# Stored data for newform 448.2.q.a, downloaded from the LMFDB on 24 April 2024. {"label": "448.2.q.a", "space_label": "448.2.q", "level": 448, "weight": 2, "hecke_orbit": 1, "hecke_orbit_code": 1099545182656, "dim": 8, "is_polredabs": true, "nf_label": "8.0.12960000.1", "trace_hash": 2214611372670616319, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[3, [25, 0, -5, 0, 1]], [5, [25, 0, 5, 0, 1]]], "qexp_display": "q+(-\\beta _{2}+\\beta _{7})q^{3}+\\beta _{6}q^{5}+(2\\beta _{1}-\\beta _{5}+\\cdots)q^{7}+\\cdots", "char_order": 6, "char_parity": 1, "char_degree": 2, "char_conductor": 56, "char_orbit_label": "q", "char_is_real": false, "Nk2": 1792, "analytic_conductor": 3.577298010553361, "hecke_ring_index": 16, "level_radical": 14, "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": false, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.803", "prec": 17}, "analytic_rank_proved": true, "char_values": [448, 6, [127, 197, 129], [3, 3, 1]], "hecke_ring_generator_nbound": 7, "inner_twist_count": 8, "level_primes": [2, 7], "conrey_indexes": [31, 159], "field_disc": 12960000, "field_disc_factorization": [[2, 8], [3, 4], [5, 4]], "field_poly": [1, 0, -3, 0, 8, 0, -3, 0, 1], "hecke_ring_index_factorization": [[2, 4]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.137", "prec": 17}, {"__RealLiteral__": 0, "data": "7.905", "prec": 17}, {"__RealLiteral__": 0, "data": "14.958", "prec": 20}, {"__RealLiteral__": 0, "data": "760.507", "prec": 24}, {"__RealLiteral__": 0, "data": "2225.802", "prec": 27}, {"__RealLiteral__": 0, "data": "94870.140", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "1.2.3.c6", "trace_display": [0, 0, 0, 0], "traces": [0, 8, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 36, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 60, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, -120, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -36, 0, 0, 0, 0, 0, 0, 0, 44, 0, 0, 0, 0, 0, 0, 0, -36, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -80, 0, 0, 0, 0, 0, 0, 0, -96, 0, 0, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -36, 0, 0, 0, 0, 0, 0, 0, 120, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, -104, 0, 0, 0, 0, 0, 0, 0, 20, 0, 0, 0, 0, 0, 0, 0, 180, 0, 0, 0, 0, 0, 0, 0, 28, 0, 0, 0, 0, 0, 0, 0, 180, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 60, 0, 0, 0, 0, 0, 0, 0, 60, 0, 0, 0, 0, 0, 0, 0, 40, 0, 0, 0, 0, 0, 0, 0, -108, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 192, 0, 0, 0, 0, 0, 0, 0, 40, 0, 0, 0, 0, 0, 0, 0, -60, 0, 0, 0, 0, 0, 0, 0, -60, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 108, 0, 0, 0, 0, 0, 0, 0, -128, 0, 0, 0, 0, 0, 0, 0, -60, 0, 0, 0, 0, 0, 0, 0, -108, 0, 0, 0, 0, 0, 0, 0, 104, 0, 0, 0, 0, 0, 0, 0, -144, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -120, 0, 0, 0, 0, 0, 0, 0, -40, 0, 0, 0, 0, 0, 0, 0, -132, 0, 0, 0, 0, 0, 0, 0, -156, 0, 0, 0, 0, 0, 0, 0, -120, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 88, 0, 0, 0, 0, 0, 0, 0, -96, 0, 0, 0, 0, 0, 0, 0, 20, 0, 0, 0, 0, 0, 0, 0, -60, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -96, 0, 0, 0, 0, 0, 0, 0, 200, 0, 0, 0, 0, 0, 0, 0, 60, 0, 0, 0, 0, 0, 0, 0, 108, 0, 0, 0, 0, 0, 0, 0, -56, 0, 0, 0, 0, 0, 0, 0, -180, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -52, 0, 0, 0, 0, 0, 0, 0, 360, 0, 0, 0, 0, 0, 0, 0, -108, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -252, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 120, 0, 0, 0, 0, 0, 0, 0, 288, 0, 0, 0, 0, 0, 0, 0, 100, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 84, 0, 0, 0, 0, 0, 0, 0, 60, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 300, 0, 0, 0, 0, 0, 0, 0, 256, 0, 0, 0, 0, 0, 0, 0, 140, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -216, 0, 0, 0, 0, 0, 0, 0, 180, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 324, 0, 0, 0, 0, 0, 0, 0, 56, 0, 0, 0, 0, 0, 0, 0, -180, 0, 0, 0, 0, 0, 0, 0, -180, 0, 0, 0, 0, 0, 0, 0, 80, 0, 0, 0, 0, 0, 0, 0, -252, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -360, 0, 0, 0, 0, 0, 0, 0, 120, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -72, 0, 0, 0, 0, 0, 0, 0, 36, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 108, 0, 0, 0, 0, 0, 0, 0, -248, 0, 0, 0, 0, 0, 0, 0, 60, 0, 0, 0, 0, 0, 0, 0, 252, 0, 0, 0, 0, 0, 0, 0, 100, 0, 0, 0, 0, 0, 0, 0, -48, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -160, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -120, 0, 0, 0, 0, 0, 0, 0, -120, 0, 0, 0, 0, 0, 0, 0, -120, 0, 0, 0, 0, 0, 0, 0, -180, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 112, 0, 0, 0, 0, 0, 0, 0, -540, 0, 0, 0, 0, 0, 0, 0, -36, 0, 0, 0, 0, 0, 0, 0, -360, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 4, 2, -1, 2, 0], [1, 1, 7, 4, -1, 6, 0], [1, 1, 8, 2, 1, 2, 0], [1, 1, 8, 4, -1, 2, 0], [1, 1, 28, 6, 1, 6, 0], [1, 1, 56, 10, -1, 6, 0], [1, 1, 56, 13, 1, 6, 0]], "char_orbit_index": 17, "prim_orbit_index": 13, "minimal_twist": "448.2.q.a", "char_is_minimal": true, "conrey_index": 31, "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, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -1, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 0, 0, 0, -1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -2, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -1, 0, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, -5, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [3, 0, 0, 0, -3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -3, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, -4, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, -1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [10, 0, 0, 0, 5, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 3, 0, 0, 0, 0, -2], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 6, 0, 0, -3, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-6, 0, 0, 0, -12, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -2, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 0, 0, 0, 6, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [3, 0, 0, 0, 8, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -3, 0, 0, 0, 0, 6], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -1, 0, 0, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -10, 0, 0, 0, -5, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-15, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -1, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 6, 0, 0, 0, 4, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -3, 0, 0, 0, 0, -3], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, -6, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-3, 0, 0, 0, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -1, 0, 0, 5, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -13, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [11, 0, 0, 0, 11, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, -2], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -3, 0, 0, 6, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -10, 0, 0, 0, 10, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-6, 0, 0, 0, -3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -2, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 15, 0, 0, 0, 15, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-2, 0, 0, 0, -4, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -4, 0, 0, 0, 0, 2], [0, 0, 0, 0, 0, 0, 0, 0]]}