# Stored data for newform 2200.1.dd.a, downloaded from the LMFDB on 25 April 2024.
{"label": "2200.1.dd.a", "space_label": "2200.1.dd", "level": 2200, "weight": 1, "hecke_orbit": 1, "hecke_orbit_code": 5566294395032, "dim": 8, "is_polredabs": true, "nf_label": "8.0.4000000.1", "trace_hash": 700742167993641668, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[3, [1, 0, 1, 0, 6, 0, -4, 0, 1]]], "qexp_display": "q+\\zeta_{20}^{3}q^{2}+(\\zeta_{20}-\\zeta_{20}^{7})q^{3}+\\zeta_{20}^{6}q^{4}+\\cdots", "char_order": 10, "char_parity": -1, "char_degree": 4, "char_conductor": 440, "char_orbit_label": "dd", "char_is_real": false, "Nk2": 2200, "analytic_conductor": 1.0979430277926052, "hecke_ring_index": 1, "level_radical": 110, "projective_image": "D5", "projective_image_type": "Dn", "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 20, "field_poly_is_real_cyclotomic": false, "projective_field_label": "5.1.937024.1", "hecke_ring_index_proved": true, "self_twist_type": 1, "is_self_dual": false, "is_self_twist": true, "is_cm": true, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.760", "prec": 17}, "analytic_rank_proved": true, "char_values": [2200, 10, [551, 1101, 177, 1201], [5, 5, 5, 2]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 8, "level_primes": [2, 5, 11], "conrey_indexes": [499, 1499, 1699, 2099], "field_disc": 4000000, "field_disc_factorization": [[2, 8], [5, 6]], "field_poly": [1, 0, -1, 0, 1, 0, -1, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "-0.078", "prec": 20}, {"__RealLiteral__": 0, "data": "7.510", "prec": 17}, {"__RealLiteral__": 0, "data": "-12.545", "prec": 24}, {"__RealLiteral__": 0, "data": "714.739", "prec": 24}, {"__RealLiteral__": 0, "data": "-3073.619", "prec": 30}, {"__RealLiteral__": 0, "data": "151180.078", "prec": 34}], "related_objects": [], "self_twist_discs": [-8], "cm_discs": [-8], "rm_discs": [], "relative_dim": 2, "trace_display": [0, 0, 0, 0], "traces": [0, 8, 0, 0, 2, 0, 6, 0, 0, 6, 0, -2, 0, 0, 0, 0, -2, 0, 0, -6, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 4, 0, 0, 0, 0, -4, 0, 0, -8, 0, 0, 0, 0, 2, 0, 2, 0, 0, 8, 0, 0, 0, 0, -6, 0, 0, 0, 0, 2, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 4, 0, 0, 0, 0, 0, 0, -4, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, -4, 0, 0, 4, 0, 6, 0, 0, 4, 0, 0, 0, 0, -4, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, -4, 0, 0, 2, 0, -2, 0, 0, 0, 0, -2, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, -2, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 4, 0, 6, 0, 0, -6, 0, 2, 0, 0, -12, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, -4, 0, 0, 0, 0, 2, 0, 0, -2, 0, -4, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 6, 0, -8, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 6, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, -6, 0, 0, 0, 0, -6, 0, 0, 0, 0, 4, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 4, 0, 2, 0, 0, 0, 0, 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, 4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 6, 0, 0, -6, 0, 2, 0, 0, 6, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, -2, 0, -4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 12, 0, 0, 0, 0, 6, 0, 0, -6, 0, 0, 0, 0, -8, 0, -2, 0, 0, 8, 0, 6, 0, 0, 2, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, -8, 0, 0, 0, 0, -4, 0, 0, -6, 0, 16, 0, 0, 0, 0, 4, 0, 0, 8, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, -8, 0, 0, 4, 0, 0, 0, 0, 0, 0, -4, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, -2, 0, 0, 0, 0, -8, 0, 0, 2, 0, 0, 0, 0, 0, 0, -4, 0, 0, 4, 0, 0, 0, 0, 8, 0, 0, 0, 0, 2, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 4, 0, 2, 0, 0, 0, 0, 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, -4, 0, 0, 0, 0, 0, 0, 0, -16, 0, 12, 0, 0, 2, 0, 6, 0, 0, -2, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, 0, 4, 0, -4, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, 0, 6, 0, 0, 0, 0, -2, 0, 0, 4, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 6, 0, 0, 4, 0, 0, 0, 