# Stored data for newform 88.2.g.a, downloaded from the LMFDB on 14 January 2026.
{"Nk2": 352, "analytic_conductor": 0.7026835377872673, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 88, "char_degree": 1, "char_is_minimal": true, "char_is_real": true, "char_orbit_index": 7, "char_orbit_label": "g", "char_order": 2, "char_parity": 1, "char_values": [88, 2, [23, 45, 57], [1, 1, 1]], "cm_discs": [-8], "conrey_index": 43, "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": [[3, [-2, 1]]], "hecke_orbit": 1, "hecke_orbit_code": 412350414936, "hecke_ring_generator_nbound": 2, "hecke_ring_index": 1, "hecke_ring_index_factorization": [], "hecke_ring_index_proved": true, "inner_twist_count": 4, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 8, 4, -1, 2, -8], [1, 1, 11, 2, -1, 2, 0], [1, 1, 88, 7, 1, 2, 0]], "is_cm": true, "is_largest": false, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": false, "is_self_twist": true, "is_twist_minimal": true, "label": "88.2.g.a", "level": 88, "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": [2, 11], "level_radical": 22, "minimal_twist": "88.2.g.a", "nf_label": "2.0.8.1", "prim_orbit_index": 7, "qexp_display": "q+\\beta q^{2}+2q^{3}-2q^{4}+2\\beta q^{6}-2\\beta q^{8}+\\cdots", "related_objects": ["EllipticCurve/2.2.88.1/1.1/a", "ModularForm/GL2/TotallyReal/2.2.88.1/holomorphic/2.2.88.1-1.1-a", "EllipticCurve/2.0.8.1/121.3/CMa", "EllipticCurve/2.0.8.1/121.1/CMa"], "relative_dim": 2, "rm_discs": [], "sato_tate_group": "1.2.1.d2", "self_twist_discs": [-8], "self_twist_type": 1, "space_label": "88.2.g", "trace_display": [0, 4, 0, 0], "trace_hash": 1915731114120338697, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.924", "prec": 17}, {"__RealLiteral__": 0, "data": "0.067", "prec": 17}, {"__RealLiteral__": 0, "data": "22.669", "prec": 20}, {"__RealLiteral__": 0, "data": "2.739", "prec": 17}, {"__RealLiteral__": 0, "data": "298.770", "prec": 24}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.754", "prec": 17}, "traces": [0, 2, 0, 4, -4, 0, 0, 0, 0, 2, 0, -6, -8, 0, 0, 0, 8, 0, 0, 0, 0, 0, 4, 0, 0, 10, 0, -8, 0, 0, 0, 0, 0, -12, -16, 0, -4, 0, 24, 0, 0, 0, 0, 0, 12, 0, 0, 0, 16, -14, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, -16, 0, 8, 28, 0, 0, 0, 0, 0, 0, 0, 20, 0, 0, 0, 0, 0, -22, -32, 0, 0, 0, -24, 0, -8, 36, 0, 0, 0, 0, 0, 0, 0, 20, 0, -6, -20, 0, -32, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, -36, 48, 0, 0, 0, 0, 0, 0, 14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24, 0, 0, 0, 32, 12, 0, 0, 0, 0, 0, 0, 8, 0, 48, -28, 0, 0, 0, 0, -48, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, -8, 0, 0, -26, 0, 0, 0, 0, 0, 0, -24, -24, 0, -36, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, -32, 0, 0, 0, 28, 0, 4, 0, 0, 56, 0, 0, 0, 0, 0, 0, 0, -24, 0, 0, 0, 0, 56, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, -24, -20, 0, 0, -64, 0, 0, 0, 0, 12, 0, 0, 0, 0, 32, 60, -48, 0, 0, 0, 40, 0, -16, 0, 0, 72, -56, 0, 0, 0, 0, 0, 0, -30, 0, 0, -24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -30, 0, 40, 0, 0, 0, 0, 0, 24, 0, 0, -40, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, -20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 96, 44, 0, 0, 0, 64, 0, 0, -52, 0, 0, 0, 0, 0, 0, 0, -72, 