# Stored data for newform 243.2.e.a, downloaded from the LMFDB on 07 October 2024. {"Nk2": 972, "analytic_conductor": 1.9403647691171133, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 27, "char_degree": 6, "char_is_minimal": false, "char_is_real": false, "char_orbit_index": 5, "char_orbit_label": "e", "char_order": 9, "char_parity": 1, "char_values": [243, 9, [2], [4]], "cm_discs": [], "conrey_index": 28, "dim": 12, "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], "field_poly_is_cyclotomic": false, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 0, "has_non_self_twist": 1, "hecke_cutters": [[2, [9, -27, 81, -117, 63, 36, -21, -27, 9, 6, 3, 3, 1]]], "hecke_orbit": 1, "hecke_orbit_code": 274911461619, "hecke_ring_generator_nbound": 4, "hecke_ring_index": 3, "hecke_ring_index_factorization": [[3, 1]], "hecke_ring_index_proved": true, "inner_twist_count": 2, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 27, 5, 1, 9, 0]], "is_cm": false, "is_largest": false, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": false, "is_self_twist": false, "is_twist_minimal": false, "label": "243.2.e.a", "level": 243, "level_is_powerful": true, "level_is_prime": false, "level_is_prime_power": true, "level_is_prime_square": false, "level_is_square": false, "level_is_squarefree": false, "level_primes": [3], "level_radical": 3, "minimal_twist": "27.2.e.a", "nf_label": "12.0.1952986685049.1", "prim_orbit_index": 5, "qexp_display": "q+(-\\beta _{2}-\\beta _{8}-\\beta _{11})q^{2}+(-1-\\beta _{1}+\\cdots)q^{4}+\\cdots", "related_objects": [], "relative_dim": 2, "rm_discs": [], "sato_tate_group": "1.2.3.c9", "self_twist_discs": [], "self_twist_type": 0, "space_label": "243.2.e", "trace_display": [-3, 0, -6, 3], "trace_hash": 1233186984035508499, "trace_moments": [{"__RealLiteral__": 0, "data": "0.007", "prec": 17}, {"__RealLiteral__": 0, "data": "11.723", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "449.013", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "36815.292", "prec": 30}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.007", "prec": 17}, "traces": [0, 12, -3, 0, 3, -6, 0, 3, -6, 0, -3, 6, 0, 3, 21, 0, 9, -9, 0, -3, -24, 0, 12, 12, 0, 12, 30, 0, -12, 24, 0, 12, -27, 0, 0, -12, 0, -3, 30, 0, -15, -6, 0, -15, -3, 0, -3, -12, 0, -33, -21, 0, -45, 18, 0, -12, -30, 0, -51, 3, 0, -33, 12, 0, 12, -21, 0, -6, -9, 0, -15, -27, 0, 6, 21, 0, 6, 12, 0, 21, -42, 0, -12, 6, 0, 36, 21, 0, 42, -9, 0, 6, 3, 0, 48, -3, 0, 39, 45, 0, 18, 15, 0, 39, 6, 0, 54, 18, 0, -12, 0, 0, 12, 3, 0, 21, 24, 0, -3, -18, 0, -6, 39, 0, -36, 24, 0, -3, -3, 0, -24, -15, 0, -30, -60, 0, 36, 24, 0, -42, 24, 0, -54, -6, 0, -3, -24, 0, -12, -69, 