# Stored data for newform 161.2.a.d, downloaded from the LMFDB on 19 April 2024.
{"label": "161.2.a.d", "space_label": "161.2.a", "level": 161, "weight": 2, "hecke_orbit": 4, "hecke_orbit_code": 13510798915666081, "dim": 5, "is_polredabs": true, "nf_label": "5.5.2147108.1", "trace_hash": 1372652543621287929, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[2, [-27, 16, 17, -9, -2, 1]]], "qexp_display": "q+\\beta _{1}q^{2}+\\beta _{3}q^{3}+(2+\\beta _{2})q^{4}+(-1+\\cdots)q^{5}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 644, "fricke_eigenval": -1, "atkin_lehner_string": "-+", "analytic_conductor": 1.285591472542614, "hecke_ring_index": 1, "level_radical": 161, "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": true, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.008", "prec": 17}, "analytic_rank_proved": true, "char_values": [161, 1, [24, 120], [1, 1]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 1, "level_primes": [7, 23], "conrey_indexes": [1], "field_disc": 2147108, "field_disc_factorization": [[2, 2], [536777, 1]], "field_poly": [-27, 16, 17, -9, -2, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.035", "prec": 17}, {"__RealLiteral__": 0, "data": "4.750", "prec": 17}, {"__RealLiteral__": 0, "data": "1.512", "prec": 17}, {"__RealLiteral__": 0, "data": "67.920", "prec": 20}, {"__RealLiteral__": 0, "data": "46.653", "prec": 20}, {"__RealLiteral__": 0, "data": "1595.991", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 5, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[7, -1], [23, 1]], "trace_display": [2, 0, -4, 5], "traces": [0, 5, 2, 0, 12, -4, -3, 5, 3, 11, -8, -4, 3, -6, 2, 10, 10, -12, -19, 6, 0, 0, 14, -5, -36, 19, 1, 0, 12, -4, -48, 30, 8, -22, 6, -4, -1, 4, -40, 16, -50, 6, -3, -12, -26, -12, -2, 10, 25, 5, -2, -4, -21, 16, 33, 18, 3, 6, 13, 22, 30, -18, 15, 11, 25, -26, 4, -2, 12, 0, -8, 4, -41, -2, 38, -30, 10, -4, 41, 30, -10, -3, -7, 8, 3, -12, 8, -12, 4, -20, 34, -6, -12, -26, -25, 8, -1, -12, 2, -8, 56, -10, -12, 26, 8, 10, 2, -14, 17, 18, 98, 46, 10, 2, -12, 4, -83, -10, -40, -12, 6, 17, -50, 36, 69, -30, -19, 4, 18, -20, -40, -38, -72, 6, 104, 38, 70, -24, 3, -4, 0, -66, -1, -32, -57, -32, -13, 0, 20, -8, 13, 40, -62, -78, 14, -34, -1, -40, -8, -6, -106, -5, 2, 8, 27, -64, 16, 28, -36, -11, -76, 60, -48, 14, 111, 19, -94, 16, 34, -12, 92, -20, 1, -36, -3, 4, -5, -38, 61, 0, 0, 34, 18, 20, 14, -14, 12, 24, 72, 60, 77, -28, -36, -4, 8, 46, 6, -11, 15, -36, -48, -24, -12, 68, -80, -72, -18, 30, 22, -28, 46, 32, -20, 6, 8, 41, -6, 24, 90, 26, 8, -22, -14, 20, 28, -6, 58, 16, 6, 4, 36, -4, 34, -50, -44, -4, -67, -14, 54, -20, 14, 34, -1, 4, -35, 10, -12, 30, 108, 4, -86, 50, -65, -16, 82, -32, -40, -48, 38, -6, -56, 38, 116, 16, -48, -40, -3, -16, 