# Stored data for newform 729.2.c.e, downloaded from the LMFDB on 19 April 2024. {"label": "729.2.c.e", "space_label": "729.2.c", "level": 729, "weight": 2, "hecke_orbit": 5, "hecke_orbit_code": 18014535981990617, "dim": 12, "is_polredabs": true, "nf_label": "12.0.1952986685049.1", "trace_hash": 2147976638829685423, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[2, [9, -27, 81, -72, 117, -63, 123, -45, 45, -15, 12, -3, 1]]], "qexp_display": "q+(-\\beta _{6}-\\beta _{8}+\\beta _{10})q^{2}+(-1+\\beta _{2}+\\cdots)q^{4}+\\cdots", "char_order": 3, "char_parity": 1, "char_degree": 2, "char_conductor": 9, "char_orbit_label": "c", "char_is_real": false, "Nk2": 2916, "analytic_conductor": 5.82109430735134, "hecke_ring_index": 27, "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": "0.041", "prec": 17}, "analytic_rank_proved": true, "char_values": [729, 3, [2], [1]], "hecke_ring_generator_nbound": 4, "inner_twist_count": 2, "level_primes": [3], "conrey_indexes": [244, 487], "field_disc": 1952986685049, "field_disc_factorization": [[3, 18], [71, 2]], "field_poly": [3, -27, 108, -258, 420, -504, 463, -330, 186, -80, 27, -6, 1], "hecke_ring_index_factorization": [[3, 3]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "10.649", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "499.271", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "51065.290", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 6, "sato_tate_group": "1.2.3.c3", "trace_display": [3, 0, 6, 0], "traces": [0, 12, 3, 0, -3, 6, 0, 0, -12, 0, 6, 12, 0, 0, 6, 0, 3, -18, 0, 6, 6, 0, -6, 15, 0, 6, -30, 0, -12, 12, 0, 0, 0, 0, 0, -24, 0, 6, -3, 0, -6, 15, 0, 0, -6, 0, 6, 21, 0, 12, 3, 0, -12, -18, 0, -12, -6, 0, 12, 24, 0, 9, 24, 0, -24, -6, 0, 9, -9, 0, -15, -54, 0, -12, -12, 0, -6, -12, 0, 0, 42, 0, -12, 12, 0, 0, -21, 0, -12, -18, 0, -12, 6, 0, -6, 12, 0, 0, 90, 0, -36, 12, 0, 9, -6, 0, 0, -18, 0, -12, -9, 0, -9, -21, 0, -15, 48, 0, 6, 18, 0, 24, -48, 0, 24, 48, 0, 6, -60, 0, -6, 24, 0, 9, 60, 0, 36, -33, 0, 0, -15, 0, 0, -12, 0, 6, -39, 0, -6, -12, 0, 9, -6, 0, 6, -24, 0, 0, -66, 0, 18, 30, 0, 42, -39, 0, -15, 15, 0, 30, 36, 0, 6, -24, 0, -21, 12, 0, -27, 0, 0, 6, 3, 0, -6, -33, 0, -27, 84, 0, 48, 39, 0, 9, -12, 0, 21, 54, 0, 6, -39, 0, -6, -21, 0, -15, -12, 0, 54, -3, 0, -27, 0, 0, 0, -96, 0, -30, -30, 0, -21, -18, 0, -27, 54, 0, 60, 21, 0, -27, -9, 0, 24, 54, 0, 60, 51, 0, 36, 60, 0, 0, 12, 0, -84, 0, 0, 36, -15, 0, -15, -90, 0, 60, 6, 0, 33, 15, 0, 36, 30, 0, 60, 21, 0, -27, 30, 0, 24, -36, 0, -30, 18, 0, 12, -24, 0, 0, -12, 0, -30, 21, 0, -27, 18, 0, -39, -78, 0, -78, 9, 0, 30, -21, 0, 3, -78, 0, -12, 39, 0, -12, 51, 0, 42, 66, 0, -66, -3, 0, 48, 69, 0, -27, -84, 0, -102, -33, 0, -33, 6, 0, -42, 36, 0, -12, 42, 0, 12, 42, 0, -27, -132, 0, -102, 48, 0, 0, -9, 0, 9, -48, 0, -66, 12, 0, 48, 15, 0, 0, 6, 0, 36, -60, 0, -27, 63, 0, -27, -90, 0, -90, 87, 0, 9, -24, 0, 9, 6, 0, -114, 36, 0, 0, 18, 0, 42, 78, 0, 42, 57, 0, 12, 51, 0, -15, -138, 0, 6, -33, 0, 0, -9, 0, 54, 12, 0, 6, -21, 0, -3, -3, 0, -30, -204, 0, 96, 42, 0, -54, -27, 0, 24, 120, 0, 6, 36, 0, 33, -3, 0, -54, -102, 0, 54, -18, 0, 42, 18, 0, -24, -108, 