# Stored data for newform 93.2.e.a, downloaded from the LMFDB on 18 January 2026. {"Nk2": 372, "analytic_conductor": 0.7426087387979076, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 31, "char_degree": 2, "char_is_minimal": true, "char_is_real": false, "char_orbit_index": 5, "char_orbit_label": "e", "char_order": 3, "char_parity": 1, "char_values": [93, 3, [32, 34], [3, 1]], "cm_discs": [], "conrey_index": 25, "dim": 4, "field_disc": 576, "field_disc_factorization": [[2, 6], [3, 2]], "field_poly": [4, 0, 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, [-2, 0, 1]]], "hecke_orbit": 1, "hecke_orbit_code": 274911461469, "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, 31, 3, 1, 3, 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": "93.2.e.a", "level": 93, "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": true, "level_primes": [3, 31], "level_radical": 93, "minimal_twist": "93.2.e.a", "nf_label": "4.0.576.2", "prim_orbit_index": 3, "qexp_display": "q+\\beta _{3}q^{2}+(1+\\beta _{2})q^{3}+(-\\beta _{1}-2\\beta _{2}+\\cdots)q^{5}+\\cdots", "related_objects": [], "relative_dim": 2, "rm_discs": [], "sato_tate_group": "1.2.3.c3", "self_twist_discs": [], "self_twist_type": 0, "space_label": "93.2.e", "trace_display": [0, 2, 4, 4], "trace_hash": 692609956002903239, "trace_moments": [{"__RealLiteral__": 0, "data": "0.033", "prec": 17}, {"__RealLiteral__": 0, "data": "3.944", "prec": 17}, {"__RealLiteral__": 0, "data": "0.264", "prec": 17}, {"__RealLiteral__": 0, "data": "56.069", "prec": 20}, {"__RealLiteral__": 0, "data": "13.646", "prec": 20}, {"__RealLiteral__": 0, "data": "1313.371", "prec": 27}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.018", "prec": 17}, "traces": [0, 4, 0, 2, 0, 4, 0, 4, 0, -2, -4, 0, 0, 2, -8, 8, -16, -8, 0, 2, 0, -4, 4, -8, 0, -2, -8, -4, 0, -8, -8, 8, 0, 0, -8, 32, 0, -2, 8, 4, 8, 0, 8, -6, 0, 4, 32, 8, -8, -10, 16, 8, 0, 0, 0, 4, 16, -2, -8, 0, 0, -16, 0, -8, 32, -12, 8, 12, 0, -4, -48, -12, 0, -2, 0, 2, 0, -16, -16, -20, -16, -2, 12, 12, 0, -16, 24, -4, -8, -32, -4, 40, 0, -14, -8, -8, 0, -12, 32, 0, 0, -56, 8, -10, 16, 16, 4, 12, 0, 4, -8, 2, -16, 20, -8, -24, 0, 2, 24, 0, 16, 18, -48, 0, 0, 0, 16, -22, 0, 6, 20, 24, 0, 12, 24, -4, 16, 28, 16, 56, 0, 4, 0, 8, 8, -4, -8, -20, 0, 12, -16, -20, -16, 16, 16, 44, 0, 20, -16, 0, 0, -40, 0, 4, 0, -4, 4, -4, -16, 8, 0, -4, 0, 4, -4, 36, 0, 0, -56, 36, 0, -18, -48, -8, -64, -8, 0, -16, 