# Stored data for newform 891.2.n.c, downloaded from the LMFDB on 15 December 2025.
{"Nk2": 3564, "analytic_conductor": 7.114670820096082, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 99, "char_degree": 8, "char_is_minimal": false, "char_is_real": false, "char_orbit_index": 14, "char_orbit_label": "n", "char_order": 15, "char_parity": 1, "char_values": [891, 15, [650, 244], [10, 3]], "cm_discs": [], "conrey_index": 136, "dim": 8, "field_disc": 1265625, "field_disc_factorization": [[3, 4], [5, 6]], "field_poly": [1, -1, 0, 1, -1, 1, 0, -1, 1], "field_poly_is_cyclotomic": true, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 15, "has_non_self_twist": 1, "hecke_cutters": [[2, [1, 4, 10, 26, 39, -14, -5, -1, 1]]], "hecke_orbit": 3, "hecke_orbit_code": 9008092641493883, "hecke_ring_generator_nbound": 4, "hecke_ring_index": 1, "hecke_ring_index_factorization": [], "hecke_ring_index_proved": true, "inner_twist_count": 4, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 9, 3, 1, 3, 0], [1, 1, 11, 3, 1, 5, 0], [1, 1, 99, 13, 1, 15, 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": "891.2.n.c", "level": 891, "level_is_powerful": false, "level_is_prime": false, "level_is_prime_power": false, "level_is_prime_square": false, "level_is_square": false, "level_is_squarefree": false, "level_primes": [3, 11], "level_radical": 33, "minimal_twist": "33.2.e.b", "nf_label": "8.0.1265625.1", "prim_orbit_index": 13, "qexp_display": "q+(2\\zeta_{15}-\\zeta_{15}^{2}-\\zeta_{15}^{5}+2\\zeta_{15}^{6}+\\cdots)q^{2}+\\cdots", "related_objects": [], "relative_dim": 1, "rm_discs": [], "sato_tate_group": "1.2.3.c15", "self_twist_discs": [], "self_twist_type": 0, "space_label": "891.2.n", "trace_display": [1, 0, 3, -1], "trace_hash": 1476348608780698776, "trace_moments": [{"__RealLiteral__": 0, "data": "0.005", "prec": 17}, {"__RealLiteral__": 0, "data": "7.646", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "235.966", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "13091.054", "prec": 30}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.013", "prec": 17}, "traces": [0, 8, 1, 0, 9, 3, 0, -1, 26, 0, 4, 11, 0, -7, 4, 0, -1, 24, 0, -20, -3, 0, -4, 8, 0, -6, 4, 0, -12, -6, 0, 12, 30, 0, -12, 6, 0, 18, 10, 0, 6, 3, 0, 0, 72, 0, -6, -17, 0, -6, -6, 0, -3, 8, 0, 4, -12, 0, 24, 6, 0, 21, -54, 0, 26, 14, 0, 6, 27, 0, -3, 30, 0, 28, 26, 0, -60, -1, 0, 11, 26, 0, -6, -13, 0, 9, -15, 0, 37, -48, 0, 6, -3, 0, -17, -5, 0, -3, 72, 0, -72, -3, 0, -22, -9, 0, 1, 34, 0, -96, 8, 0, 1, 19, 0, -11, -72, 0, 58, 12, 0, -19, -54, 0, -42, -34, 0, 28, -8, 0, 4, -2, 0, 10, -12, 0, -42, 17, 0, 27, 3, 0, 50, -56, 0, 36, 26, 0, 24, 3, 0, -10, -50, 0, 32, -24, 0, 24, -44, 0, -15, 6, 0, 32, -18, 0, 2, -35, 0, -24, -18, 0, 90, -36, 0, -14, 14, 0, -11, 6, 0, -34, -3, 0, 1, -7, 0, 3, -204, 0, -30, 13, 0, -14, -33, 0, 36, -12, 0, 0, -27, 0, 42, 6, 0, 4, -96, 0, -44, -30, 0, 0, -6, 0, -17, -30, 0, -26, -12, 0, 12, -66, 0, 21, -30, 0, -38, 27, 0, -14, -6, 0, -72, 30, 0, -18, -51, 0, -3, -1, 0, -60, -42, 0, -18, 12, 0, 5, -16, 