# Stored data for newform 162.2.e.b, downloaded from the LMFDB on 25 April 2024.
{"label": "162.2.e.b", "space_label": "162.2.e", "level": 162, "weight": 2, "hecke_orbit": 2, "hecke_orbit_code": 4503874538832034, "dim": 12, "is_polredabs": true, "trace_hash": 1690733347863799967, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[5, [5184, 7776, 2592, 3672, 3564, -5184, 1053, 27, 162, -24, 9, -3, 1]]], "qexp_display": "q+(\\beta _{4}+\\beta _{8})q^{2}-\\beta _{6}q^{4}+(1-\\beta _{2}+\\beta _{7}+\\cdots)q^{5}+\\cdots", "char_order": 9, "char_parity": 1, "char_degree": 6, "char_conductor": 27, "char_orbit_label": "e", "char_is_real": false, "Nk2": 648, "analytic_conductor": 1.2935765127447423, "hecke_ring_index": 27, "level_radical": 6, "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": "0.010", "prec": 17}, "analytic_rank_proved": true, "char_values": [162, 9, [83], [8]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 2, "level_primes": [2, 3], "conrey_indexes": [19, 37, 73, 91, 127, 145], "field_disc": 40419192196881, "field_disc_factorization": [[3, 18], [17, 2], [19, 2]], "field_poly": [57, -342, 936, -1584, 1905, -1698, 1225, -678, 318, -110, 33, -6, 1], "hecke_ring_index_factorization": [[3, 3]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "11.560", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "408.525", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "23635.323", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "1.2.3.c9", "trace_display": [0, 0, 3, -3], "traces": [0, 12, 0, 0, 0, 3, 0, -3, 6, 0, -3, 12, 0, 12, 3, 0, 0, 6, 0, -9, -6, 0, -12, -30, 0, -9, -18, 0, 12, -15, 0, 0, 0, 0, -15, -3, 0, -15, -3, 0, -3, 12, 0, 9, 3, 0, 3, 9, 0, -39, 27, 0, 12, 12, 0, 18, 3, 0, -3, -12, 0, -36, 12, 0, -6, 15, 0, 36, -3, 0, 39, -12, 0, -21, -33, 0, 3, -3, 0, 39, -6, 0, 6, -18, 0, 45, -9, 0, 6, -12, 0, -6, 6, 0, 36, 15, 0, 39, 12, 0, -15, 69, 0, -18, 6, 0, -12, 30, 0, 6, 45, 0, -3, 36, 0, -36, 3, 0, 3, -69, 0, -36, -9, 0, -27, -12, 0, -3, 0, 0, -15, 39, 0, -18, -42, 0, 12, 12, 0, -48, -39, 0, -15, -39, 0, 0, -18, 0, -30, -84, 0, 18, 9, 0, 3, -75, 0, 54, 42, 0, -3, 12, 0, -6, 12, 0, 0, 45, 0, 48, 0, 0, -12, 18, 0, 6, -6, 0, -15, -42, 0, 12, 9, 0, -6, -102, 0, -54, 18, 0, -60, -12, 0, -36, -39, 0, -3, 6, 0, 0, -36, 0, 3, 87, 0, -72, 21, 0, -9, 42, 0, -6, 3, 0, -12, 96, 0, 6, 45, 0, 45, 21, 0, 81, 6, 0, 27, 90, 0, 27, -27, 0, -12, 3, 0, 54, -12, 0, 69, 81, 0, 96, 6, 0, 24, -81, 0, 39, 27, 0, 75, 30, 0, 45, 36, 0, 0, -27, 0, 6, -3, 0, 24, 6, 0, 18, -54, 0, 36, -78, 0, -30, -3, 0, -48, -42, 0, -18, 6, 0, 3, -123, 0, -117, 24, 0, -33, -39, 0, 30, 9, 0, 18, 24, 0, -63, -30, 0, -6, 66, 0, -6, -18, 0, 12, 24, 0, -12, 51, 0, -24, -42, 0, -75, 21, 0, 0, -21, 0, 18, -6, 0, -75, 12, 0, -72, -78, 0, 15, 108, 0, -6, -27, 0, 36, 96, 0, -57, 24, 0, -45, 78, 0, 9, 27, 0, -18, -135, 0, -48, 24, 0, 6, -60, 0, -54, 15, 0, -30, -27, 0, 39, -24, 0, -45, 87, 0, -81, -3, 0, 12, -39, 0, 39, -18, 0, 36, -138, 0, -114, 15, 0, 21, -195, 0, 54, 3, 0, -18, -3, 0, 45, -42, 0, 84, 6, 0, -21, -39, 0, 36, 12, 0, 69, -12, 0, -96, -3, 0, 51, 72, 0, 27, 12, 0, 18, 6, 0, 48, 54, 0, 60, -54, 0, 6, 105, 0, 129, 30, 0, 66, 42, 0, 