# Stored data for newform 729.2.e.s, downloaded from the LMFDB on 24 March 2023. {"level_primes": [3], "is_polredabs": true, "sato_tate_group": "1.2.3.c9", "rm_discs": [], "conrey_indexes": [82, 163, 325, 406, 568, 649], "cm_discs": [], "trace_hash": 1265490404708287237, "level_radical": 3, "hecke_ring_index_proved": true, "self_twist_type": 0, "related_objects": [], "prim_orbit_index": 5, "is_cm": false, "hecke_orbit": 19, "analytic_conductor": 5.82109430735134, "inner_twist_count": 2, "field_disc_factorization": [[3, 18], [379, 2]], "is_rm": false, "char_order": 9, "level_is_square": true, "weight_parity": 1, "label": "729.2.e.s", "field_poly_is_real_cyclotomic": false, "is_self_twist": false, "is_twist_minimal": true, "minimal_twist": "729.2.a.b", "field_poly_is_cyclotomic": false, "dim": 12, "trace_zratio": {"__RealLiteral__": 0, "data": "0.005", "prec": 17}, "traces": [0, 12, 3, 0, -3, -12, 0, -3, 6, 0, -6, 3, 0, 6, 6, 0, 27, -9, 0, -12, -39, 0, -39, -21, 0, 6, -48, 0, 6, -6, 0, 6, -27, 0, -18, 30, 0, -3, -3, 0, 33, 15, 0, -30, -33, 0, 3, 21, 0, -3, -6, 0, 0, 18, 0, 30, -15, 0, -3, -30, 0, -30, -30, 0, -6, 12, 0, -39, -18, 0, 51, 0, 0, -12, -57, 0, 57, 24, 0, 15, 42, 0, -42, 21, 0, 54, 60, 0, 12, -9, 0, -18, 15, 0, 33, -42, 0, -12, 18, 0, 15, 57, 0, -12, 48, 0, -72, 72, 0, -12, 9, 0, -66, -12, 0, 60, -33, 0, 30, 0, 0, -3, 33, 0, -117, 39, 0, -12, 48, 0, 60, -57, 0, 75, -84, 0, -18, -15, 0, -39, 93, 0, 0, 33, 0, 21, -75, 0, -105, -12, 0, -3, 75, 0, 57, 75, 0, -12, 33, 0, 0, -6, 0, -30, 15, 0, 33, 6, 0, 6, -9, 0, 60, 12, 0, -9, 75, 0, 72, -27, 0, 15, 21, 0, -75, 30, 0, -81, 30, 0, -84, -33, 0, 51, 105, 0, 141, -27, 0, -30, -12, 0, 60, -102, 0, -21, 6, 0, 3, -3, 0, 96, -54, 0, 54, 12, 0, 0, 15, 0, -33, -45, 0, -30, -27, 0, -15, 48, 0, -75, 0, 0, 39, 27, 0, 3, -57, 0, -27, 15, 0, -3, -6, 0, 132, 63, 0, -6, -24, 0, -102, 36, 0, 21, -12, 0, -3, 123, 0, -15, 12, 0, -15, 21, 0, -18, 21, 0, -9, 36, 0, 150, -27, 0, -84, -87, 0, 51, 33, 0, 3, -114, 0, 60, -72, 0, -51, -24, 0, 21, 9, 0, 75, 69, 0, 51, -78, 0, -114, 3, 0, -66, -39, 0, -135, -33, 0, -48, 132, 0, 69, -12, 0, -39, -84, 0, -129, -60, 0, -21, -84, 0, -75, 72, 0, -84, -84, 0, 231, -21, 0, 33, 39, 0, -114, 93, 0, 15, -117, 0, 63, -12, 0, -45, -132, 0, -147, -75, 0, -12, -12, 0, 0, 93, 0, -36, -63, 0, 27, 36, 0, 0, 42, 0, 93, 102, 0, 123, -93, 0, 6, -90, 0, -57, -36, 0, 102, -102, 0, 24, 12, 0, 60, 51, 0, -165, -3, 0, 78, -87, 0, -18, 54, 0, 36, -114, 0, 51, 33, 0, -48, 78, 0, -39, -6, 0, 66, -156, 0, 96, -180, 0, -81, -6, 0, 12, -126, 0, -78, -48, 0, 24, -12, 0, 63, -90, 0, 114, -45, 0, 42, -162, 0, -48, -42, 0, -168, 39, 0, 6, 9, 0, -45, 102, 0, 54, 150, 0, -102, 54, 0, -33, 60, 0, 78, 6, 0, 42, 222, 0, 186, 12, 0, -57, -42, 0, 45, -9, 0, 0, 36, 0, -3, -30, 0, 3, -45, 0, -15, -24, 