43, 66, -50, -20, -45, 12, 9, 116, -122, 6, -51, 47, 142, 18, -99, 12, -3, 36, -4, 24, -58, 6, 11, -12, -41, -40, -8, 48, -40, 36, -26, -6, 0, 60, 34, -82, -18, -12, 38, 34, 60, 68, -144, -34, -2, -36, -16, -18, 25, -40, -80, 10, 32, 20, 0, -38, 30, 10, 25, -8, 53, -32, -168, -2, -80, 5, 88, -10, -48, 32, -117, -22, -2, -8, -90, 30, -72, -14, -40, -4, -131, 34, -2, -3, -44, -12, -21, -6, -22, -56, -10, 10, -112, 16, -17, 26, -146, 92, 78, 28, 33, 86, 132, 48, 12, -46, 93, 18, 57, -20, -46, -78, 108, 12, 3, 26, -39, -58, 0, 30, 90, 6, 74, 50, -50, -52, 16, -114, 13, -16, 112, -30, -56, -26, 12, 22, 19, -88, 89, 110, 96, -64, 30, 26, -64, 14, -20, 10, 9, -18, 2, 88, 16, 6, 43, -58, 15, -78, 138, -6, 103, 84, 214, 11, 52, -24, -14, 24, -44, -22, 25, 38, -177, -12, 18, -48, -84, -26, -134, -22, -4, -4, 0, -34, 4, 80, -205, 84, -69, 56, -64, -2, 44, 16, -100, -20, 50, 42, 12, 90, 43, 6, 18, 34, 16, 0, 128, 100, 28, 44, -52, -8, -8, -76, 71, -102, 68, -54, 35, 4, 96, -52, -106, -76, 54, 34, -41, 20, -14, -46, -65, 18, 206, -2, 71, -66, -27, -40, -72, -6, 38, -32, 14, -10, 144, -30, -143, -30, 82, -68, -40, 5, 68, 92, 10, -22, -4, 36, 166, 8, -21, -4, 14, -20, 88, -4, 134, 4, 41, -16, -182, 4, -22, -34, 36, 30, -19, -144, 41, 20, -138, 76, -10, 96, 80, -134, 35, 60, 58, -3, -58, -16, -196, -18, -66, 58, -7, -19, 13, 2, 158, -106, 12, 8, -66, 20, -72, -4, -2, -4, 3, 30, -24, 58, 78, 54, 34, -12, -16, 60, -1, -36, -126, -10, 8, -152, 61, 136, -46, 40, -74, -12, 136, -80, -114, -92, -50, -34, 4, -28, 54, -58, -30, 0, 89, -20, -113, -63, -92, -52, -36, 4, 34, 32, -18, -116, 68, -102, -38, -6, -46, 12, -24, -30, -52, -14, -12, 20, 36, -14, 159, -34, 43, -26, -1, -44, -124, 34, 35, 102, -25, 14, -232, 24, 25, -116, 100, 8, 90, 4, 216, -52, -18, 42, -1, 52, -64, -84, -29, 16, -76, -12, -168, 0, 80, 24, 156, -88, 2, 82, -20, -6, 48, 64, -8, -8, 16, -22, 70, -40, -157, -32, 56, 148, -65, -68, -156, 208, -45, -10, 132, -2, -152, 120, 78, -30, -12, -40, 15, 4, 144, 68, 320, 26, -162, 28, -62, -56, -247, -18, 8, -91, 240, 72, 38, -18, 72, 10, -8, 100, 20, -4, -72, -50, 2, -40, -184, -112, -52, 24, -162, -14, 44, 0, 63, 14, -57, 54, 17, 42, 234, 22, -80, 18, 171, 18, 138, 184, 82, -64, -133, -6, 98, -72, -67, -42, 8, 144, -114, 46, -122, 26, 6, -84, -6, -18, 10, 92, 71, -68, 161, 70, -46, 2, 192, -48, 53, 20, 178, -54, -12, 48, 116, -94, -76, 104, -196, 4, -35, -108, 30, -22, 6, -18, -83, 88, -60, 74, -76, -40, -5, -10, 146, -2, 246, 44, -14, -14, -40, -24, 1, 6, -16, -8, 112, -12, -23, 36, -116, -30, 104, 54, 6, 93, -22, 98, -92, 138, -234, 17, -106, -100, 188, -4, 75, -90, -50, -92, -38, -2, 74, -40, -232, 36, -78, -8, -17, 44, -170, 38, 69, -60, 32, -34, 142, -28, 40, -30, -99, 50, -9, -122, 26, 26, -19, 112, 