0, 0, 24, 0, 48, 0, 0, 0, 0, 0, 0, 0, 16, -60, 0, 0, -72, 0, 0, 0, 0, -106, 0, 28, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 48, 0, 0, 0, 0, -76, 0, 0, 0, 0, 0, 0, 48, 0, -40, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 40, 12, 0, 0, 0, 0, 0, 0, 64, 0, 0, 24, 0, 0, 0, 0, 0, 0, -72, 36, 0, 0, -72, 0, 0, 0, 0, 0, 0, 0, 0, 0, -32, 76, 0, 0, 0, 0, 96, 0, 0, -14, 0, -84, 0, 0, 0, 0, 0, 84, 0, 32, 72, 0, 8, 0, -96, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 60, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, 0, -48, 0, -28, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, -16, -28, 0, 0, 0, 0, 0, 0, 0, -52, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, -48, 46, 0, -12, 0, 0, 0, 0, 0, -72, 0, 42, 0, 0, 0, 0, -64, 0, 0, 0, -24, 0, 20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 32, 80, 0, 0, 0, -72, 0, 0, 0, 0, 0, 0, 0, 0, 0, -16, 68, 0, 0, 0, 0, 0, 0, -96, 0, 0, -12, 56, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 28, 0, 0, 0, 0, 96, 0, 0, 0, 0, 0, -24, 0, 0, -60, 0, 52, 0, 0, 0, 0, 0, 50, 0, -48, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -84, 112, 100, 0, 0, 0, 0, 0, 36, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 96, -40, 52, 0, 0, 0, 0, 0, 0, -84, 0, 0, 0, 0, 0, 0, 0, -92, 0, 0, -104, 0, 0, -128, 0, 0, 0, 0, 0, 0, 48, 0, 0, 0, 48, 0, 0, 0, 0, 0, 0, 0, 72, 0, 0, 0, 0, 0, 0, 0, 0, 0, -48, 0, 0, 26, 0, -96, 0, 0, 0, 0, 0, -84, -32, 0, 0, 0, 0, 0, 0, 0, 0, 0, -32, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 64, 0, 0, 120, 0, 0, -24, 0, 0, 0, 0, 192, 0, 0, 0, 0, -56, 0, 80, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 36, 0, -48, -112, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 144, -96, 0, 0, 0, 0, 0, 0, -60, 0, 0, 0, 0, 0, 0, 0, 0, -48, 0, 48, 0, 0, 0, 0, -58, 0, 0, 0, 0, 0, 0, 0, 0, -80, 0, 0, 0, 0, 0, -112, 0, 0, 116, 0, 0, 0, 0, 0, 0, 0, -60, 0, 0, 0, 0, 0, 20, 0, 0, 0, 0, 0, 0, 0, 36, 0, 4, 0, 0, 0, 0, 0, 0, 0, 66, 0, 0, 0, 0, 0, 0, 0, 0, -20, 0, 96, 0, 0, 0, 0, -20, 0, 0, 0, 0, 0, 8, -96, 0, 0, 0, 64, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -108, 0, 0, 0, 0, 0, 0, 0, 0, 0, -40, 0, 0, 0, 0, -48, 0, 72, -60, 0, 0, 120, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 62, 0, 0, 0, 0, 0, 0, 48, 192, 0, 108, 40, 0, 0, 0, 0, 12, 0, -108, 0, 0, -40, 0, 128, 0, 0, 0, 0, 0, 0, 0, 0, -104, 0, 0, 0, 0, 0, 0, 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], [0, 1], [2, 0], [-2, 0], [0, 0], [0, 2], [0, 0], [0, -2], [1, 0], [0, 0], [-3, -1], [-4, 0], [0, 0], [0, 0], [0, 0], [4, 0], [0, 4], [0, 1], [0, -6], [0, 0], [0, 0], [2, -3], [0, 0], [0, -4], [5, 0], [0, 0], [-4, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 4], [-6, -2], [-8, 0], [0, 0], [-2, 0], [0, 0], [12, 0], [0, 0], [0, 0], [0, 8], [0, 0], [0, 6], [6, 2], [0, 0], [0, 0], [0, 0], [8, 0], [-7, 0], [0, 5], [0, 8], [0, 0], [0, 0], [0, -4], [0, 0], [0, 0], [0, -12], [0, 0], [-6, 0], [0, 0], [0, 0], [0, 0], [0, 0], [-8, 0], [0, 0], [4, -6], [14, 0], [0, -8], [0, 0], [0, 0], [0, 0], [0, -2], [0, -12], [0, 0], [10, 0], [0, 12], [0, 0], [0, 0], [0, 0], [0, 0], [-11, 0], [-16, 0], [0, 2], [0, 0], [0, 0], [-12, 0], [0, 0], [-4, 6], [18, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 8], [10, 0], [0, -7], [-3, -1], [-10, 0]]}