0, -2, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -4, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 4, 0, 6, 0, 0, -16, 0, 0, 0, 0, -2, 0, 0, 0, 0, 4, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -6, 0, 0, 0, 0, -4, 0, -4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 4, 0, -8, 0, 0, -6, 0, 0, 0, 0, 4, 0, 0, 0, 0, -8, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -4, 0, 0, 4, 0, 6, 0, 0, 0, 0, 6, 0, 0, -2, 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, 0, -4, 0, -4, 0, 0, 4, 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, 12, 0, 0, -6, 0, -4, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 4, 0, 0, 0, 0, -6, 0, 0, 8, 0, 0, 0, 0, 0, 0, -4, 0, 0, -6, 0, -4, 0, 0, 2, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -6, 0, 8, 0, 0, 8, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -4, 0, 0, 4, 0, -4, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, -4, 0, 0, 4, 0, 0, 0, 0, 8, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -4, 0, 0, 0, 0, -4, 0, 0, 2, 0, 2, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, -16, 0, 2, 0, 0, 0, 0, 2, 0, 0, 8, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 6, 0, 2, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 8, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, -8, 0, -4, 0, 0, 4, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, -16, 0, 6, 0, 0, 0, 0, -4, 0, 0, 0, 0, 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, -2, 0, 6, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, -6, 0, 6, 0, 0, -6, 0, -2, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -4, 0, 0, 0, 0, 2, 0, 0, 8, 0, 0, 0, 0, 8, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, -6, 0, 0, 0, 0, 2, 0, 0, 8, 0, 2, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 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, 0, -8, 0, 0, -4, 0, 6, 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, 0, 0, 0, 6, 0, 0, 0, 0, 6, 0, 0, 4, 0, 0, 0, 0, -4, 0, -4, 0, 0, 4, 0, -4, 0, 0, -2, 0, 0, 0, 0, -2, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 2, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, -12, 0, 0, -2, 0, -4, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 2, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 4, 0, -6, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0], "projective_field": [-23, 3, -8, -4, -1, 1], "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, 8, 4, -1, 2, -8], [1, 1, 5, 2, 1, 2, 0], [1, 1, 11, 3, 1, 5, 0], [1, 1, 40, 5, -1, 2, 0], [1, 1, 55, 10, 1, 10, 0], [1, 1, 88, 12, -1, 10, 0], [1, 1, 440, 34, -1, 10, 0]], "char_orbit_index": 82, "prim_orbit_index": 34, "minimal_twist": "88.1.l.a", "char_is_minimal": false, "conrey_index": 499, "id": null, "fricke_eigenval": null, "atkin_lehner_string": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "sato_tate_group": null, "atkin_lehner_eigenvals": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[], [[1, 0]], [[1, 3]], [[1, 1], [-1, 7]], [[1, 6]], [], [[1, 0], [1, 4]], [], [[1, 9]], [[1, 2], [-1, 4], [-1, 8]], [], [[1, 4]], [[1, 3], [1, 7]], [], [], [], [[-1, 2]], [[-1, 1], [1, 3]], [[1, 1], [1, 5], [-1, 7]], [[-1, 0], [-1, 8]], [], [], [[1, 7]], [], [[-1, 0], [1, 6]], [], [], [[-1, 1], [1, 3], [-2, 5], [1, 5], [-1, 9]], [], [], [], [], [[-1, 5]], [[1, 1], [1, 5]], [[-1, 4], [1, 6]], [], [[1, 0], [1, 4], [1, 8]], [], [[1, 1], [-1, 3]], [], [], [[-1, 2], [-1, 6]], [], [[-1, 3], [-1, 7]], [[-1, 0]], [], [], [], [[-1, 3], [1, 9]], [[1, 2]], [], [[1, 0], [-1, 2], [1, 4], [1, 8]], [], [], [[1, 2], [-1, 4], [1, 6], [-1, 8]], [], [], [[-1, 1], [-1, 5], [1, 7], [-1, 9]], [], [[-1, 0], [1, 2]], [], [], [], [], [[-1, 8]], [], [[1, 4], [1, 8]], [[-1, 1], [-1, 9]], [[-1, 7], [1, 9]], [], [], [], [[-1, 1], [1, 3], [1, 7]], [[-1, 3], [1, 9]], [], [], [[1, 4], [-1, 6]], [], [], [], [], [[2, 0], [-1, 0], [-2, 2], [1, 2], [1, 4], [-2, 6], [1, 6], [1, 8]], [[-1, 5], [-1, 9]], [[1, 5], [1, 9]], [], [], [[1, 0], [-1, 6]], [], [[-1, 3]], [[1, 2], [-1, 8]], [], [], [], [], [], [], [[-1, 2], [-1, 6]], [[-1, 1], [-1, 5]], [[1, 5]], [[1, 2], [1, 6], [-1, 8]], []]}