# Stored data for newform 729.2.e.u, downloaded from the LMFDB on 24 April 2024. {"label": "729.2.e.u", "space_label": "729.2.e", "level": 729, "weight": 2, "hecke_orbit": 21, "hecke_orbit_code": 90072267458872025, "dim": 12, "is_polredabs": true, "trace_hash": 1551648749192478049, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[2, [9, 81, 324, 144, 360, -144, -69, 72, -18, -12, 15, -6, 1]], [5, [25281, -10017, 2808, -3978, 846, 711, 363, -135, -9, 21, 15, 6, 1]], [7, [18496, -21216, 79680, -33104, 144, 1296, 921, -522, 162, -2, -12, 3, 1]]], "qexp_display": "q+(\\beta _{1}+\\beta _{5}-\\beta _{6}-\\beta _{8})q^{2}+(-1+2\\beta _{1}+\\cdots)q^{4}+\\cdots", "char_order": 9, "char_parity": 1, "char_degree": 6, "char_conductor": 27, "char_orbit_label": "e", "char_is_real": false, "Nk2": 2916, "analytic_conductor": 5.82109430735134, "hecke_ring_index": 3, "level_radical": 3, "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": "0.005", "prec": 17}, "analytic_rank_proved": true, "char_values": [729, 9, [2], [4]], "hecke_ring_generator_nbound": 4, "inner_twist_count": 2, "level_primes": [3], "conrey_indexes": [82, 163, 325, 406, 568, 649], "field_disc": 55649466460449, "field_disc_factorization": [[3, 18], [379, 2]], "field_poly": [1, 0, 132, 0, 306, 0, 266, 0, 105, 0, 18, 0, 1], "hecke_ring_index_factorization": [[3, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "11.988", "prec": 20}, {"__RealLiteral__": 0, "data": "5.662", "prec": 17}, {"__RealLiteral__": 0, "data": "421.386", "prec": 24}, {"__RealLiteral__": 0, "data": "723.326", "prec": 24}, {"__RealLiteral__": 0, "data": "24062.704", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "1.2.3.c9", "trace_display": [6, 0, -6, -3], "traces": [0, 12, 6, 0, 6, -6, 0, -3, -6, 0, -6, -12, 0, -3, -15, 0, -36, 9, 0, -12, -42, 0, 6, -6, 0, 6, 48, 0, 6, -12, 0, 6, -54, 0, -9, -30, 0, -3, -42, 0, -57, -24, 0, 6, 33, 0, 3, -21, 0, 33, -21, 0, 45, -18, 0, 30, -3, 0, 33, -15, 0, 33, 30, 0, -6, 6, 0, 42, 18, 0, 24, 0, 0, -12, 3, 0, -87, 57, 0, -48, -42, 0, -42, -12, 0, -36, 30, 0, 30, 9, 0, -18, 48, 0, 33, -30, 0, -3, -18, 0, 15, 78, 0, 33, 6, 0, 36, -72, 0, -12, 72, 0, -3, 48, 0, -39, 33, 0, 30, 27, 0, -30, 93, 0, 81, -39, 0, -12, 60, 0, 6, -24, 0, -33, 84, 0, -18, -30, 0, -12, 87, 0, -72, -33, 0, 21, 3, 0, 30, 3, 0, 42, -75, 0, 57, -21, 0, -3, -60, 0, -72, 6, 0, -30, -51, 0, -66, 30, 0, 87, 9, 0, 60, 60, 0, 72, 42, 0, -126, 27, 0, 15, 33, 0, 78, 51, 0, 9, -30, 0, -84, -66, 0, -75, 39, 0, -93, 27, 0, -30, 21, 0, 6, -15, 0, -30, -6, 0, 3, 57, 0, -57, 0, 0, -81, -12, 0, 0, 111, 0, 120, -36, 0, -3, 27, 0, -15, 24, 0, -30, 27, 0, 57, -27, 0, 3, 3, 0, -63, -42, 0, -39, 6, 0, 132, 45, 0, 21, 69, 0, 96, -36, 0, 21, -33, 0, 96, 57, 0, 30, -12, 0, -15, -75, 0, 63, 6, 0, 153, -36, 0, 150, 0, 0, -48, -57, 0, -57, -33, 0, 3, -84, 0, -111, -144, 0, 57, 24, 0, 21, -9, 0, -6, 66, 0, 51, 78, 0, -114, 6, 0, 96, -60, 0, -27, 33, 0, -48, -42, 0, -75, 3, 0, -57, 84, 0, -129, 6, 0, -57, 57, 0, 15, -72, 0, -84, -87, 0, -48, -78, 0, 6, -39, 0, -114, 33, 0, -21, -126, 0, -81, 12, 0, -45, -84, 0, 60, -87, 0, 60, 12, 0, 0, 78, 0, -72, -207, 0, 117, -36, 0, 0, -33, 0, -69, 15, 0, -21, 93, 0, 6, -126, 0, 6, 9, 0, -15, 102, 0, 24, -111, 0, 123, 12, 0, 51, 3, 0, 78, -57, 0, 27, -81, 0, 54, 114, 0, 51, -141, 0, 6, 30, 0, 6, 6, 0, 66, -42, 0, 69, -117, 0, 63, 6, 0, 12, -117, 0, -33, 39, 0, -21, 12, 0, 63, 9, 0, -102, -63, 0, 60, 162, 