# Stored data for newform 522.2.h.a, downloaded from the LMFDB on 11 October 2026.
{"Nk2": 2088, "analytic_conductor": 4.168190985510836, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 261, "char_degree": 2, "char_is_minimal": true, "char_is_real": false, "char_orbit_index": 8, "char_orbit_label": "h", "char_order": 6, "char_parity": 1, "char_values": [522, 6, [407, 379], [4, 3]], "cm_discs": [], "conrey_index": 115, "dim": 4, "field_disc": 144, "field_disc_factorization": [[2, 4], [3, 2]], "field_poly": [1, 0, -1, 0, 1], "field_poly_is_cyclotomic": true, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 12, "has_non_self_twist": 1, "hecke_cutters": [[5, [4, -2, 1]]], "hecke_orbit": 1, "hecke_orbit_code": 481069892106, "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, 9, 3, 1, 3, 0], [1, 1, 29, 2, 1, 2, 0], [1, 1, 261, 9, 1, 6, 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": "522.2.h.a", "level": 522, "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, 3, 29], "level_radical": 174, "minimal_twist": "522.2.h.a", "nf_label": "4.0.144.1", "prim_orbit_index": 9, "qexp_display": "q+\\zeta_{12}q^{2}+(-\\zeta_{12}-\\zeta_{12}^{3})q^{3}+\\zeta_{12}^{2}q^{4}+\\cdots", "related_objects": [], "relative_dim": 2, "rm_discs": [], "sato_tate_group": "1.2.3.c6", "self_twist_discs": [], "self_twist_type": 0, "space_label": "522.2.h", "trace_display": [0, 0, 4, -2], "trace_hash": 641010378203279300, "trace_moments": [0, {"__RealLiteral__": 0, "data": "4.015", "prec": 14}, 0, {"__RealLiteral__": 0, "data": "94.019", "prec": 17}, 0, {"__RealLiteral__": 0, "data": "3308.987", "prec": 24}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.509", "prec": 10}, "traces": [0, 4, 0, 0, 2, 4, 0, -2, 0, -6, 0, 0, 0, 8, 0, 0, -2, 0, 0, 0, -4, 0, 2, 0, 6, 2, 0, 0, -4, -4, 12, 0, 0, 0, -4, -8, -12, 0, 2, 0, 0, 0, 6, 0, 0, -24, 0, 0, 0, 12, 0, 12, -8, 8, 18, 0, 0, -6, 10, -8, 0, 0, 16, -6, -4, -16, 0, -4, 0, 0, 0, 28, 0, 0, 4, 0, 0, 0, 24, 0, -8, -18, -8, 8, 0, 0, -18, 0, -2, 0, 0, -16, 0, -24, 12, 0, 6, 0, 0, 0, 4, 0, 0, -38, 0, 0, 0, 16, 0, 24, -4, -12, -2, 0, 0, 0, -8, -48, 0, 0, 12, -20, -26, 12, 0, 48, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, -8, 0, 0, -20, -4, 0, 0, 0, -6, -16, 8, 0, 0, 24, -6, 32, 4, 0, -4, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 