# Stored data for newform 27.2.e.a, downloaded from the LMFDB on 18 April 2024. {"label": "27.2.e.a", "space_label": "27.2.e", "level": 27, "weight": 2, "hecke_orbit": 1, "hecke_orbit_code": 274911461403, "dim": 12, "is_polredabs": true, "nf_label": "12.0.1952986685049.1", "trace_hash": 1251911866554662276, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [], "qexp_display": "q+(-1-\\beta _{3}+\\beta _{8})q^{2}+(-1-\\beta _{2}+\\beta _{6}+\\cdots)q^{3}+\\cdots", "char_order": 9, "char_parity": 1, "char_degree": 6, "char_conductor": 27, "char_orbit_label": "e", "char_is_real": false, "Nk2": 108, "analytic_conductor": 0.21559608545745704, "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": "0.006", "prec": 17}, "analytic_rank_proved": true, "char_values": [27, 9, [2], [1]], "hecke_ring_generator_nbound": 4, "inner_twist_count": 2, "level_primes": [3], "conrey_indexes": [4, 7, 13, 16, 22, 25], "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, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "11.333", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "433.446", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "36298.178", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "1.2.3.c9", "trace_display": [-6, -6, -3, -6], "traces": [0, 12, -6, -6, -6, -3, 0, -6, 6, 0, -3, 3, 12, -6, 15, 9, 0, 9, 9, -3, -3, -12, 3, -12, -18, 3, -30, -9, -12, -6, -9, 3, 0, 0, 9, 12, 18, -3, 42, 33, 21, 15, 18, 3, 3, -9, -3, -15, -15, 12, -33, -18, 9, -18, -54, -12, -33, -3, 21, -12, 0, 12, -12, 9, 12, 3, -9, -15, 9, 9, -15, 27, 18, 6, 33, 39, -48, 15, 18, -42, 42, 36, -12, 39, 6, -27, 51, 9, -30, 9, 18, 6, -39, -39, -15, -33, 0, 3, -45, -27, 18, -15, 0, 30, 21, -27, 27, -18, -9, -12, 0, -3, 39, -66, -9, 39, -24, -36, -3, -36, -36, 39, -30, -63, 63, -24, 9, -3, 3, 15, 30, 69, 63, 42, 60, 72, 36, 48, 54, 3, 12, 9, -18, 6, -36, -3, -66, 0, -48, -3, -45, -60, 3, 18, -3, -6, -66, -69, -3, 45, -90, 30, 27, 42, 6, -9, -114, 42, -9, -60, -18, -45, -3, 30, -9, -36, -42, 36, -54, 0, -18, -3, 12, 51, 30, 39, 45, 36, 84, 45, 48, -15, 57, 48, -21, -9, 57, -27, 0, -3, 51, -57, 93, -30, -27, 75, 6, -90, -27, -30, 45, 66, -72, -9, 54, -96, 63, -30, 24, -84, 15, 36, -54, -6, -27, -9, -30, -60, 42, -6, 27, -9, -21, -27, 9, -30, 42, -21, -27, 6, 0, -15, 12, -81, -84, 18, 36, 15, -33, 72, -15, 45, -45, -30, -3, 45, -6, 15, -72, 15, -15, 90, -30, 21, 9, -27, -15, -9, 27, -36, -45, -30, 0, 3, 102, 30, -27, 75, 6, 72, 15, 21, -9, 75, 0, 90, 60, 39, 18, 39, 9, -39, 78, -12, -54, 3, -78, -27, -12, 12, -33, -51, -3, 54, -9, -33, 45, 33, 