0, -48, -111, 0, 84, -21, 0, -66, -9, 0, -45, -111, 0, -72, 57, 0, -66, -54, 0, -33, -33, 0, 123, -87, 0, 33, -222, 0, 186, 78, 0, 78, 33, 0, -135, 9, 0, 0, 18, 0, -39, -6, 0, 39, 45, 0, -15, -3, 0, 39, 39, 0, -51, 60, 0, 114, 231, 0, -126, -69, 0, 81, -57, 0, 12, -36, 0, 51, 15, 0, -99, -45, 0, 30, 90, 0, 30, 93, 0, 93, 102, 0, 120, -21, 0, -84, 150, 0, -33, 72, 0, -3, 228, 0, 159, -108, 0, -66, -126, 0, -51, 42, 0, -72, 42, 0, -234, -90, 0, -174, -24, 0, -81, 69, 0, -75, -165, 0, -39, 165, 0, 15, -33, 0, 45, -54, 0, -36, 141, 0, -120, -105, 0, -129, 66, 0, -216, 51, 0, -3, 102, 0, -3, 48, 0, 24, -12, 0, 39, 21, 0, -36, -75, 0, -114, -21, 0, 84, 45, 0, -9, -36, 0, -180, -6, 0, -21, 219, 0, -138, 6, 0, -21, 30, 0, 15, 171, 0, 78, 30, 0, 78, 57, 0, -21, 39, 0, 78, -174, 0, 138, -9, 0, 36, -78, 0, 45, 117, 0, 33, -84, 0, 6, 123, 0, 12, -135, 0, 147, 123, 0, 33, -75, 0, 63, 216, 0, -42, -51, 0, -132, 147, 0, -57, 210, 0, 147, -39, 0, 42, 30, 0, 66, 12, 0, 93, 12, 0, 150, -114, 0, -39, -168, 0, 6, 60, 0, 96, 162, 0, 129, -117, 0, 129, 132, 0, -84, 117, 0, 177, 42, 0, 84, -66, 0, -54, 129, 0, 3, 162, 0, 30, -174, 0, -120, -132, 0, 105, -108, 0, -72, 33, 0, 168, 45, 0, 72, -63, 0, 36, 171, 0, -132, -3, 0, -111, -186, 0, 24, -72, 0, 96, -114, 0, 0, 75, 0, 33, 132, 0, 0, -24, 0, 78, 102, 0, 45, 108, 0, -174, 42, 0, -240, -210, 0, -30, 12, 0, 39, 66, 0, -24, 123, 0, -33, 15, 0, -12, -99, 0, 90, -63, 0, -102, 69, 0, 114, -102, 0, 180, -162, 0, -264, 69, 0, -111, 36, 0, 123, 33, 0, 36, 93, 0, 75, -51, 0, -63, 54, 0, -123, -15, 0, 165, 114, 0, 129, 108, 0, -66, -42, 0, -15, 105, 0, -42, 30, 0, -210, -84, 0, -48, 195, 0, 15, 63, 0, -57, 9, 0, -102, 54, 0, -12, 66, 0, -150, 42, 0, -48, 75, 0, 63, 90, 0, -30, 198, 0, 36, -3, 0, -129, -48, 0, -18, 24, 0, 6, -12, 0, 36, -54, 0, -24, -87, 0, -195, 12, 0, -21, -102, 0, 69, -213, 0, 42, -168, 0, -78, -99, 0, 69, -81, 0, -228, 30, 0, 102, -126, 0, 6, 120, 0, 171, -159, 0, -117, -105, 0, -36, -63, 0, -129, -147, 0, 258, -102, 0, 21, -3, 0, -30, 111, 0, -198, 222, 0, 168, 90, 0, 132, -18, 0, -42, -69, 0, 117, 69, 0, -78, 9, 0, 72, 27, 0, -30, -201, 0, 93, -15, 0, 141, 138, 0, 372, 33, 0, 12, 66, 0, 9, 9, 0, 39, -312, 0, -75, 39, 0, -84, 168, 0, -12, -39, 0, 249, -60, 0, 231, 18, 0, 198, 120, 0, 123, -159, 0, -180, -126, 0, -15, 51, 0, -81, 54, 0, -180, 42, 0, -39, 9, 0, -36, -129, 0, -120, 66, 0, 192], "weight_parity": 1, "has_non_self_twist": 1, "level_is_prime": false, "level_is_prime_power": true, "level_is_square": true, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 27, 5, 1, 9, 0]], "char_orbit_index": 5, "prim_orbit_index": 5, "minimal_twist": "729.2.a.b", "char_is_minimal": false, "conrey_index": 82, "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, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 1, -1, 0, -1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 2, 0, -1, -1, 1, -2, 0, -1, 0, -1, 1], [0, 1, 0, 0, 1, -1, -1, -1, -1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 1, -1, -1, 1, 0, 1, 0, 0, -1, 1], [-2, 3, -1, -1, -1, -2, -2, -2, 0, -1, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 3, 1, -1, 0, 2, -3, -1, -1, 0, 0, 1], [0, 0, 0, 1, 1, 1, -2, 1, 0, 2, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 1, 1, 0, -1, 1, 0, -1], [-1, 0, 0, -1, 0, -2, 5, -1, 1, -2, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-5, 0, 0, -1, -2, -2, -2, -3, 0, -2, 1, 1], [0, 0, 1, 1, 0, -2, 1, -3, 