# Stored data for newform 363.2.d.b, downloaded from the LMFDB on 15 May 2025.
{"Nk2": 1452, "analytic_conductor": 2.898569593372478, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 33, "char_degree": 1, "char_is_minimal": true, "char_is_real": true, "char_orbit_index": 4, "char_orbit_label": "d", "char_order": 2, "char_parity": 1, "char_values": [363, 2, [122, 244], [1, 1]], "cm_discs": [], "conrey_index": 362, "dim": 2, "field_disc": -8, "field_disc_factorization": [[-1, 1], [2, 3]], "field_poly": [2, 0, 1], "field_poly_is_cyclotomic": false, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 0, "has_non_self_twist": 1, "hecke_cutters": [[2, [-1, 1]]], "hecke_orbit": 2, "hecke_orbit_code": 4503805819355499, "hecke_ring_generator_nbound": 3, "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, 33, 4, 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": true, "label": "363.2.d.b", "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.d.a", "nf_label": "2.0.8.1", "prim_orbit_index": 4, "qexp_display": "q+q^{2}+(1+\\beta )q^{3}-q^{4}+2\\beta q^{5}+(1+\\cdots)q^{6}+\\cdots", "related_objects": ["EllipticCurve/2.2.33.1/121.1/h", "ModularForm/GL2/TotallyReal/2.2.33.1/holomorphic/2.2.33.1-121.1-h"], "relative_dim": 2, "rm_discs": [], "sato_tate_group": "1.2.3.c2", "self_twist_discs": [], "self_twist_type": 0, "space_label": "363.2.d", "trace_display": [2, 2, 0, 0], "trace_hash": 1294383677999476665, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.884", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "14.329", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "135.950", "prec": 24}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.518", "prec": 17}, "traces": [0, 2, 2, 2, -2, 0, 2, 0, -6, -2, 0, 0, -2, 0, 0, -8, -2, 12, -2, 0, 0, 4, 0, 0, -6, -6, 0, -10, 0, -4, -8, -4, 10, 0, 12, 8, 2, 16, 0, -12, 0, 12, 4, 0, 0, -16, 0, 0, -2, 10, -6, 12, 0, 0, -10, 0, 0, 12, -4, 0, 8, 0, -4, 8, 14, -24, 0, 4, -12, 0, 8, 0, 6, 0, 16, -6, 0, 0, -12, 0, 0, -14, 12, -32, -4, 0, 0, -4, 0, 0, -16, 12, 0, -4, 0, 24, 10, -4, 10, 0, 6, -20, 12, 16, 0, 8, 0, -32, 10, 0, 0, 16, 0, 0, 12, 0, 4, -24, 0, 0, 24, 0, 0, 12, 4, 0, 8, 0, -6, 12, -24, 0, 0, -12, 4, -8, -36, 0, 0, 0, -8, -8, 0, 0, 2, 0, 0, 10, -16, 12, -6, 0, 0, -12, 0, 0, 12, -40, 0, -16, 0, 0, -14, 40, -12, 0, -32, 24, -12, -10, 0, 24, 0, 12, -4, 0, 0, 32, 0, 0, 16, -20, 12, 28, 0, 0, -4, 0, 0, 4, 24, 0, 14, 0, -4, -24, -10, 44, 0, 4, 18, 4, -20, 0, -12, 0, 16, 0, 0, 0, 8, 0, 0, -8, -32, 24, 30, 0, 0, 4, 0, 0, 16, 48, 0, 6, 0, -48, -12, -48, 0, 0, 12, -20, -24, -16, 0, -12, 0, -32, 8, 0, 0, 2, 0, 0, 12, 36, 12, -32, 0, 0, -8, 0, 0, -48, -34, 0, 12, 0, 24, 4, 0, 0, 0, -32, -12, 0, -4, 0, -8, 0, -12, 12, 0, 0, 0, 0, 0, 4, -24, 12, -8, 0, 0, 24, 0, 0, -10, 38, 0, -4, 0, -4, 10, 64, -48, 0, 12, 0, 6, -12, 0, -20, 0, 56, -12, 0, 0, 16, 0, 0, 36, 24, -40, -8, 0, 0, -16, 0, 0, -32, 0, 0, 14, 0, 40, 12, -36, 8, 0, -40, 32, -16, 24, 0, -4, 0, -10, -8, 0, 0, 24, 0, 0, 0, 12, -32, 4, 0, 0, -12, 0, 0, 32, -16, 0, 24, 0, 40, 48, 2, -20, 0, -12, 8, 28, 16, 0, -12, 0, 16, 4, 0, 0, -16, 0, 0, 4, 24, -24, 28, 0, 0, -6, 0, 0, 24, 4, 0, -24, 0, -30, 0, 44, -24, 0, 4, 4, -12, 