0, 42, -6, 0, 66, -33, 0, 36, -54, 0, 108, -60, 0, 0, 132, 0, -18, 54, 0, 60, 15, 0, -60, -3, 0, 0, 24, 0, -60, -6, 0, -27, -33, 0, -81, -72, 0, 114, 27, 0, -87, -48, 0, -15, 18, 0, 168, 66, 0, 9, 87, 0, 45, 138, 0, -120, -15, 0, 45, 24, 0, 0, 120, 0, 72, -45, 0, 36, -24, 0, 54, -72, 0, 114, 18, 0, -87, -21, 0, 54, -84, 0, -120, -51, 0, -33, -15, 0, 51, 18, 0, 42, 24, 0, -60, 18, 0, 33, -72, 0, 48, 3, 0, 54, 3, 0, -81, 72, 0, -12, 51, 0, 18, -69, 0, 63, 174, 0, -42, 69, 0, 42, 15, 0, -57, 162, 0, -120, 21, 0, -33, -57, 0, 3, -120, 0, 36, -33, 0, 0, 51, 0, 30, 60, 0, -120, -87, 0, -66, -66, 0, 0, 48, 0, -102, -33, 0, 63, -36, 0, -12, 180, 0, 90, 60, 0, -69, 42, 0, -54, -96, 0, -66, -120, 0, 54, -45, 0, 39, 24, 0, -12, 15, 0, 3, -75, 0, 63, 102, 0, 150, -54, 0, 66, 6, 0, -12, -72, 0, 6, -6, 0, -6, 3, 0, 24, 90, 0, -66, -105, 0, 9, -51, 0, 27, -54, 0, 150, -66, 0, -69, -138, 0, 39, -66, 0, 6, -15, 0, -45, -3, 0, -57, 24, 0, 6, -102, 0, -6, 6, 0, -81, 132, 0, 12, 3, 0, 42, 36, 0, -12, 342, 0, 60, 12, 0, 90, -99, 0, -27, 30, 0, 114, -42, 0, -81, 15, 0, -24, 0, 0, -24, -42, 0, -69, -66, 0, -54, -54, 0, 72, 57, 0, 12, -9, 0, 0, -90, 0, 114, 54, 0, 48, 21, 0, 36, 114, 0, -168, -27, 0, 108, -3, 0, -81, 150, 0, 114, 12, 0, 27, -12, 0, 93, 96, 0, -36, -135, 0, -54, 12, 0, 69, 30, 0, -138, -102, 0, -48, 24, 0, 9, -132, 0, 6, 3, 0, -81, 18, 0, -21, 180, 0, -48, 57, 0, 102, -69, 0, -54, -108, 0, -114, -42, 0, 36, -153, 0, 93, -204, 0, -210, -3, 0, 102, 15, 0, -54, 0, 0, -210, 6, 0, -12, 48, 0, -93, 0, 0, -12, 24, 0, -21, 21, 0, -72, 132, 0, -150, -60, 0, -27, 30, 0, -42, 36, 0, -210, -27, 0, 54, -45, 0, 30, 78, 0, 42, 93, 0, 24, 132, 0, -93, 36, 0, -102, -45, 0, 27, 3, 0, 63, -42, 0, -54, -15, 0, 0, 3, 0, 108, 0, 0, 96, 177, 0, 27, 6, 0, 78, 48, 0, -222, -30, 0, 0, -93, 0, 51, -18, 0, 6, 63, 0, -33, 78, 0, 9, -126, 0, 204, -3, 0, -108, 51, 0, 108, 24, 0, 108, 9, 0, -33, -51, 0, -108, -276, 0, 42, 147, 0, -33, -84, 0, -120, -24, 0, 24, -45, 0, 120, -27, 0, 66, -48, 0, 72, 66, 0, -12, 144, 0, -54, 54, 0, 168, -15, 0, 6, 60, 0, -69, 60, 0, -174, -78, 0, -54, 87, 0, -63, -72, 0, 222, 78, 0, -141, 114, 0, 84, -114, 0, 276, 66, 0, 63, -57, 0, 84, -144, 0, -192, 33, 0, 54, -12, 0, -27, 90, 0, 276, -6, 0, 108, -18, 0, 75, 48, 0, 204, 108, 0, -99, 3, 0, 90, -12, 0, -120], "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, 9, 3, 1, 3, 0]], "char_orbit_index": 3, "prim_orbit_index": 3, "minimal_twist": "27.2.e.a", "char_is_minimal": false, "conrey_index": 244, "id": 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, 0, 0, 0, 0, 0, -1, 0, -1, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 1, -1, 1, 0, -1, 0, 0, 0, 1, 1], [1, -1, 0, 0, 0, -1, 0, -1, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, -1, 1, 0, -1, 1], [-1, 0, 2, 0, 1, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, -1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, -1, 0, -2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, -1, 0, -2, 0, -1, -2, -1, 0, 1, 0, 0], [1, 0, 1, 0, -1, -1, 0, 0, -1, 1, 2, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 1, 1, -1, -1, 1], [-1, 0, 1, 