6, -57, 0, 27, -15, 0, 45, 9, 0, -12, 0, 0, 9, 45, 0, 6, 90, 0, 0, -27, 0, -90, 93, 0, -63, 66, 0, 18, 183, 0, -6, 12, 0, -48, 39, 0, 42, 9, 0, -24, -66, 0, 48, -33, 0, 18, -117, 0, -63, 12, 0, -36, -102, 0, 72, -9, 0, -126, 69, 0, 0, 3, 0, -12, 30, 0, -9, 51, 0, -21, -27, 0, 27, 72, 0, -36, 48, 0, 30, -12, 0, 108, -39, 0, -54, -6, 0, -42, 51, 0, 6, -60, 0, -15, 57, 0, 72, -45, 0, -15, -48, 0, 9, -9, 0, -3, 0, 0, -24, 18, 0, -15, -120, 0, 72, -15, 0, -21, -39, 0, 81, 9, 0, 60, 33, 0, -90, 33, 0, 123, 36, 0, 72, 30, 0, -24, -39, 0, 168, 33, 0, 57, -102, 0, -165, 9, 0, 63, -162, 0, -18, 21, 0, -24, 51, 0, 24, -117, 0, -30, 42, 0, 18, -84, 0, 78, -84, 0, -99, -24, 0, -3, -105, 0, 24, 15, 0, 21, 27, 0, -66, 63, 0, -51, 39, 0, -63, 60, 0, -30, 192, 0, -36, 75, 0, -45, 21, 0, 3, -3, 0, -33, -39, 0, -69, -36, 0, -3, -24, 0, -207, -51, 0, 6, 72, 0, 54, -93, 0, -75, 132, 0, -207, 3, 0, -27, 60, 0, -126, -93, 0, -18, -51, 0, -27, 0, 0, -96, -21, 0, -69, 60, 0, -6, 15, 0, -81, 45, 0, 21, -90, 0, 9, 12, 0, 18, 78, 0, -63, -9, 0, 9, -75, 0, -27, 39, 0, 6, -42, 0, 210, -6, 0, 69, -123, 0, -6, -63, 0, 12, -33, 0, 99, -69, 0, 54, -36, 0, 114, -21, 0, 24, 66, 0, 9, -12, 0, 192, -105, 0, 36, 81, 0, 30, 150, 0, 51, 69, 0, 93, -63, 0, 99, 0, 0, 9, 132, 0, -111, 9, 0, 21, -84, 0, 114, -24, 0, 48, -18, 0, -24, -21, 0, 33, -42, 0, 165, 45, 0, 9, -99, 0, -3, 15, 0, 3, 33, 0, 90, 72, 0, 24, 177, 0, 9, -84, 0, -177, 0, 0, -72, 0, 0, -6, -99, 0, 72, 15, 0, -66, -165, 0, -81, -6, 0, 3, 132, 0, -12, 87, 0, -42, 114, 0, -57, -21, 0, 27, 6, 0, 30, 9, 0, -129, 141, 0, -108, 72, 0, -6, -36, 0, 108, 6, 0, -54, 45, 0, 63, -60, 0, 30, 108, 0, -78, -15, 0, 21, 138, 0, 153, 21, 0, 15, -54, 0, 78, -30, 0, 57, 6, 0, -108, 81, 0, 30, 123, 0, -39, 3, 0, -39, 129, 0, 96, 72, 0, 0, 12, 0, 9, 30, 0, 0, 30, 0, 21, 18, 0, -48, -99, 0, 81, -6, 0, 117, -3, 0, 45, -45, 0, 9, 6, 0, 111, -27, 0, 15, 81, 0, -63, -144, 0, 27, -84, 0, -12, -27, 0, 60, -159, 0, 24, -18, 0, -3, -162, 0, 12, 48, 0, -21, 9, 0, 21, -30, 0, -9, 87, 0, -45, 6, 0, -114, -126, 0, -183, -48, 0, -30, -90, 0, -18, 0, 0, -171, -84, 0, -162, -3, 0, 12, -120, 0, -27, -54, 0, -186, -306, 0, 90, -48, 0, -36, 60, 0, -135, 36, 0, -33, 6, 0, -198, -90, 0, 3, -24, 0, 60, 0, 0, -30, -84, 0, -171, -96, 0, -24], "weight_parity": 1, "has_non_self_twist": 1, "level_is_prime": false, "level_is_prime_power": false, "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": "54.2.e.b", "char_is_minimal": false, "conrey_index": 19, "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, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0], [1, 0, -1, 0, 0, 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, -1, 1, 0, 1, 1, -1], [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, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 1, 0, 2, 1, -1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, -2, -1, 1, 1, 2, 2, 0, 0, -1, -1, 0], [0, 0, -1, 0, 0, -1, -1, 0, -1, -1, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [1, 0, 1, -1, 0, 0, 1, 1, 1, 0, 1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, 0, 2, -1, -1, -1, 1, 0, -2, 0, 0, 0], [-1, 1, 1, -1, -1, 0, 0, 0, 0, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -1, -1, 