# Stored data for newform 667.2.a.a, downloaded from the LMFDB on 24 April 2024.
{"label": "667.2.a.a", "space_label": "667.2.a", "level": 667, "weight": 2, "hecke_orbit": 1, "hecke_orbit_code": 33555099, "dim": 10, "is_polredabs": true, "trace_hash": 1581836519587963960, "analytic_rank": 1, "is_twist_minimal": true, "hecke_cutters": [[2, [43, 101, -28, -182, -29, 118, 32, -32, -10, 3, 1]]], "qexp_display": "q-\\beta _{1}q^{2}+(-1-\\beta _{6})q^{3}+(1+\\beta _{2})q^{4}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 2668, "fricke_eigenval": 1, "atkin_lehner_string": "--", "analytic_conductor": 5.326021814819401, "hecke_ring_index": 1, "level_radical": 667, "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": "0.005", "prec": 17}, "analytic_rank_proved": true, "char_values": [667, 1, [465, 553], [1, 1]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 1, "level_primes": [23, 29], "conrey_indexes": [1], "field_disc": 189300794673397, "field_disc_factorization": [[11, 1], [17, 2], [59547277343, 1]], "field_poly": [43, -101, -28, 182, -29, -118, 32, 32, -10, -3, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "8.420", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "206.424", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "8143.202", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 10, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[23, -1], [29, -1]], "trace_display": [-3, -9, -10, 1], "traces": [0, 10, -3, -9, 9, -10, 4, 1, -9, 7, -6, 0, -17, -13, -12, 2, -5, -22, 12, -2, 3, -7, 3, 10, -6, 10, -25, -24, 19, 10, -3, -22, -31, -9, 13, -15, 19, -9, -10, 4, -6, -25, -34, 3, -27, -28, -3, -17, -3, 17, 2, 38, -18, -43, -47, -11, -7, 18, -3, -7, -21, -6, 3, 11, 33, 11, 55, 11, -51, -9, 34, -17, 34, -44, 9, 1, 24, -71, 38, 5, 38, 18, 33, -32, 14, 16, -9, -9, 18, -10, -9, -3, 9, -8, 47, -8, 60, 6, -73, 26, -37, -22, 10, 22, 26, 58, 12, -11, -40, 28, 8, 10, 64, -46, 39, -10, 9, -12, -27, 9, 103, 18, 82, 7, 33, -54, 87, 16, 26, -50, 67, -78, 19, -48, 38, 97, 42, -70, 4, 6, -5, 7, 55, 9, -8, -10, 22, -39, -26, 38, 78, 37, -8, -103, 73, 55, 24, -38, 25, 122, -13, 1, 123, 3, 21, 0, 70, 0, -11, 9, 24, 13, -10, -82, 4, 43, -60, 24, -18, -11, 20, 41, 50, -6, -9, -70, -2, -36, 30, -55, -73, 14, -17, -20, 26, 73, 33, -64, -109, 30, 10, 8, -3, 1, 173, 11, -40, 7, 59, 24, 65, -5, -56, -56, -46, 2, -57, -2, 7, -5, 37, -25, -25, 15, -59, 35, -37, 66, -50, 11, -6, 61, -9, 17, -131, 31, -70, -53, -41, 