# Stored data for newform 2255.1.h.i, downloaded from the LMFDB on 01 November 2024.
{"Nk2": 2255, "analytic_conductor": 1.1253916034874205, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 2255, "char_degree": 1, "char_is_minimal": true, "char_is_real": true, "char_orbit_index": 8, "char_orbit_label": "h", "char_order": 2, "char_parity": -1, "char_values": [2255, 2, [452, 1641, 826], [1, 1, 1]], "cm_discs": [-2255], "conrey_index": 2254, "dim": 4, "field_disc": 2000, "field_disc_factorization": [[2, 4], [5, 3]], "field_poly": [5, 0, -5, 0, 1], "field_poly_is_cyclotomic": false, "field_poly_is_real_cyclotomic": true, "field_poly_root_of_unity": 20, "has_non_self_twist": 1, "hecke_cutters": [[2, [5, 0, -5, 0, 1]], [3, [5, 0, -5, 0, 1]], [7, [0, 1]], [19, [-1, 1, 1]]], "hecke_orbit": 9, "hecke_orbit_code": 36029278072080591, "hecke_ring_generator_nbound": 2, "hecke_ring_index": 1, "hecke_ring_index_factorization": [], "hecke_ring_index_proved": true, "inner_twist_count": 4, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 2255, 8, -1, 2, -2255], [1, 1, 5, 2, 1, 2, 0], [1, 1, 451, 2, -1, 2, 0]], "is_cm": true, "is_largest": false, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": true, "is_self_twist": true, "is_twist_minimal": true, "label": "2255.1.h.i", "level": 2255, "level_is_powerful": false, "level_is_prime": false, "level_is_prime_power": false, "level_is_prime_square": false, "level_is_square": false, "level_is_squarefree": true, "level_primes": [5, 11, 41], "level_radical": 2255, "minimal_twist": "2255.1.h.i", "nf_label": "4.4.2000.1", "prim_orbit_index": 8, "projective_field": [-125, 0, 146, 0, -39, 0, -9, 0, 1, 0, 1], "projective_field_label": "10.2.129287396253125.1", "projective_image": "D10", "projective_image_type": "Dn", "qexp_display": "q+\\beta _{3}q^{2}-\\beta _{1}q^{3}+(1-\\beta _{2})q^{4}-q^{5}+\\cdots", "related_objects": [], "relative_dim": 4, "rm_discs": [], "self_twist_discs": [-2255], "self_twist_type": 1, "space_label": "2255.1.h", "trace_display": [0, 0, -4, 0], "trace_hash": 1313345400909653258, "trace_moments": [{"__RealLiteral__": 0, "data": "0.016", "prec": 17}, {"__RealLiteral__": 0, "data": "3.058", "prec": 17}, {"__RealLiteral__": 0, "data": "-0.918", "prec": 20}, {"__RealLiteral__": 0, "data": "147.268", "prec": 24}, {"__RealLiteral__": 0, "data": "-64.187", "prec": 24}, {"__RealLiteral__": 0, "data": "9204.420", "prec": 27}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.769", "prec": 17}, "traces": [0, 4, 0, 0, 6, -4, 0, 0, 0, 6, 0, -4, 0, 0, 0, 0, 4, 0, 0, -2, -6, 0, 0, 0, 10, 4, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, -6, -6, 0, 0, 0, 4, 0, 0, 0, 0, -10, 4, 0, 0, 0, -2, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 2, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 10, 0, 0, -6, 6, -2, 0, 0, 0, 0, 10, 0, 0, 2, 0, 0, 0, 0, -10, 0, -2, 0, 0, 0, -10, 4, 0, 0, -8, -4, 0, 0, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -2, 0, 0, 0, -2, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 4, 0, 2, 0, 0, -10, 0, -4, 0, 0, 0, -4, 0, 0, 0, 0, 0, -10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 2, 0, 2, 0, 0, -10, 0, 0, 0, 0, 10, 6, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, -4, 0, 0, 0, -10, 0, 2, 0, 0, 0, 0, 4, 0, 0, 0, 0, 8, 0, 0, -10, 0, 0, 0, 0, -2, 10, 0, 0, 0, -10, -4, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, -6, 0, 0, 0, -4, 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, 0, 10, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 8, -10, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -10, -2, -4, 0, 0, 0, 4, -2, 0, 0, 2, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 2, 0, 6, 0, 0, 0, 0, 0, 0, 0, -2, 0, -4, 0, 0, 0, 0, -10, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, -10, 0, 0, -10, -2, 0, 0, 0, -2, -10, 0, 0, 0, 6, 0, -10, 0, 0, 0, 0, 0, 0, 0, 0, 6, -12, 0, 0, 0, -6, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -10, -8, 0, 0, 0, 0, 10, 0, 0, -4, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, 10, -2, 0, 0, 0, 0, 4, 0, 0, 0, 2, 0, 0, 0, 10, 0, 0, 0, 0, 6, 0, 0, 0, 0, 10, 0, -8, 0, 0, 2, 10, -8, 0, 0, 2, -4, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 8, 0, 0, 0, 0, 4, 10, 0, 0, 0, 0, -8, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 10, 0, 4, 0, 0, 8, 0, -2, 0, 0, -10, 0, 0, 0, 0, 0, -10, 0, 0, 0, 10, 0, 6, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 2, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10, 2, 10, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, -10, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -10, 0, 0, 0, 0, 8, 0, 0, 0, 0, 2, 0, 0, 8, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -10, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 10, 0, 0, 0, 0, 0, 10, 0, 0, 0, 4, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, -10, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 10, 0, 0, -8, 0, 2, 0, 0, 0, 0, 0, 0, 0, -8, 0, 10, 0, 0, 0, 0, -10, 0, 0, 0, 10, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, -10, 0, 0, 10, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, -2, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10, 0, 0, 2, 0, 2, 0, 0, -4, 4, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, -10, 0, 0, 0, 0, 2, 0, 0, 0, -2, -10, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 10, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, -10, -10, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, -2, 0, 0, 0, 0, -4, 0, 0, 8, -6, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10, 0, 0, 0, 0, -8, 0, 0, 10, 0, 10, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, 10, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 4, -10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, 8, 0, 0, 0, 0, 10, -2, -10, 0, 0, 0, 0, 0, 0, 0, -8, 0, 10, 0, 0, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0, 2, -4, 0, 0, 0, -10, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, -8, -10, 0, 0, 0, 0, 0, 0, 0, -10, 0, 0, 0, 0, 2, 10, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, -10, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 8, 0, 0, 0, 0, 4, 10, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 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, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, -10, 0, 0, 10, 0, 0, 0, 0, -2, 0, 0, 0, 0, 8, -4, 0, 0, 0, 0, 0, 0, 0, 0, -10, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -10, 0, 0, 0, 0, 0, 0, 0, -10, -2, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 2, 0, 4, 0, 0, 0, 0, -10, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 12, 6, 0, 0, -10, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10, 0, 0, 0, 2, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 6, 0, 0, 0, 2, 0, 0, 0, 0, -2, 0, 0, 0, 0, -10, 0, 8, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 4, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 0, 8, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, -10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, -2, 0, 0, -6, -2, 0, 0, 0, -10, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, -2, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -10, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, -8, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, 0, 10, 0, -8, 0, 0, -4, 0, 0, 0, 0, 0, 0, -10, 0, 0, -10, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 10, 0, 0, 0, 2, 0, 0, 0, -2, 4, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4], "weight": 1, "weight_parity": -1, "id": null, "artin_degree": null, "artin_field": null, "artin_field_label": null, "artin_image": null, "atkin_lehner_eigenvals": null, "atkin_lehner_string": null, "embedded_related_objects": null, "fricke_eigenval": null, "sato_tate_group": null, "qexp": [[0, 0, 0, 0], [1, 0, 0, 0], [0, 0, 0, 1], [0, -1, 0, 0], [1, 0, -1, 0], [-1, 0, 0, 0], [-1, 0, -2, 0], [0, 0, 0, 0], [0, -1, 0, 1], [2, 0, 1, 0], [0, 0, 0, -1], [-1, 0, 0, 0], [0, -1, 0, 1], [0, 0, 0, 0], [0, 0, 0, 0], [0, 1, 0, 0], [0, 0, -2, 0], [0, 0, 0, 0], [0, 1, 0, 1], [0, 0, 1, 0], [-1, 0, 1, 0], [0, 0, 0, 0], [0, 0, 0, -1], [0, 0, 0, 0], [2, 0, -1, 0], [1, 0, 0, 0], [0, 0, 0, 0], [0, -1, 0, -1], [0, 0, 0, 0], [1, 0, 1, 0], [1, 0, 2, 0], [0, 0, 1, 0], [0, -1, 0, 1], [0, 1, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [1, 0, 0, 0], [0, 0, 0, 0], [0, 1, 0, -1], [0, 0, 0, 0], [0, 1, 0, -1], [1, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-1, 0, 1, 0], [-2, 0, -1, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 2], [1, 0, 0, 0], [0, 0, 0, 1], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 1], [-3, 0, -1, 0], [1, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, -1], [0, 1, 0, 0], [-1, 0, -1, 0], [0, 1, 0, -1], [0, 0, 0, 0], [0, 1, 0, -1], [0, 0, 0, 0], [1, 0, -1, 0], [0, 0, 0, 0], [1, 0, 2, 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, -1, 0, 0], [0, 0, 0, 0], [0, -1, 0, 0], [-1, 0, 2, 0], [0, 0, 0, 0], [0, 0, 0, 0], [1, 0, 1, 0], [0, 0, 2, 0], [2, 0, 2, 0], [0, 0, 0, 1], [0, 1, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -1, 0, -1], [0, 1, 0, -1], [0, 0, 0, 0], [0, -1, 0, -1], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, -1], [0, 0, 0, 0], [0, 0, -1, 0], [2, 0, -1, 0], [0, 0, 0, 0], [0, 0, 0, 1], [-2, 0, -1, 0], [1, 0, -1, 0]]}