42, -21, -87, 6, 54, -105, 42, -9, 51, -15, 27, -105, 15, -126, -105, 36, -45, -12, -93, 15, -105, -48, -27, -114, 66, 45, 51, 21, 60, -87, 72, 45, -27, 24, -27, 33, -51, -45, -51, -39, 9, -42, 6, -9, 36, -96, -90, 27, 36, 27, 90, 45, 45, 45, 24, 57, 6, 111, 117, 75, -3, 72, 57, 54, -39, 39, 0, 0, 51, 78, -90, 42, -42, 78, 21, -75, 27, -15, 69, 45, -3, 111, -36, 27, 45, -9, -27, -6, -27, -3, -165, 12, 3, -93, -45, 12, -204, -108, 96, -30, -81, 3, -54, -171, -45, -60, 90, -3, 0, 42, 15, -48, -27, 30, 51, -36, -27, -54, -81, 21, 63, -36, 75, -108, 0, 42, 57, -63, 51, 3, 144, 66, 27, -81, -54, -33, 96, 90, -75, -72, 48, -27, 72, -30, 105, 24, 3, -66, -54, -15, 24, -27, -60, 3, -45, -24, 57, -18, -72, 36, 45, -57, 18, 69, -60, 87, 135, -3, -9, -27, -84, 93, 45, -12, 42, 108, -102, 138, 162, -120, 111, 69, -45, 132, 36, 9, -60, 90, -36, 18, -90, -42, 57, -27, -108, 36, -45, -57, 90, 27, 6, -30, 45, 24, -84, 9, -120, -15, 87, 21, -6, -90, 15, -9, -198, -21, -57, -3, 12, -36, -90, 48, 36, 72, -24, -105, 54, 27, -6, -9, 81, 72, 27, -12, -21, -3, 63, -105, -18, 66, -87, -153, 21, 15, -36, 75, -111, -72, 9, -81, -90, 60, -51, -45, 57, -39, -54, 30, -120, 72, 36, -60, -63, 3, -84, 45, 48, -30, -162, 60, 21, -75, 87, -66, 9, -27, -24, 54, 51, 138, 45, 87, 36, 162, 81, 180, 99, 90, 87, 105, -42, 150, 36, -33, 48, 72, 33, -84, 18, -33, 63, -18, -15, -12, 9, 6, -66, -72, -24, 87, 36, -78, 102, -9, 150, -99, 51, -81, 51, 9, -36, 36, 18, -3, -6, -93, -42, -150, -36, -57, -45, -117, 33, 84, 27, -159, 48, 36, -45, -54, 27, 150, 33, -15, -57, -48, 9, -123, 33, 9, -3, -132, -63, -96, -21, -54, 60, -12, 9, -3, -156, -12, -51, -93, -45, -96, 132, -9, 12, 183, -63, -78, -36, -63, -30, -171, 108, -30, -96, -48, -24, 27, -108, -51, -15, 54, -57, 30, 0, 54, 267, 171, 6, 0, 63, -24, 57, 126, 129, 105, 0, 75, 27, 0, -36, 21, 63, -6, -135, -18, 135, 45, -36, -57, -9, 60, 33, 84, -81, 111, 114, -27, -168, 27, -21, 111, -138, 72, 117, -75, 0, -57, -24, -6, 81, 132, 18, 75, -48, 9, 18, 9, 144, 93, -60, 81, -57, 30, 63, -138, 87, -18, 42, -39, -117, -48, 66, -45, -3, -42, -177, -60, 18, 180, -81, -90, -108, 24, 21, -60, -132, 57, -9, 9, -108, 0, -114, 30, 27, -6, -27, -108, -42, 102, 36, 105, -39, 0, -21, -129, -99, 9, 0, 63, 105, -39, 78, 6, 3, 0, -30, 0, -54, -12, -84, 42, -66, 93, 63, -21, -66, 0, 75, 57, 45, -6, -24, -54, -15, -18, 54, 105, 54, -174, -150, -9, -117, 3, 78, -9, 42, -141, -36, -6, 42, 45, -144, -18, -45, 51, -9, -48, 9, -78, 144, -87, 21, -81, 27, -60, 45, -15, -15, -90, -54, 0, 0, 96, 69, -6, -21, 15, 117, 165, -24, 72, 111, -3, -48, 