# Stored data for newform 729.2.a.b, downloaded from the LMFDB on 23 May 2025.
{"Nk2": 2916, "analytic_conductor": 5.82109430735134, "analytic_rank": 0, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[3, -1]], "atkin_lehner_string": "-", "char_conductor": 1, "char_degree": 1, "char_is_minimal": true, "char_is_real": true, "char_orbit_index": 1, "char_orbit_label": "a", "char_order": 1, "char_parity": 1, "char_values": [729, 1, [2], [1]], "cm_discs": [], "conrey_index": 1, "dim": 6, "field_disc": 7459857, "field_disc_factorization": [[3, 9], [379, 1]], "field_poly": [-8, -12, 12, 13, -6, -3, 1], "field_poly_is_cyclotomic": false, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 0, "fricke_eigenval": -1, "has_non_self_twist": 0, "hecke_cutters": [[2, [-3, 18, 0, -21, -6, 3, 1]]], "hecke_orbit": 2, "hecke_orbit_code": 4503599660925657, "hecke_ring_generator_nbound": 5, "hecke_ring_index": 1, "hecke_ring_index_factorization": [], "hecke_ring_index_proved": true, "inner_twist_count": 1, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "is_cm": false, "is_largest": false, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": true, "is_self_twist": false, "is_twist_minimal": true, "label": "729.2.a.b", "level": 729, "level_is_powerful": true, "level_is_prime": false, "level_is_prime_power": true, "level_is_prime_square": false, "level_is_square": true, "level_is_squarefree": false, "level_primes": [3], "level_radical": 3, "minimal_twist": "729.2.a.b", "nf_label": "6.6.7459857.1", "prim_orbit_index": 1, "qexp_display": "q+(-\\beta _{1}-\\beta _{3})q^{2}+(1+\\beta _{1}+\\beta _{2}+\\beta _{4}+\\cdots)q^{4}+\\cdots", "related_objects": [], "relative_dim": 6, "rm_discs": [], "sato_tate_group": "1.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "729.2.a", "trace_display": [-3, 0, 3, 6], "trace_hash": 109766499157733312, "trace_moments": [{"__RealLiteral__": 0, "data": "0.105", "prec": 17}, {"__RealLiteral__": 0, "data": "5.691", "prec": 17}, {"__RealLiteral__": 0, "data": "1.882", "prec": 17}, {"__RealLiteral__": 0, "data": "92.693", "prec": 20}, {"__RealLiteral__": 0, "data": "53.062", "prec": 20}, {"__RealLiteral__": 0, "data": "2275.210", "prec": 27}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.005", "prec": 17}, "traces": [0, 6, -3, 0, 9, 3, 0, 6, -6, 0, 6, 6, 0, 6, -24, 0, 15, 9, 0, 12, 21, 0, 3, 12, 0, 9, -24, 0, 3, -21, 0, 15, 0, 0, 0, -30, 0, 3, -15, 0, 3, 12, 0, 6, 33, 0, -3, 15, 0, 12, 24, 0, 3, 9, 0, 15, -12, 0, -15, -6, 0, 24, 30, 0, 6, 15, 0, 15, -36, 0, -15, 0, 0, 12, -24, 0, 9, -15, 0, 24, 21, 0, -21, 6, 0, -18, 30, 0, -21, 9, 0, 18, -6, 0, -6, 33, 0, -21, -18, 0, -15, 6, 0, 24, -30, 0, -27, 36, 0, -6, 54, 0, -21, 3, 0, 3, 33, 0, -30, 18, 0, 0, 30, 0, -6, -39, 0, 12, -66, 0, -60, -6, 0, -15, -42, 0, -9, -39, 0, 15, -21, 0, -54, -33, 0, -21, -51, 0, -63, 39, 0, 24, -75, 0, -57, -3, 0, -21, 12, 0, -36, -3, 