# Stored data for newform 231.2.i.e, downloaded from the LMFDB on 23 April 2024.
{"label": "231.2.i.e", "space_label": "231.2.i", "level": 231, "weight": 2, "hecke_orbit": 5, "hecke_orbit_code": 18014948298850535, "dim": 8, "is_polredabs": true, "trace_hash": 1365171378130121212, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[2, [9, -12, 28, 4, 21, 0, 8, 2, 1]]], "qexp_display": "q-\\beta _{1}q^{2}+(-1+\\beta _{4})q^{3}+(\\beta _{1}+\\beta _{2}+\\cdots)q^{4}+\\cdots", "char_order": 3, "char_parity": 1, "char_degree": 2, "char_conductor": 7, "char_orbit_label": "i", "char_is_real": false, "Nk2": 924, "analytic_conductor": 1.8445442866915769, "hecke_ring_index": 1, "level_radical": 231, "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": false, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.014", "prec": 17}, "analytic_rank_proved": true, "char_values": [231, 3, [155, 199, 211], [3, 2, 3]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 2, "level_primes": [3, 7, 11], "conrey_indexes": [67, 100], "field_disc": 10423593216, "field_disc_factorization": [[2, 8], [3, 4], [709, 2]], "field_poly": [9, 12, 28, -4, 21, 0, 8, -2, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.083", "prec": 17}, {"__RealLiteral__": 0, "data": "7.648", "prec": 17}, {"__RealLiteral__": 0, "data": "4.767", "prec": 17}, {"__RealLiteral__": 0, "data": "280.332", "prec": 24}, {"__RealLiteral__": 0, "data": "330.517", "prec": 24}, {"__RealLiteral__": 0, "data": "19976.696", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "1.2.3.c3", "trace_display": [-2, -4, -4, 2], "traces": [0, 8, -2, -4, -4, -4, 4, 2, 24, -4, -10, 4, -4, -4, -4, 8, -12, -2, -2, 0, 0, -4, -4, -4, -12, -4, 4, 8, -22, 16, -10, 12, -26, 4, -32, -2, 8, 4, -8, 2, 6, 4, 20, 36, 4, -4, 14, -12, 24, -4, 4, -2, 6, 12, -2, -8, 48, 0, 4, -12, 0, -2, -52, 2, 112, 4, 2, -28, 48, 8, -32, 24, -12, -6, 16, -4, -36, 4, -8, -2, -16, -4, 12, -24, -4, 36, -36, -8, 12, -8, 20, 12, -32, 12, -20, -34, -26, -88, 16, -8, 24, -32, 16, 8, 16, 16, 36, -6, -4, -14, 10, -8, -86, -32, -8, 8, 2, 2, -44, 20, -12, -4, -20, -2, 52, 24, -16, 64, -68, -18, 24, -30, -8, 32, -44, -4, 72, 0, 14, 4, 24, 24, 8, -2, -12, -2, 48, 20, -72, -2, -2, -42, 64, 4, -20, -24, 6, 16, 28, 12, 36, 82, 4, -4, -14, 4, -4, 88, -12, -64, 0, 0, -24, -14, -8, -40, -24, -12, 