6, 0, 4, 0, 20, 32, 0, 0, -36, 0, 0, -8, -16, -32, 0, 0, 0, 4, 0, 0, -8, -40, 0, -16, 0, -36, -8, -28, 32, 0, 24, -64, 10, 60, 0, 16, 0, 0, 4, 0, 0, -10, 0, 0, -16, 0, 48, 12, 0, 0, 6, 0, 0, 12, -48, 0, -36, 0, -48, -60, 0, 44, 0, 48, 4, 16, -20, 0, 24, 0, -16, -40, 0, 0, -12, 0, 0, -32, -32, 56, -40, 0, 0, 0, 0, 0, 2, 4, 0, 40, 0, 40, -12, -24, 36, 0, 4, 8, -32, -28, 0, 24, 0, -32, -24, 0, 0, -10, 0, 0, -48, -4, -22, 12, 0, 0, -12, 0, 0, 12, 72, 0, 4, 0, 0, -12, 0, -24, 0, 46, -32, 64, 12, 0, 0, 0, -12, -8, 0, 0, 8, 0, 0, -20, 60, 24, 12, 0, 0, 56, 0, 0, 0, 12, 0, -64, 0, -4, 4, 36, -8, 0, 12, 24, 8, -16, 0, -16, 0, -76, 24, 0, 0, -56, 0, 0, -14, -64, 38, -60, 0, 0, -4, 0, 0, 24, -4, 0, -10, 0, 64, 44, -16, -44, 0, 48, -12, 4, 0, 0, 18, 0, -12, -4, 0, 0, -20, 0, 0, -8, 56, -24, 12, 0, 0, -48, 0, 0, 16, -40, 0, 0, 0, 0, 12, -62, 24, 0, 40, 96, -8, -28, 0, 76, 0, 56, 16, 0, 0, -16, 0, 0, -32, 24, 0, 24, 0, 0, 42, 0, 0, -8, -40, 0, 12, 0, -12, 8, 8, 0, 0, -40, -40, -72, 96, 0, -16, 0, -24, 48, 0, 0, 20, 0, 0, 30, 10, -76, -8, 0, 0, -48, 0, 0, -24, -16, 0, -48, 0, -48, 0, 40, -12, 0, -32, 8, 12, 72, 0, -20, 0, 12, -12, 0, 0, -16, 0, 0, -32, -64, -16, -24, 0, 0, 24, 0, 0, -32, 40, 0, 16, 0, 2, 12, 20, 12, 0, 4, -36, 46, 8, 0, -28, 0, 16, -40, 0, 0, -12, 0, 0, 36, 16, -32, 12, 0, 0, 32, 0, 0, -16, 4, 0, 72, 0, 24, -4, 40, 24, 0, -72, -20, 28, -12, 0, -96, 0, 96, -34, 0, 0, 32, 0, 0, 24, 12, 12, 32, 0, 0, 24, 0, 0, 20, -10, 0, 0, 0, -44, 0, -24, 8, 0, 84, 4, -32, -4, 0, -12, 0, -30, 0, 0, 0, -4, 0, 0, 80, 60, 100, 32, 0, 0, -84, 0, 0, -12, -36, 0, -12, 0, 84, -8, -48, -48, 0, -32, 24, 0, -28, 0, -12, 0, 60, 4, 0, 0, 20, 0, 0, -24, -50, -40, 12, 0, 0, -16, 0, 0, -76, -36, 0, 8, 0, -28, -24, 96, -44, 0, -40, -24, 24, -64, 0, -50, 0, 60, 38, 0, 0, 16, 0, 0, 4, 0, 16, -4, 0, 0, -4, 0, 0, -10, 92, 0, 64, 0, -48, -48, -28, 0, 0, -48, 24, 12, -16, 0, 0, 0, 8, -6, 0, 0, -12, 0, 0, 12, 24, 48, 20, 0, 0, -12, 0, 0, 56, 48, 0, -60, 0, 0, 12, 44, -24, 0, -48, 48, -16, -20, 0, 16, 0, 20, 80, 0, 0, 72, 0, 0, 24, 16, -76, -40, 0, 0, -40, 0, 0, 12, 12, 0, 72, 0, -4, -32, -112, 32, 0, 56, 8, -56, -54, 0, 32, 0, -120, 0, 0, 0, 72, 0, 0, -2, -4, 4, 36, 0, 0, 40, 0, 0, 24, 40, 0, -36, 0, -24, 8, -36, 0, 0, -84, -20, -40, 8, 0, 32, 0, -28, -80, 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], [1, 0], [1, 1], [-1, 0], [0, 2], [1, 1], [0, -1], [-3, 0], [-1, 2], [0, 2], [0, 0], [-1, -1], [0, 3], [0, -1], [-4, 2], [-1, 0], [6, 0], [-1, 2], [0, -3], [0, -2], [2, -1], [0, 0], [0, 0], [-3, -3], [-3, 0], [0, 3], [-5, 1], [0, 1], [-2, 0], [-4, 2], [-2, 0], [5, 0], [0, 0], [6, 0], [4, 0], [1, -2], [8, 0], [0, -3], [-6, 3], [0, -6], [6, 0], [2, -1], [0, -3], [0, 0], [-8, -2], [0, 0], [0, 2], [-1, -1], [5, 0], [-3, 0], [6, 6], [0, -3], [0, 4], [-5, 1], [0, 0], [0, 3], [6, -3], [-2, 0], [0, -8], [4, -2], [0, -7], [-2, 0], [4, 1], [7, 0], [-12, 0], [0, 0], [2, 0], [-6, 0], [0, 0], [4, 0], [0, 2], [3, -6], [0, -1], [8, 0], [-3, -3], [0, 3], [0, 0], [-6, 3], [0, 3], [0, -2], [-7, -4], [6, 0], [-16, 0], [-2, 1], [0, 12], [0, -3], [-2, -2], [0, 0], [0, 0], [-8, -2], [6, 0], [0, 0], [-2, -2], [0, 2], [12, 0], [5, 5], [-2, 0], [5, 0], [0, 0], [3, 0]]}