# Stored data for newform 798.2.k.h, downloaded from the LMFDB on 23 April 2024.
{"label": "798.2.k.h", "space_label": "798.2.k", "level": 798, "weight": 2, "hecke_orbit": 8, "hecke_orbit_code": 31525884619916062, "dim": 2, "is_polredabs": true, "nf_label": "2.0.3.1", "trace_hash": 338558699764100050, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[5, [9, -3, 1]], [11, [6, 1]], [13, [25, 5, 1]], [17, [36, -6, 1]]], "qexp_display": "q+(1-\\zeta_{6})q^{2}+(-1+\\zeta_{6})q^{3}-\\zeta_{6}q^{4}+\\cdots", "char_order": 3, "char_parity": 1, "char_degree": 2, "char_conductor": 19, "char_orbit_label": "k", "char_is_real": false, "Nk2": 3192, "analytic_conductor": 6.372062081298175, "hecke_ring_index": 1, "level_radical": 798, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 6, "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": "0.013", "prec": 17}, "analytic_rank_proved": true, "char_values": [798, 3, [533, 115, 211], [3, 3, 1]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 2, "level_primes": [2, 3, 7, 19], "conrey_indexes": [463, 505], "field_disc": -3, "field_disc_factorization": [[-1, 1], [3, 1]], "field_poly": [1, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.003", "prec": 17}, {"__RealLiteral__": 0, "data": "1.987", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "12.174", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "117.844", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "1.2.3.c3", "trace_display": [1, -1, 3, 2], "traces": [0, 2, 1, -1, -1, 3, 1, 2, -2, -1, -3, -12, 2, -5, 1, 3, -1, 6, -2, -1, -6, -1, -6, 3, 1, -4, -10, 2, -1, -6, 6, -8, 1, 6, -6, 3, -1, 16, 7, 10, -3, -6, 1, 4, 6, -6, 6, -6, -1, 2, -8, 6, -5, -12, 1, -18, -2, -7, -12, 9, 3, 13, -4, -1, 2, -30, -6, -14, -12, -6, -3, 3, 1, 4, 8, 8, 8, -12, 5, -8, 3, -1, 6, 30, 2, -18, -4, 12, 12, 6, -3, -5, 3, 4, -12, 21, -2, -8, 1, 6, -4, 6, 12, -8, 5, 3, -24, 0, -1, 4, 18, -8, -1, 42, -8, 18, -6, -5, -9, 6, -3, 50, 26, -6, 4, 6, -2, 13, 1, 4, -15, 15, -12, -1, -28, 3, -6, 3, -3, 4, -6, 12, -3, 30, 2, -36, -4, -1, -8, 24, 4, -38, 1, -12, -6, -12, -5, -17, 8, 24, 6, 3, 1, 28, 12, -18, 15, 12, 1, -12, -36, 8, -8, -15, 6, -4, 6, 9, 12, 12, 3, -5, -10, -26, -3, 24, -4, -36, -6, 2, 24, -30, -1, -5, 8, 15, -1, 0, 12, 22, 4, 28, 12, -6, 6, 18, -4, 3, 10, 6, 6, 10, -12, 3, 0, -12, -2, -8, -4, 4, 36, -60, 8, 16, 1, -4, 21, 6, -1, 10, 9, 6, 6, 21, 5, -36, -18, -8, -6, -18, -6, -8, 25, -1, 13, 3, -12, 40, 8, -15, 3, -3, -1, -18, 26, 36, -1, 6, 8, 16, 15, -6, -15, 15, -6, -72, 7, -12, -14, -18, -3, -2, 6, 10, 6, 24, 3, -8, 8, 4, -3, -6, 6, 7, -6, -24, 60, -6, 1, -19, -18, -8, -8, -54, 1, -27, -16, -12, -24, 15, -4, 4, -19, -12, -7, 78, -6, 25, 6, 4, 12, 0, -10, 16, 17, -6, 16, -18, 12, 36, 3, 0, 6, 42, 2, -20, 14, 4, 6, -6, -36, 16, -15, -8, 24, -84, -1, -5, 12, -21, -18, 48, 1, 2, -4, -9, 15, -12, -6, 4, -8, -5, -6, -24, 18, -9, 6, 6, 6, -12, 6, -37, -10, -25, -5, -12, -13, -26, -6, 12, -24, -12, -8, -32, 36, -3, 6, -30, 1, -32, 3, -26, -15, -6, 1, -18, 5, -8, 16, 0, -15, 36, -2, 15, 0, 24, 6, -2, 44, -7, 8, 3, 14, 20, 6, 3, -12, -96, -6, 34, 36, -6, 4, 9, -3, 45, 5, -8, -42, -48, 3, -20, -10, -6, 12, -48, 6, 13, 0, -60, -24, -24, -1, -8, -4, 18, -8, -24, 8, 22, 18, -1, -30, 18, 16, 36, -16, 24, 2, 30, 4, 36, -21, 19, 3, -30, 7, 34, 5, 6, -9, 9, -6, 10, 12, -12, -21, 0, 10, -14, -18, -17, -9, -24, -16, 