# Stored data for newform 804.2.i.c, downloaded from the LMFDB on 20 April 2024. {"label": "804.2.i.c", "space_label": "804.2.i", "level": 804, "weight": 2, "hecke_orbit": 3, "hecke_orbit_code": 9007749044110116, "dim": 2, "is_polredabs": true, "nf_label": "2.0.3.1", "trace_hash": 2177645584245293253, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[5, [-2, 1]], [7, [9, -3, 1]]], "qexp_display": "q+q^{3}+2q^{5}+3\\zeta_{6}q^{7}+q^{9}-\\zeta_{6}q^{11}+\\cdots", "char_order": 3, "char_parity": 1, "char_degree": 2, "char_conductor": 67, "char_orbit_label": "i", "char_is_real": false, "Nk2": 3216, "analytic_conductor": 6.419972322510943, "hecke_ring_index": 1, "level_radical": 402, "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": "0.006", "prec": 17}, "analytic_rank_proved": true, "char_values": [804, 3, [403, 269, 337], [3, 3, 1]], "hecke_ring_generator_nbound": 11, "inner_twist_count": 2, "level_primes": [2, 3, 67], "conrey_indexes": [37, 565], "field_disc": -3, "field_disc_factorization": [[-1, 1], [3, 1]], "field_poly": [1, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.004", "prec": 17}, {"__RealLiteral__": 0, "data": "2.095", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "13.492", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "131.013", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "1.2.3.c3", "trace_display": [0, 2, 4, 3], "traces": [0, 2, 0, 2, 0, 4, 0, 3, 0, 2, 0, -1, 0, 5, 0, 4, 0, 1, 0, 1, 0, 3, 0, -7, 0, -2, 0, 2, 0, 5, 0, 3, 0, -1, 0, 6, 0, -3, 0, 5, 0, -7, 0, 8, 0, 4, 0, -9, 0, -2, 0, 1, 0, 4, 0, -2, 0, 1, 0, 0, 0, 1, 0, 3, 0, 10, 0, 16, 0, -7, 0, -5, 0, 9, 0, -2, 0, 3, 0, 15, 0, 2, 0, -11, 0, 2, 0, 5, 0, -36, 0, 30, 0, 3, 0, 2, 0, -15, 0, -1, 0, -3, 0, -17, 0, 6, 0, -8, 0, -4, 0, -3, 0, -7, 0, -14, 0, 5, 0, 6, 0, 10, 0, -7, 0, -24, 0, 7, 0, 8, 0, -24, 0, 6, 0, 4, 0, 12, 0, -8, 0, -9, 0, -10, 0, 10, 0, -2, 0, -28, 0, 5, 0, 1, 0, 6, 0, 13, 0, 4, 0, -42, 0, -5, 0, -2, 0, 3, 0, -12, 0, 1, 0, 9, 0, -3, 0, 0, 0, 0, 0, -7, 0, 1, 0, -6, 0, -2, 0, 3, 0, -11, 0, 4, 0, 10, 0, -7, 0, -7, 0, 16, 0, -15, 0, -14, 0, -7, 0, -2, 0, -23, 0, -5, 0, 16, 0, -9, 0, 9, 0, -5, 0, -8, 0, -2, 0, 3, 0, 1, 0, 3, 0, -11, 0, -18, 0, 15, 0, 15, 0, -52, 0, 2, 0, -4, 0, -5, 0, -11, 0, 9, 0, 14, 0, 2, 0, -15, 0, -18, 0, 5, 0, -16, 0, 8, 0, -36, 0, 20, 0, 48, 0, 30, 0, 1, 0, 52, 0, 3, 0, 13, 0, -56, 0, 2, 0, 21, 0, 16, 0, -15, 0, -44, 0, 0, 0, -1, 0, 35, 0, 12, 0, -3, 0, 2, 0, -11, 0, -17, 0, 56, 0, -36, 0, 6, 0, 17, 0, 5, 0, -8, 0, -1, 0, -5, 0, -4, 0, 27, 0, 3, 0, -3, 0, 32, 0, -11, 0, -7, 0, 3, 0, 30, 0, -14, 0, 15, 0, 4, 0, 5, 0, -15, 0, -10, 0, 6, 0, -48, 0, 18, 0, 10, 0, 18, 0, -25, 0, -7, 0, 6, 0, -23, 0, -24, 0, 50, 0, 29, 0, 7, 0, 1, 0, 6, 0, 8, 0, 9, 0, 7, 0, -24, 0, 30, 0, 68, 0, 6, 0, 68, 0, 30, 0, 4, 0, 6, 0, 5, 0, 12, 0, 0, 0, -22, 0, -8, 0, -15, 0, 1, 0, -9, 0, -1, 0, 6, 0, -10, 0, 23, 0, 29, 0, 10, 0, 7, 0, 37, 0, -2, 0, 39, 0, -72, 0, -28, 0, 9, 0, -7, 0, 5, 0, 60, 0, 17, 0, 1, 0, -36, 0, 1, 0, 6, 0, -7, 