4, -3, -20, 32, 17, -6, 45, 2, 24, -1, 0, -2, 0, 12, -13, 27, -16, -1, 33, -2, 6, -7, 2, -16, -18, 5, 14, -24, -20, -15, 1, -9, 20, -8, -4, -3, -26, 2, 0, 14, 0, 3, 10, -22, -16, 14, -2, -17, 12, 1, -7, -10, 15, 4, -28, -6, 4, -5, -32, -6, -2, 2, 9, -32, 2, 15, 8, 10, -11, 9, 2, 15, -20, 4, 2, -8, 3, -7, 8, -16, -2, 2, 16, -8, -28, 8, -15, 1, 16, -8, 6, 6, 40, -24, 12, 2, 39, -6, -8, -2, 12, 18, -30, 12, 27, 1, -5, 8, 24, -4, 16, -6, 6, 4, -28, 10, 29, 12, -33, 24, -24, -2, -22, 4, -30, -3, 8, 0, 28, 3, 0, 30, 4, -20, 2, 7, -22, 3, 60, 3, 28, -17, -4, 22, 5, 1, -30, 28, -8, 0, 28, 16, -4, -12, -6, -8, -36, -8, -56, -6, 3, 2, 40, -4, -28, -2, -7, -24, -11, -2, -37, -8, 6, 20, -18, 2, -2, 9, -8, 9, -12, -2, 8, -60, -8, -2, 34, 10, -36, 0, 25, 1, 0, -11, -8, 12, -6, 2, 28, -2, -22, -1, 15, -8, -8, -6, 34, -12, -32, 6, 18, 6, 10, 32, -5, 7, 0, 1, 41, 29, 2, -2, -6, 24, 32, -10, -27, -27, -72, 1, -2, -10, -4, -4, 42, 7, -26, -3, 16, -3, 23, 1, 30, -11, 24, -16, -36, 15, -48, -8, -18, 24, 5, 8, -23, 17, 3, -6, 12, 4, 5, -12, -14, -12, 4, -3, 44, -32, 55, -12, 13, -14, -6, -12, 17, -16, 4, 2, 68, -15, 10, 4, 1, -4, 42, -6, -12, -2, 0, 5, -24, 10, 6, 33, -28, -5, 2, 2, 32, 9, 6, -15, -30, -8, 20, 0, 8, -9, 8, 0, -15, -15, -5, 8, -18, 1, 8, 22, -55, 7, -17, -3, 13, -36, 12, -2, -36, 28, 8, -1, 6, 16, -40, 8, -1, -3, -16, 8, 0, 29, 12, 6, -21, 24, 32, 8, -2, 5, -8, 15, -2, 15, 2, 4, 27, -18, -45, 7, 24, -26, -15, -1, -35, -24, -8, -6, 9, -8, -88, -2, 6, -30, 8, -4, 4, -3, -25, 2, 8, -12, -17, 8, -24, 40, 42, -4, -2, 8, -4, -25, 3, 3, 24, 11, 0, -8, 18, -3, 12, 8, -30, 2, -15, -4, -3, -15, -7, -4, 64, -3, -4, -20, 6, 32, 12, 17, 29, -6, -22, 45, 23, 2, -15, 24, -28, -1, 6, 0, 48, -2, -40, 0, 20, 12, -4, -13, 8, 27, 48, -16, -21, -1, 6, 33, 2, -2, -6, 6, -8, -7, -12, 2, -50, -16, 24, -18, 54, 5, 24, 14, 8, -24, -20, -20, -3, -15, 4, 1, -72, -9, 13, 20, -9, -8, -18, -4, 34, -3, 60, -26, -2, 2, 54, 0, 2, 14, -8, 0, 0, 3, -1, 10, 40, -22, -3, -16, -12, 14, -88, -2, 53, -17, -4, 12, 12, 1, -12, -7, 8, -10, 36, 15, 5, 4, 12, -28, -2, -6, -22, 4, 12, -5, -55, -32, -2, -6, -7, -2, -24, 2, -7, 9, -29, -32, 7, 2, 8, 15, -60, 8, -12, 10, -9, -11, 27, 9, -46, 2, -28, 15, 10, -20, -51, 4, 33, 2, 14, -8, 24, 3, 48, -7, 3, 8, -28, -16, 0, -2, 11, 2, 8, 16, 0, -8, 30, -28, -6, 8, -32, -15, -24, 1, -4, 16, -8, -8, -17, 6, 100, 6, 28, 40, -10, -24], "weight_parity": 1, "has_non_self_twist": 0, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": false, "level_is_squarefree": true, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "38.2.a.b", "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], [1], [1], [-1], [1], [-4], [-1], [3], [1], [-2], [-4], [2], [-1], [-1], [3], [4], [1], [3], [-2], [-1], [-4], [-3], [2], [-1], [-1], [11], [-1], [5], [3], [-5], [4], [-8], [1], [-2], [3], [-12], [-2], [-2], [-1], [1], [-4], [-8], [-3], [4], [2], [8], [-1], [8], [-1], [2], [11], [-3], [-1], [-1], [5], [-8], [3], [1], [-5], [15], [4], [2], [-8], [-6], [1], [4], [-2], [3], [3], [1], [-12], [2], [-2], [9], [-2], [-11], [-1], [6], [1], [-10], [-4], [1], [-8], [-6], [-3], [-12], [4], [5], [2], [0], [8], [-3], [-1], [8], [8], [4], [-1], [-2], [2], [-4], [11]]}