1, -1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 1, -1, -1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, -2, -1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, -1, 1, -2, 0, -2, -2, -1, -1, 0, 2, 0], [3, 1, 0, 1, 0, -1, 1, 1, -2, 2, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, -1, 2, -1, 0, 1], [-3, -1, 3, -1, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 2, 0, -1, -3, -2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -2, 0, 0, -1, 0, 0, -2, 2, 0, -2, -1], [0, 2, 2, 0, 1, 0, 0, 2, -2, 0, 4, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 2, 2, -1, -1, 1, -1], [-2, 1, -1, 0, -2, -1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, -2, -1, -1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 3, -5, 0, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 2, 1, 0, 2, 0, 0, -2, 1, 1], [2, 0, 0, -1, 3, -1, -1, 0, -1, 3, 1, 3], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, -2, -3, -1, 1, 1, -1], [-2, 0, 4, -3, 2, 2, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 1, -2, 3, 2, 2, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 1, -2, -4, -1, -3], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, 0, 0, 2, 1, 4, 2, 0, 4, 1, -4, 1], [-1, -2, 3, -3, 0, -2, -3, -2, 0, 2, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 2, 2, -2, 1, -3, -1], [0, 3, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, -2, -2, 0, -1, -4, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 2, 1, -2, 0, 3, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, 3, -5, 2, -2, -3, 2, 3, -6, 1, 1, -2], [4, 2, -3, 0, -3, -1, 0, 2, -3, 4, 0, -3], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, -5, 0, 0, 1, 2, -1], [2, -3, 2, 0, -2, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-4, -1, 0, -4, 2, -5, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, -2, -1, 0, 2, -2, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, 4, 1, 3, -1, 5, 3, 4, 1, 0, 0, -1], [0, 1, -2, 3, -1, 0, 3, 1, -1, -3, -1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, -1], [-4, 0, -2, 1, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 3, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, -2, -3, 1, 3, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 4, -5, 2, 0, 0, 2, 4, -4, -2, -1, 0], [-2, -2, -1, 0, 1, -1, 0, -2, 1, -2, -2, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, -4, 1, -6, 2, 6, 0], [3, 0, 1, -1, -1, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, -4, -3, 5, 0, -2, 3], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 2, 3, 2, -1, 4, 2, 2, 2, -1, 1, -1], [-4, -4, 5, -1, 1, 2, -1, -4, 6, -3, -1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 2, 0, -3, 1, -2, -2], [-2, 0, -1, -1, 4, -3, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 3, 2, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, -2, -3, 4, 0, 2, 3], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 1, -5, 0, -1, -1, 0, 1, -2, -1, -3, -1], [2, -2, 0, 0, -3, 1, 0, -2, 3, 2, -3, -3], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, -2, 3, -1, 1, -2, -1], [9, 1, -2, 3, -4, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-5, -3, 4, -4, 1, 0, 0, 0, 0, 0, 0, 0]]}