0, -8, 0, -40, 2, 4, 44, 0, 26, 2, 88, 2, 40, 4, -56, -12, 20, -8, -76, 28, 2, 68, 80, -28, 72, -28, -96, 36, 8, -4, -18, 0, 40, -28, -32, -12, 72, -66, 24, 74, -80, -6, 0, -4, 16, -72, -112, 8, 82, 16, 18, -28, 84, -2, -8, -8, 4, -8, 24, 4, -106, 60, -16, 24, -2, -4, 52, 44, -24, 20, 54, 12, 4, -16, 26, -8, -12, -18, -84, 4, 72, 4, -8, -8, -44, -36, 12, -16, -16, 16, 4, -24, -10, -18, -236, 24, 16, 4, 16, 16, -44, -24, -120, -16, -20, 30, -8, -34, 8, -40, 52, -16, -36, 44, -118, 8, 16, -16, 58, 4, 16, 34, -48, 56, -56, -32, 60, -16, 16, 44, 4, -16, 72, 36, -8, 48, 60, -14, -12, 56, -18, 8, -52, 12, 16, 88, -4, 38, -50, -14, 56, 0, -20, 16, 0, 4, 28, -24, 118, 16, 22, 16, 50, -12, 16, 14, 64, 8, 24, -50, 2, -148, -64, -4, 26, 20, 22, 12, 176, 8, 32, -22, 6, -4, 52, 8, -16, -128, -20, 28, 124, -2, -28, 54, -104, -6, -16, -12, -82, -40, -4, -152, 18, -32, -24, 16, 136, -16, -152, -18, 56, 56, 24, 52, 180, 60, -16, 48, 4, 16, -168, -4, -232, 40, 22, -48, -86, 8, -10, 8, 72, 2, -20, 0, 32, 60, -28, 4, 32, -2, 8, 56, -18, 32, 40, -12, -94, -58, -16, -44, -180, -2, -52, -34, -12, -136, -140, 4, 46, -24, -24, 42, 12, -16, -36, -20, 36, 80, -46, 4, 186, -32, -2, 2, 96, -42, 32, -64, -128, -42, 0, -2, 20, -28, 16, 40, 44, 12, 4, 0, -12, 54, 68, 16, -36, 18, 28, 184, 120, -24, 4, 0, -18, -6, 96, -62, 8, 28, -2, -84, -48, 8, 38, -4, -14, -16, 34, 4, -144, 18, 8, -32, 28, -44, -80, -44, -36, 36, -14, 32, 2, -60, 0, -52, 180, 0, 108, 40, -24, -24, 44, 28, -52, -48, 4, 18, 132, 74, 112, -54, 12, -8, 96, 24, -76, -32, 0, 48, -102, -8, -4, -20, 0, 2, 44, 20, 204, -40, -16, -64, -96, -2, 2, -12, -88, 124, 40, 0, -28, 2, 26, -32, 22, -4, 32, 22, -44, 84, 144, -4, 164, -30, -20, -44, -6, -8, -90, 152, -56, -12, -98, -12, -20, 84, -40, -12, -196, 4, -104, 80, -28, -44, 14, -14, 96, 20, -4, -24, -152, 68, -8, 36, 80, -16, 72, 56, -36, -4, -36, 82, -128, -16, -16, 10, 48, 4, 96, -72, 12, 16, 8, 20, 40, -4, -76, 8, 36, -12, -12, 0, 24, 96, -8, -32, 28, 14, 86, -58, 64, -4, 8, -12, -130, -36, 72, 104, -118, 132, -94, 32, -12, 12, -64, -70, 160, 4, 40, -52, 26, 12, -76, 0, 0, 12, 16, -4, 96, -128, -32, -56, 48, 36, -24, -4, -16, -12, -60, -4, 68, -26, -164, 18, -176, 16, -26, -40, 18, -160, -136, 56, -106, -72, -42, 4, -108, -2, -32, -62, 4, 36, 96, 16, 16, 188, 4, -18, 56, -8, -4, -76, -48, 28, 