48, 87, -108, 60, 9, 198, -3, 108, -72, 192, -21, 72, 123, -126, -27, 204, -102, 90, 135, -21, 0, 198, -12, -36, -54, 9, -60, 129, 66, 54, 84, 138, -63, -21, 84, 33, 111, -237, -18, -18, -24, -135, 24, -63, 51, -87, -18, 36, -3, 24, 72, -36, 48, 180, -102, -54, -81, -81, -27, -171, -84, -15, 96, -111, -84, -36, -78, 60, -63, -174, -33, -219, -30, -21, 36, -63, 36, -135, -111, 6, 72, 39, 195, 72, -159, 57, 162, -138, -141, -72, -24, -75, 0, -6, -144, -54, -192, 87, -30, 30, 60, -45, 27, -45, -54, -138, 246, 126, -99, 45, 90, -45, -24, -27, -102, -63, 150, 0, 102, -90, -78, -12, 9, -120], "weight_parity": 1, "has_non_self_twist": 1, "level_is_prime": false, "level_is_prime_power": true, "level_is_square": false, "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": "27.2.e.a", "char_is_minimal": true, "conrey_index": 4, "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], [-1, 0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0], [-1, 0, -1, 0, 0, 0, 1, 0, -1, 0, 0, 0], [1, 1, 1, 1, 0, 0, -1, 0, -1, 1, 0, 0], [-1, -1, 0, 1, 0, 1, 0, 1, 1, -1, 1, 1], [2, 0, 1, 1, -1, -1, -1, 0, 0, -1, -1, -1], [-1, -1, 0, -1, 1, -1, 0, -1, 0, 1, 0, -1], [0, 0, -1, 0, 1, 0, 0, -2, -2, 0, -2, 0], [0, 0, 1, 0, 0, 1, 0, -1, 2, -1, 1, 0], [-2, 0, -1, -1, 0, 0, 2, 1, 1, -1, 0, 1], [1, 1, 1, 0, -1, -1, 0, 1, -2, 2, 1, 1], [0, 0, -1, -1, 0, 1, 0, 3, 1, 1, 2, 0], [0, 1, -1, 0, -1, 1, -1, 1, 0, -1, 0, 0], [3, 1, 0, 1, -1, 0, 0, 0, 1, 0, 0, -1], [1, 1, 0, -1, 1, -1, -1, -2, -1, 3, -3, 0], [-2, -2, -1, 0, 0, 2, 1, 0, 1, -1, 0, 0], [1, 0, 0, -1, 1, -1, 1, 1, 1, -1, 0, -2], [-3, -2, 0, -1, 2, 0, 1, -1, -2, 1, 1, 3], [1, 0, 2, 1, -2, -1, 0, -1, 1, -2, 1, 1], [2, 0, 1, 0, 0, -1, -1, -2, 0, 0, 1, -3], [-1, 1, 0, 0, 1, 0, -1, 0, 0, -2, -1, 1], [0, -1, 0, 1, 0, -1, 0, -2, 0, -1, -2, 1], [1, 0, 0, 1, -1, 0, -1, 0, -2, 0, -3, -2], [-2, 0, 1, 1, 0, 0, 1, 1, 2, 0, 3, 2], [2, 1, -1, 1, 0, 1, -1, 2, 0, 0, 0, -2], [-3, 0, 0, 0, 1, 1, 0, 2, -2, 3, 3, 0], [0, -1, -1, 2, -1, 2, -1, 2, -1, 2, -2, -1], [-1, 0, 0, 0, 0, 0, 0, 2, -2, 1, 1, 0], [-1, 0, 0, 2, 0, 0, 0, -3, 1, 0, -3, 3], [3, 1, 2, 1, -2, -1, -2, -3, 0, 0, 0, -2], [-4, -1, -2, -3, 2, 0, 3, 0, 1, 0, 1, 1], [-1, 2, 0, -2, -1, -2, 1, 1, 1, -3, 1, 3], [-1, 0, -1, -3, 1, 0, 2, 2, 0, -1, 3, -3], [2, 2, 1, 0, 0, 1, -1, 0, 0, 0, 0, 0], [-2, -1, 1, -1, -1, 1, 1, 1, 2, -1, 2, 4], [3, 1, -2, -1, -1, -2, 1, -2, 0, -3, -4, -3], [2, 0, 2, 1, 1, -1, -3, -4, -2, 4, -2, -1], [0, -3, -3, 0, 2, 3, 0, 3, 1, -1, 0, 0], [3, -2, 1, 1, 0, -1, 1, -1, 2, -1, -1, -1], [2, -1, 2, -1, 1, -2, 0, -1, 1, 3, 0, -1], [-3, -3, -1, -3, 