0, -4, 24, -8, 16, 6, -48, 12, 0, 0, 4, -4, -32, 24, -8, 0, 0, 12, -32, 4, -8, 16, -24, -6, 0, -24, -28, -72, 0, -28, 48, -4, 0, 16, 0, -22, 0, 4, 16, -16, 0, 6, 40, -8, 16, 96, -8, 12, 0, 20, -16, -12, -32, -22, 0, 2, 0, 52, 24, -28, 0, 24, 32, 36, 0, 16, 16, -8, 0, -12, -24, 4, 0, 4, 12, -40, -16, 4, -8, -16, 0, 0, 4, -12, 32, 20, 4, 32, 0, 68, 0, -22, 96, 16, -4, 28, 0, -4, -4, -48, 0, -14, 0, -6, 0, -20, 64, -48, 0, 0, 0, -36, 0, 60, 64, -28, -8, 8, 16, -38, 0, -20, -44, -40, 32, 34, 16, -16, 0, 36, 8, -4, 32, -12, 48, 24, 0, -68, -32, 2, -24, 16, 8, -6, 0, 4, -28, 0, 16, -16, 16, 40, 0, 0, -16, -112, -48, -48, -32, -32, 0, 76, -40, -2, 0, -60, -24, 24, 0, 0, -12, 12, 8, 20, 24, -18, 0, -4, -24, -10, 32, 0, 8, -16, 0, -84, -32, 0, 16, 4, 8, -14, 0, 22, 20, -24, 0, -24, -48, 12, 0, 12, -20, -16, -64, -24, -8, -48, 0, 16, 40, 24, 8, -48, 48, 22, 0, -8, 8, 0, -16, 30, -24, 56, 0, 48, -16, -20, 0, 28, 8, 24, 0, 44, 24, -4, -8, 24, 0, 32, 0, -8, 120, -20, 16, -4, 56, -8, 0, 28, -16, -10, 16, -10, 48, 12, 0, -4, -16, -12, 32, -96, -32, -12, 0, -10, -8, 64, 16, 108, 24, 8, 0, -48, 8, 44, 32, 16, 0, 8, 0, -48, -16, 10, -48, 48, 16, -30, 0, 0, -56, 12, 0, -4, 48, 40, 0, 12, 0, -30, 96, 2, -84, 8, 0, 24, 0, -8, -32, -48, 8, 44, 0, 4, 20, 24, -32, -52, -8, -8, 0, -36, 0, 24, 0, -2, -12, -12, 0, -4, -8, 8, -40, -20, 4, 24, 0, 72, -16, 56, 0, 52, -8, 0, 0, 24, -28, 104, -48, -36, 56, -32, 0, -42, -144, -36, 0, -20, -24, 2, 0, 8, -8, -12, -32, 8, -32, -4, 0, 72, 0, -108, -128, -8, -136, 24, 0, -24, 48, 4, 0, 12, 12, 14, 0, -16, 48, 68, -16, -16, -64, -6, 0, 32, -24, -4, 16, 24, -8, 24, 0, -14, 96, 0, 8, -144, -4, -16, 0, -8, 32, -20, 32, -20, -72, 12, 0, 72, -4, 30, 0, 0, -32, 12, 0, -58, 32, -12, -32, 24, -64, 84, 0, 8, -56, 24, -16, -6, -32, 8, 0, -8, 24, -52, 32, 6, 12, -120, 0, 74, -8, -12, -32, 12, 28, -4, 0, -36, 40, 120, 0, 48, 48, -44, 0, 0, 24, 72, 0, -2, -24, 80, 0, 26, 0, 8, -8, -32, 0, -16, 0, 22, -24, -24, 0, 8, 128, 2, 0, -16, 32, 36, 0, -32, 44, -72, 0, -52, 96, -6, 24, 8, 80, -4, 0, 8, -4, 56, 8, -48, 80, 48, 0, 72, 8, 2, 0, 24, 8, -48, 0, -12, -24, 40, 112, -16, -32, 40, 0, -24, -68, -44, -16, 88, -16, 22, 0, -12, 0, 10, 96, 4, 12, 24, 0, -46, -40, -52, 0, -24, 12, 26, 0, -14, 16, 8, 0, 48, -48, 12, 0, -80, 16, 30, -32, -36, 12, -52, 0, -56, -8, 32, -48, -68, -16, -44, 0, 8, 52, -96, 0, -24, 32, -24, 0, -104, -48, 14, 96, 8, 32, 48, 0, 0, -48, 8, 40, 12, -12, -26, 0, -20, 