0, -78, -39, 0, -33, -60, 0, 114, 75, 0, 54, 51, 0, -9, 57, 0, 12, -126, 0, 132, -114, 0, -9, 45, 0, 30, 126, 0, -69, -12, 0, -195, -102, 0, 120, 57, 0, 42, -159, 0, 66, -72, 0, -3, 105, 0, -111, -54, 0, 105, 126, 0, -51, -96, 0, -99, 147, 0, 117, 90, 0, -174, 123, 0, -27, 84, 0, 159, 165, 0, -39, 33, 0, -84, 51, 0, 36, 54, 0, -36, 75, 0, 51, -138, 0, 114, -66, 0, -216, 66, 0, -138, 150, 0, 6, -48, 0, 24, 57, 0, -96, 132, 0, 72, 75, 0, -114, -33, 0, -15, -18, 0, -36, 36, 0, -180, -57, 0, 60, 195, 0, 24, -6, 0, -21, -21, 0, 24, -90, 0, -273, -30, 0, 78, 78, 0, 132, 96, 0, -84, 174, 0, 138, -126, 0, -90, -75, 0, 126, -117, 0, 33, -249, 0, 33, -33, 0, -51, 135, 0, 147, 66, 0, 96, -6, 0, -63, -216, 0, -42, -12, 0, -60, 78, 0, -12, -210, 0, 147, 57, 0, 96, -39, 0, -33, -12, 0, 93, 177, 0, -12, 6, 0, 78, 168, 0, 6, -78, 0, 15, 135, 0, -24, 117, 0, 129, -141, 0, -120, 99, 0, -48, -42, 0, 84, -15, 0, 9, 87, 0, -87, -162, 0, 30, 21, 0, 141, 6, 0, -165, 108, 0, -72, 39, 0, -165, 90, 0, 27, 63, 0, 36, 180, 0, 201, 111, 0, 78, 186, 0, 24, 18, 0, 123, -12, 0, 126, -75, 0, 33, 210, 0, -108, -147, 0, -75, -102, 0, 45, 81, 0, 87, 120, 0, 165, 210, 0, -30, 114, 0, 75, 186, 0, -33, -123, 0, -33, -105, 0, 51, -198, 0, 18, 63, 0, -102, -96, 0, -12, -222, 0, -180, 162, 0, -264, -87, 0, -12, -117, 0, 114, -33, 0, 36, 78, 0, 21, 42, 0, 36, -54, 0, -123, 15, 0, -123, -87, 0, 30, -108, 0, -66, 33, 0, -177, 48, 0, 156, -30, 0, -210, -168, 0, 177, 111, 0, 42, -63, 0, -57, -36, 0, 15, 0, 0, -147, -66, 0, -150, -6, 0, 78, 42, 0, -153, -90, 0, -30, 288, 0, -54, 39, 0, 42, 48, 0, -18, -159, 0, -30, 120, 0, -18, 54, 0, -24, -138, 0, 111, -3, 0, -66, 102, 0, 69, 6, 0, -3, -165, 0, -15, 99, 0, 69, 54, 0, 213, 132, 0, 75, 126, 0, 6, 114, 0, -117, -48, 0, -99, 105, 0, -36, -126, 0, -12, -60, 0, -210, 102, 0, 21, 3, 0, 33, 51, 0, 108, -222, 0, 168, 45, 0, -66, -144, 0, -123, 69, 0, 117, 84, 0, 57, 45, 0, 0, -27, 0, -30, -42, 0, -240, -12, 0, 87, -138, 0, 372, 111, 0, -114, 78, 0, 54, -9, 0, 39, -273, 0, 168, 60, 0, -12, -168, 0, -12, -123, 0, -66, -129, 0, -84, -18, 0, 198, -102, 0, -192, -210, 0, 153, 126, 0, -15, 75, 0, -117, 162, 0, 72, -42, 0, -39, -144, 0, -162, -168, 0, 15, -66, 0, 192], "hecke_ring_index_factorization": [[3, 1]], "field_poly": [1, 0, 132, 0, 306, 0, 266, 0, 105, 0, 18, 0, 1], "has_non_self_twist": 1, "char_values": [729, 9, [2], [4]], "Nk2": 2916, "field_poly_root_of_unity": 0, "analytic_rank": 0, "char_orbit_label": "e", "weight": 2, "trace_display": [3, 0, -12, -3], "analytic_rank_proved": true, "char_parity": 1, "level_is_squarefree": false, "hecke_ring_index": 3, "level_is_prime": false, "char_is_minimal": false, "qexp_display": "q+(1-\\beta _{5}+\\beta _{6}+\\beta _{10}-\\beta _{11})q^{2}+(\\beta _{1}+\\cdots)q^{4}+\\cdots", "self_twist_discs": [], "char_is_real": false, "field_disc": 