# Stored data for newform 225.2.k.a, downloaded from the LMFDB on 25 March 2023.
{"level_primes": [3, 5], "is_polredabs": true, "sato_tate_group": "1.2.3.c6", "rm_discs": [], "conrey_indexes": [49, 124], "cm_discs": [], "trace_hash": 2051711321807076705, "level_radical": 15, "hecke_ring_index_proved": true, "self_twist_type": 0, "related_objects": [], "prim_orbit_index": 10, "is_cm": false, "hecke_orbit": 1, "analytic_conductor": 1.7966340454788086, "inner_twist_count": 4, "field_disc_factorization": [[2, 4], [3, 2]], "is_rm": false, "char_order": 6, "level_is_square": true, "weight_parity": 1, "label": "225.2.k.a", "field_poly_is_real_cyclotomic": false, "is_self_twist": false, "is_twist_minimal": false, "minimal_twist": "45.2.e.a", "field_poly_is_cyclotomic": true, "dim": 4, "trace_zratio": {"__RealLiteral__": 0, "data": "0.514", "prec": 17}, "traces": [0, 4, 0, 0, -2, 0, 0, 0, 0, -6, 0, 4, 0, 0, -6, 0, 2, 0, 0, 32, 0, 0, 0, 0, -18, 0, -8, 0, 0, -2, 0, 0, 0, 0, 8, 0, 12, 0, 0, 12, 0, -10, 0, 0, -8, 0, 12, 0, 0, 4, 0, -24, 0, 0, 18, 0, -18, 0, 0, -28, 0, -14, 0, 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0, 0, -40, 0, -42, 0, 0, 0, 0, -144, 0, 0, 28, 0, 32, 0, 0, 40, 0, -72, 0, 0, 0, 0, 14, 0, 0, -56, 0, 64, 0, 0, -16, 0, 0, 0, 0, 12, 0, -16, 0, 0, -72, 0, 62, 0, 0, -44, 0, 0, 0, 0, -192, 0, -144, 0, 0, -32, 0, 14, 0, 0, 60, 0, 30, 0, 0, 90, 0, 8, 0, 0, 96, 0, 104, 0, 0, -12, 0, 54, 0, 0, 0, 0], "hecke_ring_index_factorization": [], "nf_label": "4.0.144.1", "field_poly": [1, 0, -1, 0, 1], "has_non_self_twist": 1, "char_values": [225, 6, [101, 127], [2, 3]], "Nk2": 900, "field_poly_root_of_unity": 12, "analytic_rank": 0, "char_orbit_label": "k", "weight": 2, "trace_display": [0, 0, 0, 0], "analytic_rank_proved": true, "char_parity": 1, "level_is_squarefree": false, "hecke_ring_index": 1, "level_is_prime": false, "char_is_minimal": false, "qexp_display": "q+\\zeta_{12}q^{2}+(-\\zeta_{12}-\\zeta_{12}^{3})q^{3}-\\zeta_{12}^{2}q^{4}+\\cdots", "self_twist_discs": [], "char_is_real": false, "field_disc": 144, "level_is_prime_power": false, "relative_dim": 2, "hecke_cutters": [[2, [1, 0, -1, 0, 1]]], "space_label": "225.2.k", "level": 225, "is_self_dual": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 5, 2, 1, 2, 0], [1, 1, 9, 3, 1, 3, 0], [1, 1, 45, 10, 1, 6, 0]], "char_degree": 2, "char_conductor": 45, "char_orbit_index": 11, "hecke_ring_generator_nbound": 2, "hecke_orbit_code": 687228322017, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.810", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "91.322", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3220.037", "prec": 27}], "id": null, "projective_field": null, "embedded_related_objects": null, "projective_image_type": null, "artin_image": null, "atkin_lehner_string": null, "atkin_lehner_eigenvals": null, "artin_field": null, "projective_image": null, "artin_field_label": null, "projective_field_label": null, "fricke_eigenval": null, "artin_degree": null, "qexp": [[0, 0, 0, 0], [1, 0, 0, 0], [0, 1, 0, 0], [0, -1, 0, -1], [0, 0, -1, 0], [0, 0, 0, 0], [1, 0, -2, 0], [0, -3, 0, 0], [0, 0, 0, -3], [-3, 0, 3, 0], [0, 0, 0, 0], [2, 0, -2, 0], [0, -1, 0, 2], [0, -2, 0, 2], [0, 0, -3, 0], [0, 0, 0, 0], [1, 0, -1, 0], [0, 0, 0, -4], [0, -3, 0, 3], [8, 0, 0, 0], [0, 0, 0, 0], [-3, 0, 6, 0], [0, 2, 0, -2], [0, 3, 0, -3], [-6, 0, 3, 0], [0, 0, 0, 0], [-2, 0, 0, 0], [0, 6, 0, -3], [0, 0, 0, 3], [-1, 0, 1, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -5, 0, 5], [0, -4, 0, 2], [4, 0, -4, 0], [0, 0, 0, 0], [3, 0, 0, 0], [0, 0, 0, 4], [0, 8, 0, 0], [2, 0, 2, 0], [0, 0, 0, 0], [0, 0, -5, 0], [0, -3, 0, 6], [0, 8, 0, 0], [-2, 0, 0, 0], [0, 0, 0, 0], [3, 0, 0, 0], [0, 7, 0, 0], [0, -2, 0, 1], [0, 0, 2, 0], [0, 0, 0, 0], [-8, 0, 4, 0], [0, 2, 0, 0], [0, 0, 0, -2], [3, 0, 3, 0], [0, 0, 0, 0], [-9, 0, 9, 0], [0, -8, 0, -8], [0, -1, 0, 1], [0, 0, -14, 0], [0, 0, 0, 0], [-7, 0, 7, 0], [0, 0, 0, 0], [0, 9, 0, -9], [-7, 0, 0, 0], [0, 0, 0, 0], [-2, 0, -2, 0], [0, 3, 0, -3], [0, -4, 0, 4], [-3, 0, -3, 0], [0, 0, 0, 0], [2, 0, 0, 0], [0, 9, 0, 0], [0, 0, 0, 4], [-4, 0, 4, 0], [0, 0, 0, 0], [0, 0, -8, 0], [0, -6, 0, 6], [0, 2, 0, 2], [-6, 0, 6, 0], [0, 0, 0, 0], [0, 0, -9, 0], [0, 0, 0, -5], [0, -9, 0, 0], [6, 0, -3, 0], [0, 0, 0, 0], [0, 0, 8, 0], [0, 2, 0, -1], [0, -6, 0, 0], [15, 0, 0, 0], [0, 0, 0, 0], [6, 0, 0, 0], [0, -3, 0, 0], [0, 0, 0, 0], [0, 0, 7, 0], [0, 0, 0, 0], [5, 0, 5, 0], [0, 2, 0, 0], [0, 0, 0, 2], [0, 0, 6, 0], [0, 0, 0, 0]]}