0, 3, -3, 0, -3, 60, 0, 21, 3, 0, 36, -30, 0, 42, -24, 0, 84, 57, 0, 57, 18, 0, -3, -75, 0, 36, -21, 0, 90, 0, 0, -3, 15, 0, 12, 42, 0, -27, -84, 0, 48, -48, 0, -24, 12, 0, -24, 27, 0, -3, 21, 0, -87, -42, 0, -78, -6, 0, -27, -24, 0, -87, -90, 0, -108, 96, 0, -30, 39, 0, -48, -9, 0, -78, 27, 0, -30, 15, 0, -78, 0, 0, -39, 27, 0, -30, 66, 0, 9, -6, 0, -6, -12, 0, -84, 9, 0, -12, -12, 0, 48, -45, 0, -30, 48, 0, 93, -6, 0, 42, 15, 0, -30, -21, 0, 81, -12, 0, 81, 36, 0, -30, 27, 0, 30, 6, 0, 3, -6, 0, 15, -12, 0, 3, 27, 0, 6, -39, 0, 39, -36, 0, -57, 93, 0, -15, 78, 0, -12, -21, 0, -15, -33, 0, 9, 33, 0, 33, 30, 0, -15, 84, 0, 12, -42, 0, 51, -66, 0, 39, 66, 0, 84, -36, 0, -12, -87, 0, 57, -69, 0, 84, -66, 0, 51, 42, 0, 111, 9, 0, 9, -24, 0, 33, -57, 0, 39, -96, 0, 21, -6, 0, 36, 87, 0, -18, 18, 0, -108, -45, 0, 45, -33, 0, -12, 42, 0, -51, 3, 0, 57, 27, 0, -87, 0, 0, -57, -78, 0, 42, 33, 0, -105, -96, 0, -24, -69, 0, -3, 60, 0, -18, 90, 0, -72, 6, 0, -3, -132, 0, -51, -42, 0, -6, 204, 0, 96, -15, 0, 39, -108, 0, 81, 60, 0, -3, 0, 0, 42, 57, 0, 93, -51, 0, -27, -27, 0, 84, 126, 0, 12, 108, 0, 42, 15, 0, 42, -21, 0, 48, -27, 0, -54, 42, 0, 0, -105, 0, 3, 27, 0, -30, 57, 0, 39, -15, 0, 48, -24, 0, -60, -12, 0, 39, 60, 0, 27, -36, 0, -57, -45, 0, -42, 30, 0, 60, 9, 0, -84, -12, 0, 51, 12, 0, -12, -138, 0, -120, 150, 0, 54, 156, 0, -54, 60, 0, -36, 90, 0, -6, -39, 0, 36, -36, 0, -57, 45, 0, 6, 3, 0, -21, 84, 0, -120, -102, 0, -78, -39, 0, -39, 9, 0, -21, -33, 0, -114, 9, 0, -132, -36, 0, -24, -57, 0, -108, -48, 0, -135, -72, 0, -12, -78, 0, -99, -21, 0, -141, 87, 0, 21, 30, 0, -105, -123, 0, -36, 81, 0, 60, -3, 0, -69, -96, 0, -42, 120, 0, 36, -3, 0, -15, 21, 0, -6, 30, 0, 60, -93, 0, 24, -6, 0, 27, 24, 0, 51, 213, 0, -75, -36, 0, -36, -180, 0, 90, -132, 0, 57, 30, 0, 57, -48, 0, 33, -33, 0, 30, -36, 0, 66, 12, 0, 6, 147, 0, 48, 75, 0, 66, -102, 0, 150, -36, 0, 117, 129, 0, 36, -36, 0, -3, -66, 0, 102, -102, 0, 24, 45, 0, 33, 24, 0, 93, -21, 0, 45, 54, 0, 150, 111, 0, 15, -123, 0, 48, -33, 0, -3, -102, 0, -6, -51, 0, -12, 12, 0, -3, -60, 0, 3, -123, 0, 75, -132, 0, 12, 78, 0, 39, 36, 0, 15, 171, 0, -30, -3, 0, -6, 108, 0, -42, 15, 0, -57, -57, 0, 36, 219, 0, -21, 0, 0, -24, 42, 0, -159, 183, 0, 3, -27, 0, -36, -12, 0, 21, 81, 0, -18, -45, 0, -57, -45, 0, 33, 24, 0, 12, -114, 0, -168, -54, 0, -15, 75, 0, -27, 75, 0, -57, -75, 0, 0, 39, 0, 3, 48, 0, 18, -63, 0, -6, -48, 0, 123, -30, 0, -138, 57, 0, -21, 30, 0, 78, -66, 0, -3, 51, 0, 165, 36, 0, 144, 90, 0, 24, 114, 0, 120, 51, 0, 54, 108, 0, -114, 69, 0, 138, -135, 0, 102, -102, 0, 105, 30, 0, 150, -78, 0, 27, 0, 0, 105, 12, 0, -39, -30, 0, 51, 0, 0, -12, -42, 0, 24, -30, 0, -12, 