3, 1, 0, -5, 0, 3, 0, 0], [1, 0, -2, 2, -2, 3, 1, 1, -2, -1, 0, 1], [4, 4, 3, 0, -1, -4, -1, 1, -2, 2, 1, 1], [2, 0, 0, 2, -2, 2, -3, 1, 4, -1, -3, 0], [3, 3, 1, 2, -4, -2, 0, 5, 0, -3, 4, 1], [1, 2, -3, -1, 3, 1, -2, 2, -1, 3, -1, -4], [-3, 1, -2, 0, 0, 3, 2, 4, 0, -6, 3, 1], [-2, -1, 2, 0, -1, -1, 1, -2, 1, 0, -3, 2], [1, 0, 0, 0, -1, 2, 1, 4, -1, 1, 4, -1], [-5, 0, 1, -2, 2, 0, 2, 0, -2, 3, 1, 1], [-3, -1, -2, 0, 0, 1, -1, -3, -1, -1, 0, 1], [-2, -1, 1, 0, 0, -2, 2, -5, -2, 0, -1, 5], [0, 0, 0, 0, -3, -3, 0, -3, 3, 0, 0, 0], [-3, 3, 0, -3, 3, -3, 0, 0, 0, 3, 0, -3], [-3, -2, -1, 1, 2, 3, 0, -3, 3, -2, -2, 0], [-2, -1, 1, 1, 0, -1, 1, 1, -1, 0, -2, -1], [-2, -2, 0, 0, 3, 2, 0, 0, -4, 4, 0, -1], [4, -2, 1, 1, -3, 0, -1, 0, 2, -5, -1, -3], [2, 2, 0, -2, 3, -2, -3, 1, -2, 5, 1, -5], [-5, -3, -3, 1, 3, 5, 1, 2, 0, -2, -1, 2], [1, 0, -1, 5, -5, 1, 1, 4, 0, -5, -2, 6], [6, 3, 5, 3, -5, -3, -3, -2, 1, -3, 1, 0], [3, 0, 1, 1, 1, -2, -3, -1, 1, 4, 1, -1], [3, 0, -1, 1, -2, 2, -3, 3, 0, -3, 3, -2], [4, 2, 1, 0, 1, -2, -1, -2, -1, 1, -4, -4], [0, 2, 2, 1, 1, -1, -1, -1, -3, 3, 1, 3], [-4, -3, -1, 1, 3, 1, 4, -2, 1, -3, 0, -1], [1, 0, 2, 1, 0, -2, 1, 1, -2, 2, 0, 2], [-5, -4, 3, -2, 0, -1, 3, 0, 3, -2, 4, 6], [-1, 1, 0, 0, -1, -1, -1, 0, 2, -2, 2, 2], [4, 0, 0, 2, -2, 2, 1, 1, -2, -1, 3, -2], [6, 4, -1, 0, 0, 2, -5, 0, -2, 4, -3, -4], [-6, -3, -3, -3, 3, 3, 3, 0, -3, 3, -3, 1], [-1, -3, -3, -1, 1, 0, 3, -3, 0, 1, -3, 0], [1, -1, -2, 0, -1, 1, 1, -1, 2, -2, -1, 2], [-2, 4, 0, -4, 0, -2, 0, 0, 2, 3, 0, -3], [1, 1, -2, -1, 2, 0, 1, 0, -1, -1, 1, -2], [1, 1, -1, -4, 1, 1, -1, 2, 6, -2, -1, -3], [-6, 0, 0, -5, 0, -1, 1, 0, 2, 0, -1, 0], [4, 1, -1, 1, 0, 1, 0, 3, -3, 1, 1, 0], [0, 0, 3, -3, -3, -3, 3, 0, 3, -3, 0, 6], [1, 1, 1, -1, -3, -4, 0, -3, 3, 1, 1, 0], [5, 3, -3, -1, 0, 3, -3, 3, 1, 0, 3, -3], [-2, -1, 0, -4, 2, -1, 1, -1, 3, -1, 1, -1], [-3, -1, 0, 1, -2, 0, -1, 0, 0, 3, 0, 3], [2, -4, 0, 4, -1, 3, 1, -3, -2, -3, -3, 3], [8, 6, 4, 4, -4, -1, -4, 3, -3, 5, 2, 2], [-4, 0, -2, -2, 2, 2, 2, 2, 0, 1, 5, -3], [-1, -1, -4, 0, 4, 0, 1, 1, -5, 6, -5, -2], [-3, -4, -1, 2, 2, 5, 2, 5, -1, -1, 1, 2], [1, 0, 1, 1, 0, 0, 1, 4, 3, -4, 1, 0], [-6, 0, 3, 0, -1, 0, 3, 0, 1, -1, 6, 6], [3, 3, 1, 2, -2, -1, -3, -3, 1, -2, -2, -4], [-4, 0, -1, 1, 0, 1, 1, 2, -5, 0, 0, 5], [4, 5, 2, 3, -5, -2, -2, 1, 0, -4, 0, 0], [6, 0, 1, 2, 2, -2, -3, -4, -3, 3, 1, -8], [1, -2, -3, 0, 5, 2, -1, -5, -2, 2, -8, -8], [-8, 0, 1, -3, 4, -4, 2, -3, -2, 3, -1, 5], [-6, -5, -3, -1, 2, 3, 1, -4, 4, -5, -2, -3], [2, -1, 2, 3, -2, -3, 1, -4, -1, -3, -1, 4]]}