10, -2, -188, -112, 26, 8, 48, -30, -60, -12, 32, 144, 76, 24, 16, -44, -2, 56, 8, 8, -40, -24, -26, -94, 92, -76, -140, 28, 12, 58, 32, -40, 24, 264, 54, -46, -44, 12, 96, -72, -8, 12, -120, 8, 2, -100, -22, -16, 34, 4, 96, 10, 24, 64, -56, -18, -46, -38, -84, 96, -40, -8, 120, -28, -36, 56, -244, -26, 288, 48, 4, 12, -108, 16, -36, 136, -44, 46, -140, -36, 104, -136, -24, -12, 68, 8, 132, 128, 86, -88, 86, -8, 66, 6, -8, -86, 24, -24, -160, 94, -10, -4, 16, 36, -16, -24, 118, -76, -200, -36, 24, -34, -8, -12, 44, -8, 8, -128, 16, -72, 100, 16, -108, 160, 88, -36, -18, 12, 16, 24, 84, -152, 70, 8, -58, 8, 40, 2, 464, 30, -140, -16, -8, -104, -46, 68, 24, 32, -4, 52, 12, -4, 192, -60, -26, -20, 60, 32, 154, -4, -36, -32, 0, 44, 224, -120, 236, -46, 80, -4, 16, -16, -32, 80, 8, 8, 22, 26, -116, 64, 40, 4, -4, 18, 16, 176, -220, -68, -72, 46, 24, 70, 24, -52, -228, 108, 28, 24, -72, 64, 60, 24, 60, -12, -80, -16, 304, -180, -32, -112, 142, -22, -20, 68, -26, 48, -76, 8, -4, 44, -144, 102, 52, 36, -178, 18, -8, -8, 116, -96, -32, -40, -30, -58, -8, -2, -72, -112, 6, 28, -136, -112, 300, -36, -18, -72, 22, 8, -264, -84, 104, -36, 0, -6, -24, -40, -8, 224, -12, -44, 146, 76, 8, 112, 292, 38, -118, -28, -50, -16, 108, 28, -60, -92, -28, 94, 60, 30, 40, 22, 10, -96, 258, -32, -56, -208, 0, -60, -182, 4, -280], "weight_parity": 1, "has_non_self_twist": 1, "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], [1, 1, 7, 3, 1, 3, 0]], "char_orbit_index": 9, "prim_orbit_index": 3, "minimal_twist": "231.2.i.e", "char_is_minimal": true, "conrey_index": 67, "id": null, "nf_label": null, "fricke_eigenval": null, "atkin_lehner_string": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "atkin_lehner_eigenvals": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0], [0, -1, 0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 1, 0, 0, 0], [0, 1, 1, 1, 0, 0, 1, 0], [0, -1, 0, 0, -1, 0, 1, 0], [0, 0, 0, -1, 0, 0, 0, 0], [0, 0, 0, -1, 0, -1, 0, -1], [2, 0, -2, -1, 0, 0, 0, -1], [0, 0, 0, 0, -1, 0, 0, 0], [-2, 0, 0, 0, 2, -1, 0, -1], [1, 0, 0, 0, -1, 0, 0, 0], [0, -1, 0, 0, 0, 0, -1, 0], [0, 0, 0, 0, 0, 0, 0, -1], [1, -1, 1, -1, -2, 0, -1, 0], [1, 0, 1, -1, 0, 0, 0, 0], [0, -4, 0, 0, -1, -2, -2, 0], [-2, -1, -2, -1, 2, 0, -2, 0], [0, 1, 0, 1, 0, 0, 0, 0], [0, -1, 0, 0, 0, 1, 2, 0], [-1, 0, -1, -1, 