24, -30, 54, -6, -31, -43, -143, 6, -47, -35, -24, 17, 14, -35, 0, 62, -7, -37, -19, 85, -2, 48, 7, -7, -83, -44, 43, 57, 24, -70, -45, 31, 50, -86, 70, 48, 72, -17, -90, -14, 0, -46, 13, -174, -9, -31, -97, -61, 40, -72, 96, -6, 60, -43, -52, 59, 12, 66, 70, 10, -13, 103, -47, -75, 40, -14, -71, -128, -12, -132, -80, -35, -91, 75, -52, -23, -38, 26, -6, -57, 0, 42, -6, -12, -11, 94, -61, 47, -41, -73, 39, -160, -84, -82, 85, -39, 2, -59, 7, 76, 92, -59, -70, 37, 80, 18, 2, 31, 23, -17, 12, -109, 72, 85, -71, 78, 22, -11, 20, 146, -59, -124, 4, -7, 5, -84, 92, -111, -46, -5, 13, 63, -31, -74, 14, -9, 56, -61, -13, -48, 15, -39, 37, 34, -16, 121, 119, 22, 29, -123, -27, -26, -22, 29, 62, -97, 4, -16, -25, 27, 76, -20, 43, -20, 60, 68, -26, -12, 86, -89, -18, -109, 55, 188, -63, 12, 50, 10, -25, -36, 47, -111, -15, -170, -8, -6, 45, -151, 4, 36, -152, 20, 25, 73, -55, 90, 2, 91, -2, -43, 35, -24, 73, 193, -91, 41, 13, -43, 41, -116, 103, -83, -93, -70, 9, 65, -32, -51, -16, 9, 186, 3, -143, -67, 90, -5, 11, -183, -36, -89, 24, 115, 181, 89, 34, 80, 7, -64, -133, -57, -52, -27, 19, -56, -7, 34, -37, -304, 16, 62, 25, 254, 86, -66, -22, -29, -80, 79, -82, -156, -50, 93, -34, 18, 126, 81, 74, 3, 59, -95, -114, -70, -50, -5, -61, -90, 43, -30, -33, 28, 118, -167, -6, 12, 9, -102, -245, 36, 52, 72, 10, 68, -38, 44, 11, -3, 9, 69, -55, -74, 84, 115, 34, -7, -49, 160, 20, 77, 33, -113, 121, 84, -2, -6, -66, 43, 62, -41, -66, -35, 132, -84, -16, 5, 27, 34, 161, 39, 139, 158, 61, 13, 59, 103, 57, 15, 10, -87, 25, 12, 225, 3, -7, 90, 0, 108, 36, 7, 3, 162, 8, 36, 8, -57, 35, 118, -50, 7, -69, -25, 93, -181, -42, 152, -10, 19, -112, 16, -25, 48, -7, -23, -35, -249, 78, 63, 8, 94, -114, -103, 132, 36, -24, 39, 158, 6, 110, -16, 55, -25, -93, -102, 54, -86, 80, 158, -92, 106, 70, 3, 175, -143, -61, 95, 168, 19, 151, 2, -152, 126, 159, -35, 55, 36, -103, -164, 183, 121, 42, -103, 30, 28, -12, 118, -60, 188, 254, 77, 10, -34, 23, -127, 20, 204, -13, 172, -1, -84, -17, -8, -93, 190, 2, -142, 1, 65, 67, -56, 123, -3, 107, -3, -69, 4, -90, -63, 92, -6, 87, -125, -165, -114, -3, 280, 64, 123, -24, -28, -18, 142, 84, 85, 147, -69, -22, 186, 32, -194, 26, -172, -120, 68, 48, 127, -47, -127, 10, 84, -30, -59, 175, -9, 17, -28, -44, 27, 235, -31, -76, -38, -54, -57, -96, -63, -70, 158, -129, 26, 113, 57, 8, -256, -15, -54, 60, -25, -16, -147, -100, -135, -9, 183, 107, -50, -16, -7, 115, 22, -42, -40, -64, -119, -18, -78, -90, -243, -164, 