66, 0, 75, 114, 0, -132, -147, 0, -123, 18, 0, 105, 54, 0, -15, -18, 0, -123, -78, 0, 42, -111, 0, -78, 57, 0, -18, 18, 0, 51, -72, 0, 0, -66, 0, -51, -21, 0, 27, 6, 0, -141, -12, 0, -27, 0, 0, 96, 21, 0, 15, -51, 0, -123, 24, 0, 111, -87, 0, -51, 30, 0, -39, -9, 0, -3, 81, 0, -96, -33, 0, -111, 126, 0, 204, -78, 0, -153, -42, 0, -135, 12, 0, -54, -9, 0, -204, 60, 0, -150, -138, 0, -21, 78, 0, -69, -141, 0, -72, 24, 0, 24, -45, 0, 57, -9, 0, -30, -24, 0, -36, -93, 0, -21, -81, 0, 90, 27, 0, -84, -39, 0, 150, -24, 0, 93, -60, 0, -174, -192, 0, -3, 39, 0, 63, -36, 0, -111, 120, 0, 102, 165, 0, 120, -57, 0, -138, -129, 0, -15, 21, 0, -42, 144, 0, -192, 138, 0, -105, 12, 0, -45, 45, 0, -138, 168, 0, -54, 90, 0, -72, 24, 0, -102, -153, 0, -126, 60, 0, -123, 12, 0, -120], "weight": 2, "weight_parity": 1, "id": null, "artin_degree": null, "artin_field": null, "artin_field_label": null, "artin_image": null, "atkin_lehner_eigenvals": null, "atkin_lehner_string": null, "embedded_related_objects": null, "fricke_eigenval": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": 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, -1, 0, 0, 0, 0, 0, -1, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, -1, 0, 0, 1, 1, 1, 0, 1, -1, 0, 0], [-1, 0, 0, -1, 0, -1, 1, 0, -1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, -1, 0, 1, -1, 1, 1, 1, 1, -2, 1, 2], [-1, 0, 0, 1, -1, 1, 0, 0, -1, 0, 1, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-3, -2, -1, -1, 1, 1, 2, -1, 1, -2, 1, 0], [-1, -1, -1, 0, 1, 1, 1, 2, 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, -1, 0, 0], [3, 0, 1, 0, 0, -1, -1, -3, 0, 2, -2, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, -2, 0, -1, 2, 0, 1, -2, 1, 1, 0, -1], [1, 1, 1, 0, -1, 0, -1, 2, 2, 0, 2, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 2, -1, 1, 0, 1, 2, -1, -1, 2], [-2, 0, 0, 0, 1, 0, -1, -2, 2, 0, -2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -1, 0, 1, -1, -1, 0, 0, 1, 1], [1, 1, 1, 0, 0, -1, 0, 2, 2, -2, 2, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 1, -1, 0, 1, 0, 0, 0, -1, -1, -2, -2], [2, 0, 0, 0, 1, 1, 0, -2, 2, -3, -3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0, 0, 2, -2, 1, 1, 0], [3, 0, 2, 0, 0, 0, 0, 0, 2, -3, 3, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, 3, 2, 0, -2, -3, -1, 2, -1, 1, 1, 1], [-1, -1, 1, 2, 0, 2, -2, 1, 1, 0, -2, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 2, 0, -2, 1, 0, -1, 0, -1, 2, 0, -2], [-1, 0, 1, -1, 2, -2, -1, -3, -1, 3, -2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [5, 3, 1, 2, -1, -2, -3, 1, -1, 2, -1, -2], [5, 3, 2, 0, -3, -2, -3, 0, -3, 5, 0, 3], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, 