0, 0, 0, 0], [0, 1, 0, 1, 0, 1, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0], [0, 2, 0, 0, -1, 2, 0, 0], [-2, 1, 2, 1, 2, 1, 2, 1], [-1, 0, -2, 0, 1, -2, -2, -2], [0, 1, 0, 0, 1, 0, -1, 0], [1, 0, 0, 0, 0, 0, 0, 0], [-2, 3, 2, 3, 0, 0, 2, 1], [2, 0, 0, 1, 0, 0, 0, 1], [0, 0, 0, 0, -2, 1, 0, 0], [1, -1, -1, -1, -1, 2, -1, 2], [-2, 5, 4, 5, 2, 0, 4, 0], [0, 0, 0, 0, 1, 0, 0, 0], [-2, 0, 3, 3, 0, 0, 0, 2], [0, 0, 2, -2, -2, 1, 0, 2], [0, 0, -1, -1, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 1, 0], [-3, -2, -2, -2, 3, -2, -2, -2], [0, 0, 0, 0, 0, 1, 0, 1], [0, -2, 0, 0, 2, -3, -2, 0], [0, 0, -2, 2, 0, 0, 0, 1], [1, 1, -2, 0, 1, 0, -1, 0], [4, 0, 2, -3, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 1, 0], [-1, 1, -1, 1, 1, 0, -1, 0], [2, 1, -4, 1, -2, 0, -4, 0], [0, -1, 0, 0, -2, 0, -1, 0], [1, 0, -2, -4, 0, 0, 0, -2], [0, 2, -3, 1, -4, 0, 0, 0], [2, 0, 4, 1, 0, 0, 0, 2], [0, 1, 0, 0, -2, 0, 2, 0], [2, 0, 0, 0, -2, -1, 0, -1], [3, 3, 1, 3, -3, 4, 1, 4], [0, -1, 0, 0, 0, 0, 0, 0], [-1, 0, -1, 1, 0, 0, 0, 0], [4, -1, -1, -7, -3, 0, 3, -2], [0, 0, 2, -1, 0, 0, 0, 1], [0, -2, 0, 0, 1, 0, 2, 0], [-5, -2, 0, -2, 5, 2, 0, 2], [1, 1, 1, 1, -1, 0, 1, 0], [0, -2, 0, 0, 0, -1, 0, 0], [-4, 0, 0, 6, 0, 0, 0, 1], [0, -1, 0, 0, 0, 0, 0, 1], [8, 0, -5, -7, 0, 0, 0, 0], [0, 2, 0, 0, 0, -2, -2, 0], [0, -1, 0, -1, 0, 0, 0, 0], [-9, -3, 1, -3, 9, 2, 1, 2], [0, 7, 0, 0, 8, 3, 4, 0], [1, 0, 0, 2, 0, 0, 0, 2], [-1, 3, -1, 3, -5, 2, 1, 0], [4, 0, -1, 1, 0, 0, 0, -2], [0, -1, 0, 0, -2, -1, -2, 0], [2, 0, 6, 0, -2, -1, 6, -1], [2, -3, -2, -3, -2, -1, -2, -1], [0, 0, 0, 0, -1, 2, 2, 0], [-2, 0, 2, 3, 0, 0, 0, 0], [0, -1, 0, -1, 0, -1, 0, 0], [-1, 0, -1, 1, 0, 0, 0, 0], [0, 4, 0, 0, 0, 3, -2, 0], [-3, -1, 5, -1, 3, 2, 5, 2], [-1, 0, 0, 0, 1, 0, 0, 0], [0, -3, 0, 0, 3, -2, 1, 0], [-2, 0, 0, -2, 0, 0, 0, -4], [2, -3, 0, 0, -2, -1, -2, -1], [6, 0, 4, 0, 0, 0, 0, 1], [0, -3, 0, 0, -6, 2, -1, 0], [-2, -1, 0, -1, 2, -1, 0, -1], [2, -1, -2, -1, -2, -1, -2, -1], [0, 2, 0, 0, 0, 0, -6, 0], [2, 0, 0, 0, 0, 0, 0, 1], [5, 0, 1, 1, -6, 0, 2, 0], [0, 0, 3, 5, 0, 0, 0, 0], [0, 1, 0, 0, 1, -2, 1, 0], [-2, 5, 2, 5, 2, 1, 2, 1], [-8, 0, -4, 0, 8, -5, -4, -5], [0, -5, 0, 0, -2, 0, -4, 0], [-10, 0, 1, -1, 0, 0, 0, -2], [4, -3, -2, 2, -2, -3, -4, 0], [-1, 0, 0, 0, 0, 0, 0, 0], [0, 5, 0, 0, 2, 0, 3, 0]]}