0, -15, 84, 0, -6, -69, 0, -6, 9, 0, -60, 24, 0, 3, 42, 0, -27, 27, 0, -15, -3, 0, -51, -66, 0, 0, 15, 0, -42, 33, 0, -12, -15, 0, 3, 27, 0, 30, 30, 0, -24, 3, 0, -15, -6, 0, -3, 12, 0, 24, -27, 0, -36, 6, 0, 0, 12, 0, 6, 9, 0, 15, 27, 0, 15, -39, 0, 6, -45, 0, -30, -27, 0, -3, 39, 0, -18, 30, 0, -3, -3, 0, 66, -54, 0, 57, 69, 0, 12, -36, 0, -21, 21, 0, 9, -15, 0, 66, -12, 0, 15, -93, 0, -18, -3, 0, 39, 18, 0, 75, -36, 0, 3, -3, 0, -30, -33, 0, -3, -12, 0, 15, -36, 0, 15, 24, 0, -21, -9, 0, 99, 30, 0, 48, -39, 0, -57, 33, 0, 0, 21, 0, 66, 33, 0, 48, 39, 0, 84, 12, 0, 15, 84, 0, 129, 69, 0, 30, 84, 0, 30, 36, 0, -42, -105, 0, -78, 66, 0, 6, -39, 0, 114, 15, 0, -30, -36, 0, -54, 12, 0, 45, 114, 0, 93, 39, 0, -30, -6, 0, 0, -39, 0, 0, -45, 0, 0, -36, 0, 0, -60, 0, 48, -57, 0, 33, 93, 0, -6, 36, 0, -48, -9, 0, 123, -51, 0, 12, 6, 0, -6, -60, 0, -78, 3, 0, -78, 15, 0, 36, 45, 0, 54, 114, 0, -51, -33, 0, 36, -87, 0, -36, -3, 0, 33, 3, 0, 6, -9, 0, 111, 6, 0, -12, -45, 0, 6, -87, 0, -12, 12, 0, -63, 36, 0, -36, 153, 0, 12, -81, 0, -24, -66, 0, 81, 69, 0, 87, -9, 0, 45, -39, 0, -99, 21, 0, -39, -54, 0, 33, 57, 0, -24, 75, 0, -66, 111, 0, 93, -39, 0, -12, 24, 0, 45, 9, 0, 0, 63, 0, 12, -78, 0, -27, 45, 0, 15, -75, 0, 3, -51, 0, -6, -30, 0, 57, 6, 0, 99, -33, 0, -90, -57, 0, -12, 36, 0, 24, -3, 0, 126, -45, 0, -30, 27, 0, -36, -24, 0, 93, -51, 0, 60, 78, 0, -33, -21, 0, -84, 72, 0, 3, 66, 0, 66, 45, 0, -36, -126, 0, 51, -30, 0, 54, -183, 0, -63, 45, 0, -87, 12, 0, 117, 60, 0, 15, -165, 0, 39, -78, 0, -54, 93, 0, 66, -54, 0, 36, -66, 0, -24, 21, 0, -33, -33, 0, -108, 69, 0, -75, -51, 0, -33, 48, 0, -24, 69, 0, -48, 12, 0, -90, -75, 0, 114, -39, 0, -24, -45, 0, -105, 18, 0, -90, -33, 0, -60, -15, 0, 15, 6, 0, 21, 3, 0, 105, -72, 0, 57, 30, 0, -78, 57, 0, -78, 30, 0, -21, 87, 0, 69, 135, 0, -84, 3, 0, -132, 117, 0, -33, 42, 0, -141, -57, 0, -39, -135, 0, -147, 51, 0, -21, -57, 0, 99, -108, 0, -21, 3, 0, 9, -6, 0, 57, 210, 0, -147, -156, 0, -30, 183, 0, -30, 12, 0, -93, -222, 0, -51, 30, 0, -48, 84, 0, 3, 51, 0, 36, -18, 0, 87, -117, 0, -129, 6, 0, -120, 90, 0, -39, 42, 0, -84, -102, 0, -63, 93, 0, -117, -81, 0, 15, -21, 0, -15, 39, 0, -39, -108, 0, 72, 24, 0, -60, 180, 0, -189, -63, 0, -36, 9, 0, -9, -66, 0, 24, 93, 0, 12, 54, 0, -12, -195, 0, -81, 75, 0, -33, -201, 0, 72, 12, 0, -24, 102, 0, -45, 54, 0, 60, -147, 0, 87, 105, 0, -15, -6, 0, -165, 48, 0, -96, 123, 0, 33, 78, 0, -3, 36, 0, 39, -63, 0, 102, 51, 0, 75, -21, 0, -18, 81, 0, -132, -21, 0, -21, -72, 0, 129, 33, 0, -36, 120, 0, 198, -42, 0, 9, 54, 0, 123, 48, 0, -39, -30, 0, -57, -54, 0, -33, 66, 0, -138, -66, 0, -6, 30, 0, 210, 42, 0, -39, -48, 0, -33, 63, 0, 57, -99, 0, 159, 63, 0, -87, -33, 0, -75, 33, 0, 45, 156, 0, -51, 90, 0, 30, 63, 0, -27, -3, 0, -30, -48, 0, 18, -21, 0, -66, 24, 0, 225, 27, 0, -12, 3, 0, -105, 111, 0, 36, -102, 0, -69, 3, 0, -48, -96, 0, 186, -99, 0, -69, -18, 0, 84, 