16, 16, -8, 40, -48, -4, 0, 24, -16, -8, 0, 16, -16, 8, 0, -256, -88, 0, 16, 48, 8, -38, 0, -6, -8, 20, -32, -42, -24, -20, 0, -72, 8, 52, 64, 16, -48, 60, 0, -76, 16, 34, 16, -48, 0, 40, 0, -8, 96, -96, 48, -92, 0, 8, 0, 0, 4, -36, 0, 14, 56, 4, 0, -52, -16, 4, 56, 48, 4, -46, 0, -24, 16, 8, 0, -40, -16, -28, 0, -32, 0, 36, -96, 6, 0, -32, 0, 42, 24, 20, -16, 44, 32, -12, 0, -24, -40, -24, 0, 76, -24, 0, 0, -4, 0, 168, -64, -72, 32, -16, 0, -16, 0, 120, -32, 60, 32, -136, 0, 28, -88, 48, 8, -4, 48, 16, 0, -24, 8, 42, -80, 38, 88, 12, 0, -2, 144, -10, 0, -24, -16, 108, 0, -20, -64, 0, 16, 30, 0, -34, 0, -24, 8, 48, 0, -32, -24, -4, 0, -14, -8, -36, 32, 8, 4, 36, 0, -8, 16, 96, 64, -92, 16, -24, 0, 120, -48, -44, 0, 48, -36, -12, 0, 56, 24, -34, 64, 48, -16, -28, 0, -2, 80, 20, -48, -8, 32, -16, 0, 108, 16, 124, 0, -12, 96, 48, 0, 72, -40, 2, -64], "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, 0, 0], [1, 0, 0, 0], [0, 0, 0, 1], [1, 0, 1, 0], [0, 0, 0, 0], [0, -1, -2, -1], [0, -1, 0, 0], [2, 2, 2, 0], [0, 0, 0, -2], [0, 0, 1, 0], [0, 2, 2, 2], [0, 1, 0, 1], [0, 0, 0, 0], [0, -2, -1, -2], [-4, -2, -4, 0], [2, 0, 0, -1], [-4, 0, 0, 0], [-4, 2, -4, 0], [0, -1, 0, -1], [1, -2, 1, 0], [0, 0, 0, 0], [0, 2, 2, 2], [0, 0, -2, 0], [-2, 0, 0, 4], [0, 2, 0, 0], [-1, -4, -1, 0], [0, 1, 4, 1], [-1, 0, 0, 0], [0, 0, 0, 0], [-2, 0, 0, -1], [-2, 0, 0, 2], [5, 0, 6, 0], [0, 0, 0, 0], [0, 0, 0, 1], [-4, 4, -4, 0], [8, 0, 0, -6], [0, 0, 0, 0], [-1, 0, -1, 0], [4, -1, 4, 0], [1, 0, 0, -2], [0, -4, -4, -4], [0, 3, 0, 3], [0, -2, -4, -2], [-3, -6, -3, 0], [0, 0, 0, 0], [2, 1, 2, 0], [8, 0, 0, -2], [2, 0, 0, -1], [-4, 0, -4, 0], [0, 8, 5, 8], [8, 1, 8, 0], [0, 2, -4, 2], [0, 0, 0, 0], [0, 1, 0, 1], [0, 0, 0, -1], [2, 2, 2, 0], [8, 4, 8, 0], [0, -2, 1, -2], [-2, 0, 0, -2], [0, -6, 0, 0], [0, 0, 0, 0], [-4, 0, 0, -6], [0, -6, 0, -1], [-2, 0, 0, 2], [8, 0, 0, 0], [-6, -5, -6, 0], [2, 0, 0, 0], [0, 6, -6, 6], [0, 0, 0, 0], [-2, -4, -2, 0], [-12, 0, 0, 8], [0, 0, 6, 0], [0, 2, 0, 2], [0, -2, 1, -2], [0, 1, 0, 0], [0, -4, -1, -4], [0, 0, 0, 0], [-4, 0, 0, 2], [-4, 0, 0, 1], [-10, 4, -10, 0], [0, 4, 8, 4], [-1, 0, -1, 0], [0, 0, -6, 0], [0, 1, -6, 1], [0, 0, 0, 0], [-4, 0, 0, 0], [12, 3, 12, 0], [-2, 1, -2, 0], [0, 0, 4, 0], [-8, 0, 0, -7], [-2, -2, -2, 0], [10, 0, 0, -6], [0, 0, 0, 0], [-1, 0, 5, 0], [-2, 0, 0, 2], [-2, 0, 0, 3], [0, 0, 0, 0], [-3, 0, 0, -6], [0, -5, -16, -5], [0, -1, 0, 0], [0, 0, 0, 0]]}