0, -2, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-3, 2, -1, 0, 0, -1, -1, -1, -1, -2, 1, 1], [-5, 5, 1, -1, 0, 0, -3, -4, 0, -3, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, -1, 1, -1, -1, 4, 0, 5, 0, -4, -2, 0], [-1, -2, 1, 0, -1, 1, 1, 1, -1, 2, -1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 1, 0, 0, 1, -1, 2, -1, 1, 0], [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], [0, -1, 0, -1, -2, 3, 4, 1, 2, -1, 1, -2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 3, 1, 1, 0, -2, -2, -1, 0, 0, 2, -2], [-4, -1, -1, 1, -2, -6, 3, -1, 3, 0, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 0, 0, 1, 2, -2, 2, -1, 0, 2, 2, -1], [-3, 0, 1, 2, 2, -3, -1, -1, 1, -4, -1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, -1, -1, 0, 0, 5, -4, 5, -1, 2, -2, 1], [-3, 2, -2, -1, -2, -3, -2, -2, 2, 2, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-5, 0, -2, -3, -2, 0, 3, -3, 3, 0, 0, 2], [-5, 0, -1, 1, -1, -2, -2, -4, -1, -2, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, 2, 2, 2, 0, -4, -2, -2, 4, -2, 0], [2, 0, -3, -1, 0, 1, 2, 4, 2, -4, -1, -2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 1, 2, 1, 1, -2, 2, 2, 0, 0, 0, -2], [2, 0, -1, 2, 2, -2, 4, -3, 0, 4, 2, -2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, -1, -1, 1, 3, 1, -2, -2, -2, 2, 1, 0], [-1, -5, 0, 1, 1, 1, 4, 1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 7, 0, -2, -1, 3, -3, 2, -3, -3, -1, -1], [-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], [-1, -1, 0, 2, 3, 1, -2, -2, 0, 0, -1, 3], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [5, -5, 0, 2, 2, -5, 2, -3, 2, 3, -1, 1], [0, -2, 0, 0, 1, -1, -1, -1, -1, 4, -3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, -4, -2, 1, 0, 0, 3, 5, 0, 3, 0, -1], [5, 5, 3, -1, -1, -2, 0, 0, -2, 2, 2, -3], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [5, -6, -1, 3, 0, -8, 9, 0, 5, 1, 4, -5], [0, 4, 2, -2, -1, 3, -1, 2, -2, -2, 2, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, 0, 2, 2, 2, -2, 0, 1, -2, -2, 0, -1], [2, 0, 2, 2, 2, 3, 2, 0, -2, 3, 0, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, -8, -4, -1, 2, -1, 10, 6, 4, -6, 1, -3], [-2, 2, 2, -2, 0, -2, 0, -4, -2, -2, 0, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, 0, 0, -3, -3, 0, 0, 0, 3, -2, -3, 0], [-6, 1, -1, -1, -5, 5, -4, 7, 0, -4, -5, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-6, -1, -1, 1, -2, -11, 3, -4, 3, 0, 5, 0], [10, 3, -3, 0, 3, -10, 1, -3, 3, 0, 4, -4], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-4, -5, 0, -1, 2, 5, 1, 1, -1, 2, -3, 2], [-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], [0, -3, 0, 1, 2, -1, -3, -1, -1, 4, -1, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, -3, -4, -2, 2, -1, 5, 8, 2, 5, 0, 0], [-2, 8, 4, -4, 0, 8, -4, 6, -4, -8, -2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, -2, -4, -1, -3, 3, 0, 0, 0, 0, -3, 1], [0, -2, -4, 1, 1, 1, -2, -2, 0, 4, 0, 4], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 2, -1, 1, 0, -4, 5, -6, 1, 4, 0, -1], [6, 0, 4, 1, 5, -1, 0, -1, -4, -2, -1, -4], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [6, 0, 5, 2, 5, 4, -8, 1, -2, 4, 0, 2], [0, 0, -1, -3, -1, 2, -3, 1, 3, 2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, -1, -1, 2, 2, 3, -1, 4, 1, 4, -2, 0], [-6, 6, 2, 2, 0, 14, -16, 0, -6, 5, -4, 6], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, -8, -2, 1, 1, 5, 8, 8, 2, 5, -2, 2]]}