156, 0, 21, 63, 0, 3, -69, 0, 81, 48, 0, -45, -105, 0, 36, -90, 0, 84, -3, 0, 15, -102, 0, -21, 6, 0, -87, -6, 0, 3, -111, 0, 84, -90, 0, 237, 108, 0, 9, -69, 0, -117, -129, 0, -75, -153, 0, -45, 27, 0, 30, -21, 0, 6, -78, 0, 39, -69, 0, 186, -57, 0, -42, 21, 0, 72, 9, 0, -39, -42, 0, 3, 57, 0, -51, 168, 0, 12, -48, 0, -3, 84, 0, -105, -9, 0, 99, -33, 0, 204, 39, 0, -18, -126, 0, 15, 150, 0, 81, -18, 0, 123, 42, 0, 39, 135, 0, 18, 51, 0, 78, -33, 0, 96], "weight": 2, "weight_parity": 1, "id": null, "artin_degree": null, "artin_field": null, "artin_field_label": null, "artin_image": null, "embedded_related_objects": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp": [[0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0], [0, -1, 0, -1, 0, 0], [0, 0, 0, 0, 0, 0], [1, 1, 1, 0, 1, -1], [0, 0, 0, -1, 1, 0], [0, 0, 0, 0, 0, 0], [1, 1, 0, 1, -1, 0], [0, -1, 0, -3, -1, 0], [0, 0, 0, 0, 0, 0], [2, -1, -1, -1, 0, -1], [1, 0, -1, 1, 1, -1], [0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 1], [-4, -1, 1, 0, 0, 1], [0, 0, 0, 0, 0, 0], [2, 0, 3, 1, 2, -1], [2, -1, -2, 1, -1, 1], [0, 0, 0, 0, 0, 0], [1, 0, -1, 1, 1, 1], [4, -1, 5, -3, 1, -1], [0, 0, 0, 0, 0, 0], [1, -2, 1, -5, 0, 1], [2, -1, 1, 0, 0, 1], [0, 0, 0, 0, 0, 0], [3, -2, 1, -1, -1, 0], [-3, -1, -3, 3, -1, 0], [0, 0, 0, 0, 0, 0], [-1, 3, -4, 5, 0, 0], [-4, 2, 1, 2, 1, -2], [0, 0, 0, 0, 0, 0], [4, -2, 0, -2, -1, 0], [2, -2, -5, -1, -3, 1], [0, 0, 0, 0, 0, 0], [-1, 0, 0, 2, 1, 1], [-7, 2, 1, -1, 1, 1], [0, 0, 0, 0, 0, 0], [1, 0, -4, 4, -2, 1], [-1, -2, -5, 1, -2, 1], [0, 0, 0, 0, 0, 0], [3, -2, 1, -6, -2, -1], [2, 1, 4, 1, 1, -2], [0, 0, 0, 0, 0, 0], [2, -2, 0, -4, -2, 2], [6, 1, 3, 0, 1, -3], [0, 0, 0, 0, 0, 0], [1, -1, -4, 1, -2, 0], [3, 1, 0, -3, -2, 0], [0, 0, 0, 0, 0, 0], [3, 1, -3, 2, -2, -1], [4, 0, 2, -2, 1, -1], [0, 0, 0, 0, 0, 0], [-2, 3, 2, 4, 1, 1], [1, 0, 2, 0, -1, 2], [0, 0, 0, 0, 0, 0], [4, -4, 2, -2, 1, 0], [-3, 0, -3, 1, -1, 3], [0, 0, 0, 0, 0, 0], [-3, 1, 1, -3, -2, 2], [-3, 3, 0, -1, 1, 0], [0, 0, 0, 0, 0, 0], [5, -2, 4, -3, 1, -1], [5, -1, 4, -3, 3, -2], [0, 0, 0, 0, 0, 0], [-3, 3, 3, 2, 4, 1], [1, 2, -1, 2, -1, 2], [0, 0, 0, 0, 0, 0], [1, 1, -2, 5, 2, 0], [-6, 2, -3, 1, -2, 0], [0, 0, 0, 0, 0, 0], [-3, 4, -5, 9, -2, -1], [-2, 2, -4, 4, 0, 2], [0, 0, 0, 0, 0, 0], [2, 3, 3, 3, 0, -3], [-7, 1, 1, 4, 1, 4], [0, 0, 0, 0, 0, 0], [-2, 5, 7, 4, 3, -1], [-3, 4, -3, 7, 0, -3], [0, 0, 0, 0, 0, 0], [3, 1, 0, -3, 3, -2], [1, 3, 2, 2, 6, -4], [0, 0, 0, 0, 0, 0], [0, -4, -1, -9, -4, 1], [1, -1, 2, -1, -1, 2], [0, 0, 0, 0, 0, 0], [-5, 0, -6, 1, 2, 2], [4, 2, 2, 6, 4, -4], [0, 0, 0, 0, 0, 0], [0, -4, 2, -6, -1, -2], [3, 1, -3, 2, -4, 0], [0, 0, 0, 0, 0, 0], [2, 1, 3, -6, 0, 1], [-5, 4, 5, 1, 5, -1], [0, 0, 0, 0, 0, 0], [-1, -2, 7, -1, 5, -3], [4, 0, -4, 4, 1, 2], [0, 0, 0, 0, 0, 0], [-4, 1, 0, -1, -2, 2], [-5, -2, 8, -4, 4, 2], [0, 0, 0, 0, 0, 0], [-2, -1, -1, -6, 2, -2]]}