0, -28, -108, 0, 34, 36, 0, -27, 56, 0, -1, 18, 0, 54, -6, 0, 8, -10, 0, 9, -36, 0, -40, -3, 0, 62, 34, 0, 54, 126, 0, 2, 32, 0, -14, -15, 0, 13, 16, 0, 106, -18, 0, -6, -41, 0, 28, 176, 0, 44, 29, 0, 15, -10, 0, 95, -6, 0, 36, -9, 0, 1, 31, 0, -17, -48, 0, -198, -43, 0, -6, 26, 0, 2, 30, 0, -34, 19, 0, -9, -18, 0, -40, -36, 0, 110, -12, 0, -32, 56, 0, -54, 96, 0, -26, 75, 0, -36, -16, 0, 21, -12, 0, 180, 48, 0, -5, -69, 0, -3, 36, 0, 78, 22, 0, 18, 18, 0, 18, 46, 0, 34, -1, 0, 68, 33, 0, -44, 36, 0, -66, 15, 0, -2, 9, 0, 12, 48, 0, -126, -63, 0, 54, 78, 0, 31, 44, 0, -96, 15, 0, -69, 66, 0, 11, 174, 0, -72, 21, 0, 8, -1, 0, 12, 22, 0, -12, 30, 0, -25, -14, 0, 34, 30, 0, 16, -3, 0, -21, 102, 0, 30, 48, 0, -148, 13, 0, -108, 0, 0, -120, 18, 0, 42, -62, 0, -13, 21, 0, -17, 76, 0, -26, -114, 0, -58, -4, 0, -52, 8, 0, -42, 30, 0, -74, 6, 0, 15, 74, 0, 12, -26, 0, 82, -15, 0, 20, -36, 0, 2, -32, 0, -7, 0, 0, 114, -12, 0, 42, 132, 0, 12, -11, 0, 72, -20, 0, -176, 15, 0, -14, 18, 0, 99, -56, 0, -12, -12, 0, -6, 65, 0, -16, 122, 0, 258, 14, 0, 53, 34, 0, 8, -40, 0, 72, -78, 0, -36, 66, 0, 56, -6, 0, 90, 29, 0, 14, -18, 0, -132, 12, 0, 138, -75, 0, 45, -36, 0, -57, 144, 0, -38, 60, 0, -11, 129, 0, -27, -172, 0, 90, -2, 0, 152, -39, 0, -18, 28, 0, 240, 48, 0, 14, -33, 0, -3, 16, 0, -20, -53, 0, 18, 13, 0, 16, 216, 0, -188, -27, 0, 15, 23, 0, 29, 4, 0, 48, 12, 0, 4, -38, 0, -29, 60, 0, -120, -22, 0, 16, -105, 0, 3, 12, 0, 12, 57, 0, 43, 0, 0, 49, -78, 0, -62, 11, 0, -24, -22, 0, -144, -36, 0, -102, 77, 0, 22, -2, 0, -48, 192, 0, -52, -32, 0, 10, -12, 0, 30, 4, 0, -42, 2, 0, -54, -7, 0, 29, -24, 0, -34, 84, 0, -106, 25, 0, -11, 0, 0, 36, 75, 0, -12, -24, 0, -51, -156, 0, -48, 28, 0, -12, -27, 0, -93, -160, 0, 48, -52, 0, 75, -7, 0, 52, -432, 0, 32, -9, 0, -21, 21, 0, 39, 100, 0, -140, 52, 0, -12, 13, 0, -72, 10, 0, -206, -34, 0, -31, 18, 0, 42, 182, 0, 36, -69, 0, -42, -84, 0, 50, -18, 0, 24, -90, 0, 30, -87, 0, -30, 18, 0, -6, 27, 0, -1, 15, 0, 4, -46, 0, 216, -28, 0, 12, -163, 0, -18, 40, 0, -10, -122, 0, -50, 51, 0, 12, -144, 0, -108, 28, 0, 62, 12, 0, 39, -82, 0, 74, 39, 0, 157, 5, 0, 20, -48, 0, 168, -18, 0, 12, 84, 0, -22, -72, 0, -156, -27, 0, 45, -90, 0, 24, -150, 0, 288, 76, 0, 11, 1, 0, -61, -18, 0, -98, -36, 0, -94, 32, 0, -60, -56, 0, -42, 71, 0, 59, -184, 0, -46, -80, 0, 154, 6, 0, -9, -18, 0, 70, -390, 0, -132, -51, 0, 7, 34, 0, 30, -16, 0, -8, 24, 0, -18, -7, 0, 31, 102, 0, 118, -120, 0, 84, -45, 0, 21, -116, 0, -14, -156, 0, -78, -44, 0, 33, -312, 0, 0, 23, 0, -69, 15, 0, 17, 148, 0, 20, 36, 0, -62, -107, 0, 14, -44, 0, 252, 35, 0, 26, -17, 0, 32, -156, 0, 84, -2, 0, 73, -14, 0, 77, 24, 0, -2, -41, 0, 7, 108, 0, -6, -54, 0, 50, 8, 0, 30, -50, 0, -66, 38, 0, -180, 9, 0, -60, -45, 0, 98, -78, 0, 18, 9, 0, -24, 76, 0, -11, -8, 0, -120, -18, 0, 18, 115, 0, 24, 16, 0, 122, 6, 0, -172, -17, 0, 13, 14, 0, -180, 13, 0, -46, -113, 0, -9, 84, 0, -36, -21, 0, -201, 79, 0, -71, 144, 0, -138, 14, 0, -37, -18, 0, -15, -120, 0, -140, -75, 0, 45, -15, 0, -6, -142, 0, -248], "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], [1, 