152, 126, 43, -20, -2, 4, 120, -52, 122, 70, 120, 98, 18, -16, 172, -12, -55, -120, 130, -20, -22, -12, -75, 58, -52, -30, -40, -124, 196, -36, -178, 94, -36, -38, -112, -42, 50, 104, -129, 74, -72, -64, -52, 112, -45, -2, -298, 6, -21, 66, 66, 8, -42, 6, 104, 62, -10, -58, -96, -6, 22, 38, -252, 16, 40, -18, -192, 50, 70, 78, 6, 12, -43, 88, -142, -24, 102, 51, 16, 8, 18, -138, 3, -40, -13, 16, 108, -38, -118, -4, -191, 16, -108, 24, -65, 106, 0, -70, -11, -14, -98, -110, -222, -66, -62, 12, -2, 0, 49, 80, -1, 28, -60, 14, -37, 126, -126], "weight_parity": 1, "has_non_self_twist": 0, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": false, "level_is_squarefree": true, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "161.2.a.d", "char_is_minimal": true, "conrey_index": 1, "id": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0, 0, 0, 0, 0], [1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 0, 1, 0], [2, 0, 1, 0, 0], [-1, 0, 0, 0, -1], [0, 0, -1, 0, 1], [1, 0, 0, 0, 0], [0, 1, 1, -1, 1], [3, -1, -1, 0, 0], [-1, 0, -2, -2, -1], [-1, 1, -1, -1, -1], [1, -2, 1, 1, 0], [-1, 0, 0, 1, 1], [0, 1, 0, 0, 0], [3, -3, 1, -1, 1], [1, 0, 3, 1, 1], [-3, 0, 2, 0, 1], [-4, 2, -2, 1, -1], [2, -2, 0, 0, 0], [1, -2, -2, 0, -3], [0, 0, 0, 1, 0], [3, -1, -1, -1, -3], [-1, 0, 0, 0, 0], [-8, 2, 0, -1, 0], [4, -1, 1, -1, 1], [1, -2, 1, 2, 2], [-1, 2, 0, 1, -1], [2, 0, 1, 0, 0], [0, 1, -3, 0, 0], [-11, 3, 1, 1, 1], [6, 0, 0, -1, 0], [1, 1, 2, 1, 3], [-4, 0, 0, 0, 2], [1, -2, 4, 0, 3], [-1, 0, 0, 0, -1], [1, -3, -1, 0, -2], [0, 2, 0, 2, 0], [-8, 2, -2, 0, 0], [3, 2, -2, -1, -1], [-9, 2, -6, 0, -3], [1, 0, 0, 1, -1], [0, 0, -1, 0, 1], [-2, 0, 0, 0, 2], [-5, 3, -5, -3, -3], [-5, 2, 4, 2, -1], [0, -1, 0, 0, 0], [2, -2, 2, -3, 0], [6, -4, 1, -2, -1], [1, 0, 0, 0, 0], [-3, 4, 3, 1, 1], [-1, -1, 1, -5, -1], [-4, 0, 1, 1, 3], [4, 0, -2, 0, 0], [7, 0, -1, -2, 0], [2, 4, 0, -2, 0], [0, 1, 1, -1, 1], [0, 0, 2, 2, -2], [4, -3, -2, 3, -3], [5, -2, 0, 0, -1], [7, -5, 3, 3, 1], [-3, -2, 0, -2, -1], [0, 6, 1, 0, -1], [3, -1, -1, 0, 0], [5, 0, 2, 2, 4], [-4, -2, 0, 0, 2], [2, -6, 4, 4, 2], [-3, 5, 1, -1, -1], [1, 2, 4, 2, 5], [0, 0, 0, -1, 0], [-1, 0, -2, -2, -1], [1, 0, 0, 3, 1], [-6, -2, -4, -5, -1], [1, 0, -4, -1, -1], [8, 0, 0, 0, 2], [-8, 2, 2, 3, -2], [4, -6, 0, 2, -2], [-1, 1, -1, -1, -1], [7, 2, -1, 0, -4], [7, -1, -1, 1, 1], [3, -8, -6, 0, -3], [0, -1, 1, -1, 3], [-1, 2, -3, -2, 0], [2, 0, 0, 0, 2], [1, -2, 1, 1, 0], [1, -3, -5, 1, 1], [2, -4, 4, 4, 2], [-3, 6, -4, 3, 1], [3, -5, -3, 1, -5], [-5, 2, 0, -2, -1], [7, 0, 2, -6, 5], [-1, 0, 0, 1, 1], [-2, 0, -1, 0, 0], [-6, 1, 1, 6, 0], [-8, 4, 3, -2, -1], [0, 0, 4, 4, 0], [-1, 4, -3, -1, -2], [-3, 2, -2, 0, -3], [0, 1, 0, 0, 0], [-3, 3, 1, -1, 1], [9, 1, 6, 1, 3]]}