0, 1, -2, 2, -1, -1, 0, 0, 3, 0, 0], [-3, 0, -3, -1, 1, 3, 3, 2, 0, 0, 3, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, 4, 1, 1, -4, -1, -3, 2, -1, -1, 0, 1], [-3, -3, -2, 0, 2, 0, 3, 2, 0, 2, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -1, -3, 2, -2, -2, -5, -4, 5, -1, -3], [-2, -1, 0, 1, -3, 0, 3, -1, 2, -2, -1, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 1, -1, 2, 0, 0, 0, 1, 0, 0, -4, -1], [-5, -2, -2, 0, -1, 2, 0, 0, 2, -2, 3, 3], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-4, -1, 0, 1, -2, 0, -1, 0, -2, 4, 2, 2], [3, 0, 0, 0, -3, -3, 0, 3, -3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 2, 1, -1, -2, -3, 0, -2, 2, -1, -1, 0], [-1, 1, 1, 0, 1, 0, 0, 0, -4, 2, -1, -2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-4, -1, -3, 0, 1, 1, -2, -6, -3, 3, -3, -3], [2, 3, -3, 2, 0, 2, -2, 0, -7, 0, -3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, -5, -1, -2, 0, 3, -2, -3], [-1, 0, -3, -5, 2, -2, 3, 0, -4, 0, 4, -4], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 3, 1, -1, -1, 1, -3, 2, -2, 4, -2, 2], [-4, -2, 1, -1, 2, -1, 1, -3, -1, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, 4, 3, 1, -1, 1, -3, 1, 0, -1, 2, -1], [1, -1, 0, 2, -2, -1, 0, 0, 0, -2, 1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 1, 1, 1, -1, -1, 0, 3, -3, 0, 0, 3], [1, 1, -2, 0, 2, 0, -1, -4, -4, 0, -4, -7], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, 0, -3, -3, 0, 0, 3, 6, 0, -6, 6, -1], [1, 3, 0, -3, 0, -1, 0, 3, -1, -2, 3, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 0, 0, -2, 0, -4, 4, 5, -2, 0, 4, -5], [1, -1, -2, 0, 2, 1, -1, -1, -3, 3, -3, -3], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 5, 1, -1, 0, -1, 0, 6, 0, 2, 6], [-3, 1, -1, 1, 0, 1, 0, -1, 1, -2, -2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-3, -1, -1, 1, 3, 4, 0, -3, 3, 0, 0, 0], [-3, -3, -1, 0, -3, 0, 0, 0, 5, 0, 3, 5], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, -1, -2, 0, 0, 1, -1, 2, 0, 0, -2, -2], [2, -1, 1, -3, 0, -4, 4, 4, 4, 0, 6, -4], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, 0, 0, 0, 2, 2, -2, -3, -3, 0, -3, 0], [-1, 0, 0, 4, -4, 4, -1, 2, 5, -2, -3, 5], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 1, 1, -1, -1, 1, -3, -3, 0, -3, 2], [2, 0, -1, 3, 0, 1, 3, 3, 3, -4, 0, -3], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, 1, 0, 1, -1, 1, 0, -2, 0, 0, -4, 2], [4, 2, 5, 2, -2, -3, -5, 0, 0, 5, -3, 3], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -2, -5, 1, 2, 5, 3, 2, 2, -1, 0, -2], [1, 2, 3, -1, -3, 1, -2, 2, 3, -1, 3, 10], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, 0, 3, 2, 1, -1, 1, 0, 3, 0, -3, -2]]}