55649466460449, "level_is_prime_power": true, "relative_dim": 2, "hecke_cutters": [[2, [9, 0, 270, 585, 198, -261, -42, 36, 27, -15, 6, -3, 1]], [5, [25281, 31482, 18549, 10215, 6408, 4041, 2820, 1566, 684, 249, 69, 12, 1]], [7, [18496, 86496, 148224, 111616, 60228, 24714, 7995, 1899, 369, 52, 6, 3, 1]]], "space_label": "729.2.e", "level": 729, "is_self_dual": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 27, 5, 1, 9, 0]], "char_degree": 6, "char_conductor": 27, "char_orbit_index": 5, "hecke_ring_generator_nbound": 4, "hecke_orbit_code": 81065068204131033, "trace_moments": [{"__RealLiteral__": 0, "data": "0.080", "prec": 17}, {"__RealLiteral__": 0, "data": "11.457", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "385.354", "prec": 24}, {"__RealLiteral__": 0, "data": "38.285", "prec": 20}, {"__RealLiteral__": 0, "data": "21575.338", "prec": 30}], "id": null, "projective_field": null, "embedded_related_objects": null, "projective_image_type": null, "artin_image": null, "nf_label": null, "atkin_lehner_string": null, "atkin_lehner_eigenvals": null, "artin_field": null, "projective_image": null, "artin_field_label": null, "projective_field_label": null, "fricke_eigenval": null, "artin_degree": null, "qexp": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, -1, 1, 0, 0, 0, 1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, -1, -1, -1, -2, 1, -1, 1, 0, 1, 0], [-1, -1, 0, -1, 0, 1, 1, 1, 0, 0, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, -1, -1, -1, -1, 0, 1, 0], [-1, 3, 0, -1, 0, 1, -1, -2, -1, -1, -1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -2, 0, 1, 1, 0, 2, 2, 1, 0, -1, 0], [0, 0, 1, 0, 1, -2, 0, -1, 0, -2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 1, 0, 1, -1, -1, 0, 0, -1, 1, 0], [2, -1, -1, 0, 1, -1, 2, -4, 0, 2, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, 0, 2, 1, 2, 2, 0, 2, -1, 2, 0, 0], [-1, 2, 1, 1, 1, -2, -1, -1, -1, -2, 1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, -1, -1, 0, 0, -1, 2, 2, 2, 2, 1, -2], [-4, -5, -1, 1, 0, -2, 1, 3, 1, -1, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-3, -3, 0, -1, -1, 0, 6, 1, 2, -2, 0, -1], [-3, -1, 1, 1, 0, -1, -3, -3, -1, 0, -1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 2, 1, 1, 0, -1, -1, -2, 0, -2, 2, -2], [-4, -3, -1, 0, -1, 0, 5, -3, 1, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, -4, 0, 0, 3, -2, 2, -4, 0, 0, 0, 0], [-4, -3, 1, -1, -2, 4, 2, 0, -2, -1, -2, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 2, 2, 0, 1, -2, -2, -3, -2, 0, 0, -1], [1, -5, 0, 2, -1, -2, 2, -2, 2, 4, 3, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 1, -1, -2, -2, 1, -2, 1, 1, 0, 0], [2, -1, -1, 2, 0, -3, 4, -2, 2, -4, 1, -2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 5, 2, 