0, 0, 0, 0, 0, 0, 0], [0, 2, -1, 0, 0, -1, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0], [3, 0, 0, 0, -3, 3, 0, 0], [0, 1, 0, 0, 1, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -1, 0, 0, 0, 0, 0], [4, 0, 0, -1, 0, 0, 4, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, -1, 0, 0, 0, 1], [1, 0, 1, 1, -1, -2, 1, -1], [0, 0, 0, 0, 0, 0, 0, 0], [-2, -1, 0, 0, 0, -2, 0, 2], [2, -2, 0, 0, -1, 2, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0], [5, 3, -8, 5, -5, 0, 8, -5], [6, 0, -3, 6, 0, 0, 3, -3], [0, 0, 0, 0, 0, 0, 0, 0], [-3, 0, 0, 1, 0, 0, -3, 0], [0, 3, 0, 0, 0, 0, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-4, 7, 0, 0, 1, -4, 0, 4], [1, 2, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [3, -4, 0, 3, -3, 4, -1, -3], [0, 0, 0, -1, 0, 0, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -3, 0, 0, 0, 3, -3], [0, 0, -6, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [5, -3, 0, 0, 0, 5, 0, -5], [9, -3, 0, 0, -3, 9, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 3, 0, 0], [1, 0, -1, 0, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 5, -2, 0, 0, -2, 5], [-4, -7, 11, -4, 4, 0, -11, 4], [0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, -1, 1, 0, 3], [-1, 1, 0, 0, 3, -1, 0, 3], [0, 0, 0, 0, 0, 0, 0, 0], [-6, 6, 6, -6, 6, -3, 0, 6], [3, 0, 9, -6, 0, 0, -9, 9], [0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 1, 0, 0, 0, 0, 1], [2, -7, 0, 2, -2, 7, -5, -2], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -6, 0, 0, 0], [0, -5, 0, 0, 4, 0, 0, -5], [0, 0, 0, 0, 0, 0, 0, 0], [-6, 3, 0, -6, 6, -3, -3, 6], [1, 0, -1, 0, 0, 0, -1, -1], [0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 2, 3, 0, 0, 1, 2], [4, -4, -4, 4, -4, 5, 0, -4], [0, 0, 0, 0, 0, 0, 0, 0], [12, -12, 0, 0, -6, 12, 0, -6], [-1, 0, 0, 0, 1, -1, 0, 9], [0, 0, 0, 0, 0, 0, 0, 0], [3, -9, 6, 3, -3, 0, -6, -3], [0, 0, -11, 8, 0, 0, 8, -11], [0, 0, 0, 0, 0, 0, 0, 0], [6, 0, -6, 0, 0, 0, 5, -6], [3, -3, -3, 3, -3, -2, 0, -3], [0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 0, 0, 3, 0, 0, 0], [9, 0, 0, 0, 0, 9, 0, -9], [0, 0, 0, 0, 0, 0, 0, 0], [1, 0, -1, 1, -1, 1, 1, -1], [1, 0, 6, 1, 0, 0, -6, 6], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 2, -6, 0, 0, -6, 2], [-5, 12, 0, -5, 5, -12, 7, 5], [0, 0, 0, 0, 0, 0, 0, 0], [-21, 12, 0, 0, 12, -21, 0, 0], [0, -1, 0, 0, -2, 0, 0, 2], [0, 0, 0, 0, 0, 0, 0, 0], [0, -11, 0, 0, 0, 0, -11, 0], [5, 0, 0, 2, 0, 0, 5, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, -1, 0, 0, 0, 0], [-5, 4, 1, -5, 5, 0, -1, 5], [0, 0, 0, 0, 0, 0, 0, 0], [-3, 3, 0, 0, 9, -3, 0, 9], [-9, 12, 0, 0, 0, -9, 0, 9], [0, 0, 0, 0, 0, 0, 0, 0], [-6, 18, 3, -6, 6, -16, 12, 6], [-5, 0, -2, 2, 0, 0, 0, -2], [0, 0, 0, 0, 0, 0, 0, 0], [2, 0, 0, 3, 0, 0, 2, 0], [3, 0, 3, 3, -3, 3, 3, -3], [0, 0, 0, 0, 0, 0, 0, 0], [0, -12, 0, 0, 7, 0, 0, -12], [-1, 0, 0, 0, 1, -1, 0, -2], [0, 0, 0, 0, 0, 0, 0, 0], [0, -6, 3, 0, 0, 3, -6, 0], [6, 0, 6, -6, 0, 0, 0, 6], [0, 0, 0, 0, 0, 0, 0, 0], [-3, 0, -12, 12, 0, 0, 0, -12]]}