12, 0, -6, 0, -6, -16, 0, 0, 0, 12, 2, 0, 0, 4, 96, -12, 104, 0, 0, 0, 0, 0, -4, 0, 0, 8, 0, 0, 0, -16, 0, -12, 64, -12, -32, 0, 0, -12, -4, 12, 0, 0, 0, -16, 2, 0, 0, 4, 0, 0, 0, 0, 0, 0, -24, 0, 0, 0, -42, 0, 6, -56, -36, -6, 0, 0, 6, -10, -52, 0, 0, 8, 0, -4, 30, 0, -2, 0, 0, 0, -24, 0, 0, 8, 0, 0, 0, 6, 0, -12, 24, -2, -52, 0, 0, -32, -12, 36, 0, 0, 8, 2, -12, 4, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, -46, 0, 0, 14, -12, -8, 0, 0, 52, -20, 0, 0, 0, 36, 16, 8, 18, 0, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 16, 0, 24, 2, 36, 12, 0, 0, 0, 10, -4, 0, 0, 8, 18, 16, -34, 0, -4, 0, 0, 0, 16, 0, 0, 8, 0, 0, 0, 84, 0, 16, 6, -52, 18, 0, 0, -72, 30, 56, 0, 0, -4, -42, -24, 28, 0, 0, 0, 0, 0, 72, 0, 0, -8, 0, 0, 0, 0, 0, 16, -4, 0, -20, 0, 0, -12, -32, -18, 0, 0, 36, 0, -54, 0, 0, -40, 0, 0, 0, 48, 0, 0, -54, 0, 0, 0, -72, 0, 0, 2, 46, -12, 0, 0, 36, -20, 4, 0, 0, -8, 0, 38, 16, 0, 32, 0, 0, 0, -36, 0, 0, 52, 0, 0, 0, 0, 0, 8, 24, 36, -92, 0, 0, -8, 60, 12, 0, 0, -30, -8, -72, -32, 0, -12, 0, 0, 0, 2, 0, 0, -8, 0, 0, 0, -16, 0, 36, -12, 0, 0, 0, 0, 38, -4, 0, 0, 0, -24, 8, -24, -54, 0, -18, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 20, 0, -54, -76, 26, 102, 0, 0, 0, -20, 16, 0, 0, -14, -24, -48, 24, 0, -30, 0, 0, 0, 0, 0, 0, 48, 0, 0, 0, 0, 0, 76, -54, 12, 4, 0, 0, -148, -60, 16, 0, 0, -32, 16, 6, 46, 0, 48, 0, 0, 0, 16, 0, 0, 50, 0, 0, 0, 56, 0, -4, 24, 0, -76, 0, 0, 4, 10, 0, 0, 0, -24, 20, 48, -24, 0, 4, 0, 0, 0, 36, 0, 0, 36, 0, 0, 0, 40, 0, 0, 4, 0, 6, 0, 0, 60, -8, 8, 0, 0, 16, -48, -20, 36, 0, -8, 0, 0, 0, -172, 0, 0, -24, 0, 0, 0, 0, 0, 36, 24, 64, 40, 0, 0, 2, 30, 52, 0, 0, -40, -18, 0, -2, 0, -114, 0, 0, 0, 72, 0, 0, 38, 0, 0, 0, 16, 0, -176, 8, -78, 22, 0, 0, -48, -8, -42, 0, 0, 0, -28, 0, -108, 0, 44, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, -24, 0, 12, -32, 62, 48, 0, 0, 12, 0, 6, 0, 0, -26, -6, 22, -32, 0, -12, 0, 0, 0, -8, 0, 0, -72, 0, 0, 0, 18, 0, 16, 0, -16, 0, 0, 0, 40, 0, -8, 0, 0, -2, 0, 0, -8, 0, 72, 0, 0, 0, -80, 0, 0, 8, 0, 0, 0, 48, 0, 8, 124, 12, 76, 0, 0, 52, 4, -60, 0, 0, 108, 32, 36, -78, 0, 20, 0, 0, 0, 12, 0, 0, -24, 0, 0, 0, -48, 0, 24, -8, -8, 0, 0, 0, 90, -40, 128, 0, 0, -10, 0, 4, 44, 0, -12, 0, 0, 0, 32, 0, 0, -4, 0, 0, 0, 108, 0, 16, 0, -36, 4, 0, 0, 0, 90, -24, 0, 0, -8, 32, 0, 16, 0, -6, 