141, -21, 47, -13, -93, 125, 13, -24, -58, -30, -50, 24, -54, 37, -176, -87, -32, -21, 42, -176, -62, -70, -246, -3, -8, -127, -7, 45, -27, -15, 36, -125, -245, 52, -58, 4, 19, 27, 4, -42, 69, -77, 125, -98, 140, -89, 25, 11, -59, 97, 16, 25, 19, -58, 2, 136, -20, -24, 16, -103, 3, 44, 74, 177, 96, 10, 31, -107, 23, -28, 181, -182, 43, 45, -71, -9, -57, -6, 72, 64, -130, -54, -70, -158, 127, -187, -233, -4, 99, 109, -119, -150, -33, 134, -3, -26, -30, -112, -10, -85, -1, 6, 137, -71, 47, -101, -55, -31, 113, -64, -139, -102, -197, -16, 80, -276, 131, -132, -52, 46, 118, 4, -159, -22, -174, -39, -87, 70, 143, -7, -49, 4, 24, -111, -142, 7, -24, -38, 39, 98, 8, -35, 338, 64, -6, -74, 146, 9, 90, 121, -287, 89, -31, -67, 183, 17, 216, 142, -168, 119, -54, -36, 20, 51, -188, 27, 290, -25, -86, 43, -273, -2, -222, 19, 222, 58, 41, 69, -36, -7, 157, -9, 108, -94, -166, -66, -102, -6, 143, -174, -34, 26, -28, 30, -104, -43, -165, -100, 32, -256, -96, 161, -147, -83, -122, 112, 48, -8, 156, 189, 13, 91, 45, 3, 149, 8, -65, 233, 280, -222, -57, -27, -11, -174, 49], "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": "667.2.a.a", "char_is_minimal": true, "conrey_index": 1, "id": null, "nf_label": 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, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0, -1, 0, 0, 0], [1, 0, 1, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0, 0, -1, 0, 0], [0, 2, 0, 0, -1, 1, 0, 0, 1, 1], [0, 0, 1, -1, 0, 0, 0, 1, 0, -1], [-1, 0, -2, 0, 1, -1, 1, 0, -1, 0], [1, 0, 0, 0, 0, 0, 2, 1, -1, 0], [-1, 0, -1, 1, 1, -1, 0, 0, 0, -1], [0, 1, -1, 1, 0, 1, 1, 0, 0, 1], [-2, 0, -1, 0, 1, 0, -1, 0, 1, 0], [-2, 1, -1, 1, -1, -1, 0, 0, 0, -1], [-1, 0, -2, 1, 0, -1, 2, -1, -1, 1], [0, 0, -1, 0, 0, -1, 2, 1, 0, -1], [-1, 2, 2, -1, -2, 1, 0, 1, 0, -1], [-2, -1, 0, -1, 1, 0, -1, -1, 2, 1], [2, -2, 1, -1, 2, -1, 1, 1, -3, -1], [0, 1, 0, 0, 1, 0, 0, 0, -1, 2], [0, 2, 1, -1, -3, 2, 1, 1, 1, 0], [-1, 0, -2, 3, 2, -2, -1, -3, 0, 1], [0, 1, 2, -1, 0, 2, -2, 1, 0, -1], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 1, 2, 0, -3, 1, -1, -1, 1, -1], [1, 2, 1, -2, -1, 3, 1, 3, 1, 1], [-3, 1, 0, -1, 1, 0, -1, -1, 1, 0], [-3, 2, 0, 0, -1, 2, -1, -2, 3, 1], [2, -1, 2, 0, 2, -1, -2, 0, -1, -1], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 2, -1, 0, -1, 0, -1, -1, -1], [-2, -1, 1, 0, -1, -1, 0, -1, 1, 0], [-3, -1, -2, 2, 3, -1, -1, -1, 0, 1], [0, -1, 3, -3, -1, 2, 