32, -12, -12, -9, 18, -3, -40, -16, -6, -25, 24, -2, 16, -13, -14, -3, 30, -6, -72, 5, 36, 4, 3, 15, 4, -3, -24, -6, -24, 1, 36, -36, -12, 13, -3, 18, 4, -2, -1, 12, -12, 4, 36, 8, -15, 30, 36, 6, 4, -30, 8, -15, -24, 6, 14, -36, -18, 8, 60, -6, 0, 14, -6, 18, -12, -6, -2, 2, 10, 12, -12, 5, 22, 3, 13, 48, 48, 6, -8, -4, 24, 4, 30, 8, -40, 3, -36, -12, 30, -6, 63, -7, -1, -3, -78, -3, -80, 30, 15, 6, 12, -1, 4, -38, -5, 18, 30, -16, 72, -4, 15, -27, -36, 2, 4, -54, 0, -8, -18, -6, -18, -48, -44, -15, -9, -8, 52, -4, -14, 19, 75, -6, 64, -8, 12, 39, -30, 6, 34, -25, -36, 12, -27, -4, -50, 24, 3, 0, 6, -5, 29, 32, 42, 34, 48, -3, 40, 8, 10, -36, 78, -12, -5, 72, -6, -3, -33, 0, -23, 3, 24, 48, -48, 1, -54, 20, 4, -14, 60, 8, -45, -6, -8, -12, -6, -18, 49, 8, 30, -30, 21, -16, 18, 12, 16, -42, -78, -2, -26, 5, -4, 24, -60, 21, -8, 18, -3, 24, -60, -7, 18, 1, -5, 4, -60, 9, -26, 30, 6, 12, 24, -12, 36, 2, 21, -4, 12, -10, -8, -12, 18, -12, 6, 9, -38, -18, 16, -6, -12, 12, 180, -6, 9, 12, 36, 3, -8, -26, 16, -5, -24, 25, -20, 5, 2, -24, -24, 13, -2, -52, 3, -3, 84, 6, 34, -48, -5, -24, -21, -4, -72, -16, -15, 72, 0, 3, 40, 12, 6, 30, -57, -1, 28, -16, 36, -21, 48, -13, 4, 15, -18, 6, -90, 2, 40, 18, -12, 10, -45, -4, 16, 8, -8, 0, -42, -30, -18, 18, -6, -1, 51, 30, 58, 0, 15, 48, 42, -6, 65, 2, 36, 22, -18, -8, -72, 4, 6, -3, -24, -14, 18, 40, -18, -6, -42, 6, -20, -6, -2, -48, 42, -12, 28, 68, -5, 18, -42, -3, 13, 8, -48, -9, 36, -6, -2, -45, 4, -5, 6, -4, 72, -48, -8, -24, 12, -3, -7, 20, 12, -20, 36, 6, 50, 24, 7, -24, 24, 3, 34, 26, 3, 0, 30, -30, -44, -12, -6, -48, -72, 1, 45, -16, 38, 4, 48, -18, -70, -4, 16, -3, 6, 4, 28, -22, 27, -18, 48, -2, -2, 30, 54, 36, 54, 8, 13, 18, 6, -32, 48, 48, 18, 1, 15, 15, 24, 8, -144, -36, 4, -42, -30, -19, 34, -3, 6, -15, -30, 8, -180, 17, -39, -5, 15, -6, 58, -18, 25, -9, -30, -12, -32, 5, 4, 6, 24, -24, -1, -42, 0, 0, 108, 5, 28, -28, -32, 18, 3, -34, -36, 9, 3, 24, -6, -8, -40, 4, 36, -6, -54, 12, -45, 9, -72, 36, 3, 3, -30, -80, 0, -8, 15, -3, -41, -50, -48, 48, -33, -1, 4, 8, -20, -26, -6, 14, -36, -6, -8, -30, -18, 6, 0, -36, 12, -35, 24, 18, 13, -4, -8, -3, 132, 30, 61, -4, 16, -6], "weight_parity": 1, "has_non_self_twist": 1, "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], [1, 1, 19, 3, 1, 3, 0]], "char_orbit_index": 11, "prim_orbit_index": 3, "minimal_twist": "798.2.k.h", "char_is_minimal": true, "conrey_index": 463, "id": 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], [1, 0], [1, -1], [-1, 1], [0, -1], [3, -3], [0, 1], [1, 0], [-1, 0], [0, -1], [0, -3], [-6, 0], [1, 0], [0, -5], [1, -1], [0, 3], [-1, 1], [6, -6], [-1, 0], [-3, 5], [-3, 0], [-1, 1], [-6, 6], [0, 3], [1, -1], [0, -4], [-5, 0], [1, 0], [0, -1], [0, -6], [3, 0], [-4, 0], [0, 1], [6, -6], [0, -6], [3, -3], [-1, 1], [8, 0], [2, 3], [5, 0], [-3, 3], [-6, 6], [0, 1], [4, -4], [0, 6], [-3, 0], [3, 0], [0, -6], [0, -1], [1, 0], [-4, 0], [0, 6], [-5, 5], [0, -12], [1, -1], [-18, 18], [-1, 0], [-2, -3], [-6, 0], [9, -9], [3, -3], [0, 13], [-4, 4], [0, -1], [1, 0], [-15, 0], [0, -6], [0, -14], [-6, 0], [-3, 0], [0, -3], [3, -3], [0, 1], [4, -4], [8, -8], [4, 0], [5, -2], [-6, 0], [5, -5], [-8, 8], [0, 3], [-1, 1], [0, 6], [15, 0], [1, 0], [0, -18], [0, -4], [6, 0], [6, 0], [0, 6], [-3, 3], [0, -5], [3, -3], [4, -4], [-6, 0], [6, 9], [-1, 0], [-8, 8], [1, -1], [0, 6], [-4, 4]]}