1, 1, 0, 0, 0, 1, -1, 0, 0], [-3, -1, 1, 0, -1, 0, 0, 0, -3, 0, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 1, -4, 1, -2, -3, -1, 0, -2, 0, 1, 1], [-1, -1, 0, 0, 1, -1, -1, 0, 1, 0, -1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 0, 0, 0, 0, -1, 1, 1, 0, 0], [-3, 1, 0, 1, 1, 1, 1, -2, 1, 0, -1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, -1, 3, 1, -3, 1, -1, -1, -1, 0, -1, 1], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, -1, 0, 1, 1, 2, 0, -1, 0, -1, -1, 1], [-1, 1, 2, -2, -5, -5, -3, 0, -2, 1, 1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -1, -3, 2, -1, 5, 3, -1, 3, 0, -1, 1], [-1, 0, 2, 0, 0, -1, 1, 0, -1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -1, 1, 0, 1, 1, 0, 0, 0, 0, 1], [1, 0, 1, 1, 2, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 1, 3, 0, 0, 0, 1, -1, 2, 0, 0, -1], [0, -1, 0, 1, -1, 1, -1, -1, -1, -1, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, -1, -2, -3, 1, 1, -3, 1, 0, -1], [-1, -2, 2, 2, 2, -1, -3, -1, 0, -2, -2, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-3, 1, -1, -2, 1, -3, 0, 0, 4, 1, 1, 0], [0, 1, 2, 1, -2, 1, 2, -1, 1, -1, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, -1, 0, -1, -2, -1, -1, 1, -2, 0, 0, -1], [2, -1, -1, 0, -1, 1, 1, 1, -2, -1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, -2, -1, 0, 5, -3, -5, 1, 2, -1, -1, -1], [1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 2, -1, -2, -1, -1, 1, -1, 1, 2, -1], [-2, 1, 0, -1, -1, 0, 0, -2, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-4, 0, 0, 1, 3, 3, -1, 0, 0, -1, -1, 1], [3, 0, -2, 0, 2, 1, 3, 1, -1, 1, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, 0, -6, -2, 0, 2, -2, 2, -1, -1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 4, -1, -3, 1, 2, 2, 0, -4, 1, 2, 0], [1, 0, -1, 0, -1, -1, -1, 0, -1, 1, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, -1, 1, 1, 0, 3, 5, 0, 0, 0, 0, 1], [-2, 2, -1, -1, 4, -1, 3, 0, 3, 1, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-3, 0, 2, 3, 2, 3, 2, -1, 0, -1, 0, 1], [-1, 0, -2, 0, -2, 3, 1, 1, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 1, -2, 0, 1, -1, 0, 0, 0], [4, 2, -5, -2, 5, -2, -2, 2, 2, 1, 3, -2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, 0, -1, -2, -1, -3, -5, -1, -1, 0, -1, -1], [-1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, -1, 0, 2, -1, -2, 1, 0, -1, 0, 0], [2, -1, -2, -1, -5, -3, 1, 3, -5, 0, 2, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, 1, 2, -2, -2, -2, -2, 2, 1, -1, 0, -2], [-1, -1, 2, 0, 1, 2, 0, 0, -1, -1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, -1, -1, 0, 0, 0, 1, 0, 0, 0, 0, -1], [-2, -2, -1, 4, 6, 7, -1, -1, 7, -3, -2, 3], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, 0, -1, -3, -7, -1, -5, 3, -5, 0, 3, -3], [-1, 0, 3, -1, 0, -2, 2, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, 0, 0, -1, 2, -2, -2, 0, -1, 1, 0, -2], [0, -2, 4, 0, 3, 5, 5, 0, 4, -1, -1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, -1, -1, -2, 0, 1, 4, 3, 2, 0, 0, 1], [0, 0, 2, 1, -4, 3, -1, 0, -1, 1, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-3, 1, 3, 0, 3, 4, 2, -1, 1, 0, 1, 0]]}