0, 2, -1, 0], [0, 3, 1, 1, -4, 0, -2, -1, 3, 0], [-1, 0, -1, 2, 0, 0, -1, -2, -1, 3], [3, -2, 0, 0, 0, -1, 3, 0, -3, 0], [-1, 1, -1, 1, 1, 0, 1, 2, -2, 0], [-1, 1, 1, -2, -1, 1, 0, 3, -1, 0], [1, -3, 0, -1, 1, -2, 1, -1, -2, -2], [0, -2, -1, 0, 4, -1, -3, -1, -1, 2], [-2, -1, 3, -2, -3, 1, 0, 1, 2, 0], [-4, 1, 2, -3, -4, 3, -1, 1, 3, -2], [0, 0, -1, 1, -2, -1, 1, -1, 2, 0], [-3, 1, -3, 1, -1, 0, 1, -1, 0, 1], [-3, -1, 1, 1, 0, -1, -4, -2, 1, 0], [0, -1, 0, 0, 0, 0, 0, 0, 0, 0], [-1, -4, 1, 2, 2, -1, -1, -1, 0, -2], [0, -3, -5, 3, 5, -4, 1, -2, -2, 0], [1, 2, -1, 2, 3, -1, 1, 2, 0, 0], [0, 2, 0, 1, 0, 1, -2, 0, -1, 2], [5, -2, 2, 1, 0, -1, 4, 0, -1, 0], [-2, 2, 0, 0, -1, 2, 0, -1, 2, 2], [-5, 0, -1, 2, 0, -1, -3, 0, -2, -2], [-7, 3, -3, 3, 0, 0, -5, -2, 4, -1], [-1, -4, 1, 0, 1, -3, -2, -2, 1, -3], [0, -1, 0, -2, -3, 3, 2, 2, 1, 0], [2, 0, 2, -2, -2, 4, 0, 3, 2, -1], [0, -1, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 3, -2, 0, 2, 2, 1, 0, -1, 2], [-1, -4, -3, 2, 4, -3, 0, -2, -3, 1], [0, -2, 0, 0, -1, 0, 1, 2, -1, -1], [0, -2, -2, 0, 3, -4, -1, -1, 0, -1], [2, -2, 2, -4, -3, 2, 3, 3, 0, -2], [3, 3, 1, -1, -4, 4, 0, -1, 3, 2], [2, -1, 3, 0, -1, 2, -2, 3, -1, 1], [6, 0, -3, 3, 4, -3, 3, 1, -4, 2], [1, 0, 0, -3, -3, 1, 0, 1, 0, -1], [-6, -2, -6, 2, 3, -3, -4, -1, 0, -1], [-1, 0, 0, 0, 0, 0, -1, 0, 0, 0], [3, 1, 3, -3, 1, 2, -3, 4, 1, -1], [-1, -2, -3, 3, 3, -2, 3, -1, -3, 0], [4, -3, 0, 1, 2, -2, 1, 1, 0, -1], [-4, 0, -1, 0, 1, 0, 2, -1, -1, 1], [1, 4, 3, -3, -2, 4, 2, 2, -2, 1], [2, -3, 1, 3, 3, 0, -2, -3, -3, 4], [2, 1, 0, 0, -1, 0, 1, 1, 0, -1], [-7, -1, 2, -5, -5, 2, 0, 1, 2, -2], [5, -4, 0, 2, 2, -4, 5, 0, -3, -2], [1, 2, 2, -1, -4, 4, 3, 2, 0, 1], [4, 2, 3, 0, -4, 2, 0, 1, 1, 2], [4, -8, 1, -1, 4, -5, 2, 0, -4, -2], [3, -2, -4, 2, 6, -6, -2, -2, -1, 1], [-3, -2, -2, 0, -1, -2, 2, 0, -2, -2], [0, 3, -2, 1, 1, 0, -1, 1, 2, 0], [2, 1, -3, 0, 4, 0, 2, 1, -4, 2], [-1, -4, 1, -1, 3, -3, -5, -2, 2, -2], [-1, 0, 0, 0, 0, 0, -1, 0, 0, 0], [1, 1, 1, 1, 1, -3, -1, -1, 2, 0], [-1, 0, 3, -3, 0, 3, -1, 1, 3, -1], [-2, 3, -3, 0, -2, 1, 0, -1, 4, 2], [0, 1, 2, -3, -3, 5, -1, 2, 2, 1], [1, 0, 1, 0, 0, 0, 0, 0, 0, 0], [-1, -1, -2, 0, 1, -1, 2, -1, 2, -1], [5, 1, -1, 0, -3, 2, 5, -2, 0, 0], [-2, 2, 0, -4, -2, -1, 3, 2, 2, -3], [7, 1, 7, -5, -4, 4, 4, 4, 0, -1], [0, 0, -3, -1, -2, -2, -2, -1, 1, 1], [-7, 3, 2, -5, -8, 6, 2, 0, 0, 1], [1, 3, -3, 3, 1, -2, -3, -2, 3, 2], [-4, -1, -2, 2, 1, -2, -3, -3, -1, 0]]}