0, 15, 0, 13, 0, -4, 0, -1, 0, 4, 0, 29, 0, 15, 0, -42, 0, -30, 0, 33, 0, -5, 0, 24, 0, 10, 0, -2, 0, 15, 0, -3, 0, 3, 0, -9, 0, -6, 0, -12, 0, 36, 0, 54, 0, 1, 0, -34, 0, -9, 0, 9, 0, 76, 0, -19, 0, -3, 0, 6, 0, -26, 0, 0, 0, -70, 0, -16, 0, 0, 0, 4, 0, 20, 0, -7, 0, -8, 0, -9, 0, 1, 0, 10, 0, -45, 0, -6, 0, 37, 0, 20, 0, -2, 0, -72, 0, -14, 0, 3, 0, 9, 0, -37, 0, -11, 0, 7, 0, 17, 0, 4, 0, -66, 0, -2, 0, 10, 0, 25, 0, 6, 0, -7, 0, 21, 0, 12, 0, -7, 0, -5, 0, -19, 0, 16, 0, 20, 0, -37, 0, -15, 0, -90, 0, 13, 0, -14, 0, 76, 0, -15, 0, -7, 0, -54, 0, -38, 0, -2, 0, 3, 0, 21, 0, -23, 0, 14, 0, 10, 0, -5, 0, 25, 0, -72, 0, 16, 0, 1, 0, 0, 0, -9, 0, -39, 0, -48, 0, 9, 0, 51, 0, -20, 0, -5, 0, 12, 0, -70, 0, -8, 0, -2, 0, -52, 0, -2, 0, 29, 0, -90, 0, 3, 0, 9, 0, 24, 0, 1, 0, 10, 0, -1, 0, 3, 0, -16, 0, -14, 0, -11, 0, 33, 0, 3, 0, -18, 0, 9, 0, 41, 0, 15, 0, -42, 0, -20, 0, 15, 0, 17, 0, 51, 0, -52, 0, -5, 0, -31, 0, 2, 0, 4, 0, 37, 0, -4, 0, -5, 0, -15, 0, -5, 0, 21, 0, -56, 0, -11, 0, -12, 0, -48, 0, 9, 0, 10, 0, 21, 0, 14, 0, -36, 0, -6, 0, 2, 0, 0, 0, 21, 0, -15, 0, -15, 0, -3, 0, -18, 0, -14, 0, -5, 0, 5, 0, 26, 0, 17, 0, -16, 0, 21, 0, -5, 0, 8, 0, 21, 0, -18, 0, -36, 0, -18, 0, -84, 0, 20, 0, 92, 0, 7, 0, 48, 0, -10, 0, 4, 0, 30, 0, -47, 0, 21, 0, 1, 0, -27, 0, 52, 0, 52, 0, 2, 0, 6, 0, 3, 0, 43, 0, 4, 0, 13, 0, -24, 0, 60, 0, -56, 0, -21, 0, -19, 0, 2, 0, -84, 0, 11, 0, 21, 0, 48, 0, 18, 0, 16, 0, 15, 0, 55, 0, -15, 0, -36, 0, -31, 0, -44, 0, 37, 0, -25, 0, 0, 0, -3, 0, -21, 0, -1, 0, -18, 0, 0, 0, 35, 0, -15, 0, 2, 0, 12, 0, -14, 0, 55, 0, -3, 0, 32, 0, 22, 0, 2, 0, -36, 0, -15, 0, -11, 0, -50, 0, 3, 0, -17, 0, 36, 0, 2, 0, 56, 0, -4, 0, -100, 0, -36, 0, 28, 0, 98, 0, 6, 0, -24, 0, -45, 0, 17, 0, -76, 0, -22, 0, 5, 0, 18, 0, 22, 0, -8, 0, 8, 0, -37, 0, -1, 0, -29, 0, -12, 0, -5, 0, -39, 0, 18, 0, -4, 0, -104, 0, -14, 0, 27, 0, -28, 0, 104, 0, 3, 0, -14, 0, 12, 0, -3, 0], "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, 67, 3, 1, 3, 0]], "char_orbit_index": 9, "prim_orbit_index": 3, "minimal_twist": "804.2.i.c", "char_is_minimal": true, "conrey_index": 37, "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], [0, 0], [1, 0], [0, 0], [2, 0], [0, 0], [0, 3], [0, 0], [1, 0], [0, 0], [0, -1], [0, 0], [5, -5], [0, 0], [2, 0], [0, 0], [1, -1], [0, 0], [1, -1], [0, 0], [0, 3], [0, 0], [-7, 7], [0, 0], [-1, 0], [0, 0], [1, 0], [0, 0], [0, 5], [0, 0], [0, 3], [0, 0], [0, -1], [0, 0], [0, 6], [0, 0], [-3, 3], [0, 0], [5, -5], [0, 0], [0, -7], [0, 0], [4, 0], [0, 0], [2, 0], [0, 0], [0, -9], [0, 0], [-2, 2], [0, 0], [1, -1], [0, 0], [2, 0], [0, 0], [0, -2], [0, 0], [1, -1], [0, 0], [0, 0], [0, 0], [1, -1], [0, 0], [0, 3], [0, 0], [10, -10], [0, 0], [7, 2], [0, 0], [-7, 7], [0, 0], [0, -5], [0, 0], [9, -9], [0, 0], [-1, 0], [0, 0], [3, -3], [0, 0], [0, 15], [0, 0], [1, 0], [0, 0], [-11, 11], [0, 0], [2, -2], [0, 0], [0, 5], [0, 0], [-18, 0], [0, 0], [15, 0], [0, 0], [0, 3], [0, 0], [2, -2], [0, 0], [-15, 15], [0, 0], [0, -1], [0, 0]]}