0, 0, 0, -16, 0, 0, -24, 0, 0, 0, 8, 0, 0, 32, -150, 12, 0, 0, 24, 4, -168, 0, 0, 0, -18, 128, 24, 0, 36, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, -8, 0, -60, 12, 4, 72, 0, 0, -12, 42, 22, 0, 0, -24, -72, 40, -4, 0, 4, 0, 0, 0, 52, 0, 0, -14, 0, 0, 0, -12, 0, -132, -18, 0, -4, 0, 0, -8, 0, 16, 0, 0, 0, -24, -24, -80, 0, 30, 0, 0, 0, -104, 0, 0, -8, 0, 0, 0, 16, 0, -84, 12, 72, 96, 0, 0, -60, 80, -6, 0, 0, -54, -28, 104, -96, 0, -72, 0, 0, 0, 0, 0, 0, -156, 0, 0, 0, -116, 0, 54, 10, 56, 0, 0, 0, 228, -20, -62, 0, 0, -26, -108, -6, -16, 0, 164, 0, 0, 0, -48, 0, 0, 16, 0, 0, 0, -24, 0, -2, 0, 4, -188, 0, 0, -30, 12, -76, 0, 0, -30, 32, -24, -4, 0, 0, 0, 0, 0, 32, 0, 0, 40, 0, 0, 0, -108, 0, 4, -48, -36, -48, 0, 0, 64, -8, 36, 0, 0, -12, 172, -8, 0, 0, -32, 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, 0, 0], [1, 0, 0, 0], [0, 1, 0, 0], [0, -1, 0, -1], [0, 0, 1, 0], [0, 0, 2, 0], [1, 0, -2, 0], [-1, 0, 1, 0], [0, 0, 0, 1], [-3, 0, 3, 0], [0, 0, 0, 2], [0, 1, 0, 0], [0, 1, 0, -2], [0, 0, 4, 0], [0, -1, 0, 1], [0, 2, 0, -4], [-1, 0, 1, 0], [0, 0, 0, 2], [0, -3, 0, 3], [0, 0, 0, -1], [-2, 0, 2, 0], [0, 2, 0, -1], [0, 0, 1, 0], [0, 0, 0, 0], [2, 0, -1, 0], [1, 0, -1, 0], [0, 0, 0, 4], [0, 6, 0, -3], [-1, 0, 0, 0], [-2, 5, 2, 0], [4, 0, -2, 0], [0, 4, 0, -4], [0, -1, 0, 1], [1, 0, -2, 0], [-2, 0, 2, 0], [-2, 0, 0, 0], [-3, 0, 0, 0], [0, 0, 0, -2], [1, 0, -1, 0], [0, 4, 0, -8], [0, -2, 0, 2], [0, -2, 0, 2], [1, 0, 1, 0], [0, -9, 0, 0], [0, 0, 0, 1], [-6, 0, 0, 0], [0, 0, 0, 0], [0, 6, 0, 0], [0, 2, 0, -1], [0, 0, 6, 0], [0, 1, 0, -1], [4, 0, -2, 0], [-4, 0, 4, 0], [2, 0, 0, 0], [3, 0, 3, 0], [0, 0, 0, 2], [0, -1, 0, 0], [-2, 0, 1, 0], [0, -2, 5, 2], [0, 0, -4, 0], [0, 4, 0, -2], [0, -13, 0, 0], [4, 0, 0, 0], [0, 0, -3, 0], [-1, 0, 0, 0], [-8, 0, 8, 0], [0, 1, 0, -2], [0, 0, -2, 0], [0, -2, 0, 2], [0, 0, 0, 0], [0, -2, 0, 0], [7, 0, 0, 0], [0, -3, 0, 0], [0, 0, 0, -4], [2, 0, -2, 0], [0, -2, 0, 1], [0, 1, 0, -1], [0, -1, 0, 1], [8, 0, -4, 0], [0, -4, 0, 0], [-2, 0, 0, 0], [0, 0, -9, 0], [-2, 0, 0, 0], [4, 0, -4, 0], [0, 1, 0, 1], [0, -4, 0, 4], [0, 0, -9, 0], [5, 4, -10, -2], [-1, 0, 1, 0], [0, 0, 0, -2], [0, -6, 0, 0], [-4, 0, 0, 0], [0, 0, 0, 0], [-4, 0, -4, 0], [0, 0, 6, 0], [0, 2, 0, -2], [1, 0, 1, 0], [0, -8, 0, 0], [0, 0, 0, 6], [0, -3, 0, 3], [1, 0, 0, 0]]}