0, 0, -4, -1, -1, -1, -2, 1, -2], [-4, 0, -2, -1, -2, -4, -1, -2, 1, -4, 0, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, -1, -2, -2, -3, 3, -3, 3, 0, -3, -3, 2], [3, -4, 1, 1, -1, 1, 4, 2, 0, 4, -1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-4, 0, -2, 0, -2, 2, 2, -2, 0, 2, 0, 2], [-5, -3, -1, -1, -1, 1, 1, 1, 3, -4, -3, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, 3, 0, -1, 0, 6, -6, 2, -2, 0, -2, 2], [0, -1, 0, 0, 2, 3, -2, 3, -2, -4, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, -2, 0, 3, 1, 1, -3, -3, -1, 4, 2, 1], [0, 3, 0, -1, -1, -4, -1, -4, 0, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-3, -1, -2, -1, 1, 3, -1, -1, 1, -3, -3, 3], [1, 2, 1, 0, 0, 3, -1, 2, 1, 0, -1, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 1, 0, -4, 5, 1, 2, -1, 0, -1, 0], [2, -4, -2, 1, 3, -2, 3, 2, 3, 2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, 1, -1, 2, 2, 2, -2, 3, 1, 6, -2, 0], [-4, -1, 0, -1, 0, 1, 1, 1, -3, 0, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-3, -6, -1, 1, 0, -1, 1, 3, 1, 0, -2, 0], [1, 1, 2, -1, 0, -5, 3, -4, 1, 2, 3, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-5, 3, -4, -3, -3, 1, -3, -3, -1, -1, 1, 4], [1, 0, -1, 1, -1, 1, 4, 2, -1, 1, 0, -2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 1, 2, 2, -2, 2, 1, 0, 2, 2, -2], [-5, 3, 2, -2, -2, 2, -4, -6, 0, -4, -2, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, 0, -2, -3, -2, -6, 3, 6, 3, -6, 0, -4], [-2, 6, 0, -2, -2, -2, 0, 0, -2, -2, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-3, -3, 3, 3, 0, 0, -3, -3, -3, 2, 0, 3], [-5, 6, 4, -4, -5, -5, 1, -4, 1, -1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 10, 0, -2, 1, 5, -5, 2, -5, -6, -3, 1], [3, -4, -4, -3, 0, -1, 10, 6, 4, -6, 3, -3], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 6, -1, -3, -2, -1, -4, 3, -2, 4, -1, 1], [4, 2, 2, 0, 3, 3, -3, 2, -6, 0, -2, -4], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-4, -1, -3, 0, -4, -9, -2, -1, 4, 0, 3, 1], [3, 0, -1, 1, 2, -3, 0, -3, 2, -2, 1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, -3, 0, 2, -2, 5, 4, 1, 0, 1, -2, 4], [4, 4, 0, 0, 4, 6, -10, 0, -2, 2, -4, 4], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, -2, 2, 3, 4, -1, 6, -1, 0, -4, 0], [-4, 1, 0, 1, 0, 7, -7, 1, -4, 4, -4, 4], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-4, -5, 0, -1, -1, 7, 3, 3, -1, -4, 1, 0], [6, 0, 5, 4, 5, 4, -6, 1, -4, 4, 0, -4], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [9, -7, -2, 5, 2, -2, 8, -1, 0, 8, 2, -5], [-1, 4, 0, 1, 3, -3, 0, 4, 0, 0, 3, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, -2, 0, -2, 2, -1, 1, 0, 2, 0, -1], [1, -2, -4, 2, 2, 2, -8, -8, -2, 5, 2, 4], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 9, 2, -1, 0, 1, -3, -7, 0, -5, 2, 0]]}