# Stored data for newform 775.1.w.a, downloaded from the LMFDB on 24 April 2024. {"label": "775.1.w.a", "space_label": "775.1.w", "level": 775, "weight": 1, "hecke_orbit": 1, "hecke_orbit_code": 1511845266183, "dim": 4, "is_polredabs": true, "nf_label": "4.0.125.1", "trace_hash": 940825485116575445, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[2, [1, -2, 4, -3, 1]]], "qexp_display": "q+(1-\\zeta_{10})q^{2}+(1-\\zeta_{10}+\\zeta_{10}^{2})q^{4}+\\cdots", "char_order": 10, "char_parity": -1, "char_degree": 4, "char_conductor": 775, "char_orbit_label": "w", "char_is_real": false, "Nk2": 775, "analytic_conductor": 0.3867753847905769, "hecke_ring_index": 1, "level_radical": 155, "projective_image": "D5", "projective_image_type": "Dn", "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 10, "field_poly_is_real_cyclotomic": false, "projective_field_label": "5.1.375390625.1", "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": "0.507", "prec": 17}, "analytic_rank_proved": true, "char_values": [775, 10, [652, 251], [8, 5]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 4, "level_primes": [5, 31], "conrey_indexes": [61, 216, 371, 681], "field_disc": 125, "field_disc_factorization": [[5, 3]], "field_poly": [1, -1, 1, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "-0.036", "prec": 20}, {"__RealLiteral__": 0, "data": "3.839", "prec": 17}, {"__RealLiteral__": 0, "data": "11.024", "prec": 20}, {"__RealLiteral__": 0, "data": "93.197", "prec": 20}, {"__RealLiteral__": 0, "data": "632.503", "prec": 24}, {"__RealLiteral__": 0, "data": "4976.894", "prec": 27}], "related_objects": [], "self_twist_discs": [-31], "cm_discs": [-31], "rm_discs": [], "relative_dim": 1, "trace_display": [3, 0, -1, -2], "traces": [0, 4, 3, 0, 2, -1, 0, -2, 1, -1, -2, 0, 0, 0, 1, 0, 0, 0, -2, 3, -3, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, -1, 4, 0, 0, -2, -3, 0, 1, 0, 1, -2, 0, 0, 0, -1, 0, -2, 0, 2, 3, 0, 0, 0, 0, 0, -3, 0, 0, -2, 0, 0, 3, -2, 3, 0, 0, 3, 0, 0, -4, -2, 1, 0, 0, 0, 4, 0, 0, 0, 0, -1, -4, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 1, 3, 0, -2, -1, 0, 2, -2, 0, 3, 0, 0, 0, -2, 0, -2, 0, 0, 0, 3, 0, 0, 0, 0, -4, 0, 0, -1, 0, 0, 2, -1, -4, 0, 2, 0, 0, -2, 0, -4, 1, 0, 0, 0, 0, 0, -1, 0, -4, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, -1, 0, -2, 0, 0, -1, 0, 3, -2, -1, 0, 0, 0, 0, -1, 0, 3, 0, -2, 0, 3, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 4, 0, 1, -2, 0, 8, 1, 0, 1, 0, 0, 0, 1, 0, -4, 0, 0, 3, 1, 0, 0, 0, 0, 3, 0, 0, 1, 0, 0, 3, -4, 0, 0, 0, 0, 0, -2, -1, 6, 3, 0, 0, 0, 0, 0, 3, 0, 3, -1, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, 1, 0, -2, 0, -1, 0, 0, 0, 1, -2, 0, 0, 0, 0, -4, 0, 0, 0, 2, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -3, -2, 0, -2, -6, 0, 0, 1, -1, -1, 0, 0, 0, -2, 0, 3, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 3, 0, 0, 1, 3, 0, -2, 0, 0, -2, 0, 0, 0, 2, 0, -4, 0, -3, 1, 0, 0, 0, 0, 0, 3, 0, 0, 3, 0, 0, 0, 1, -4, 0, 0, -4, 0, 0, -2, 1, 0, 0, 0, 0, -2, 0, 0, 0, 3, 1, 2, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, -2, 0, 0, 2, 0, 0, 3, -1, 0, -4, 0, 0, 0, 6, 0, 4, 0, 0, 0, 3, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 1, 0, -1, 1, 0, 0, 0, 0, 0, -2, 0, -2, 1, 3, 0, 0, 0, 0, -1, 0, 0, 3, 0, 0, 1, 0, -6, 0, 0, 3, 0, 2, 0, -2, 0, 0, 0, 0, 1, 0, -2, 0, 4, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 0, -4, 1, 0, -3, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, -3, 3, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 6, 0, 0, -3, 0, 0, -2, -3, 3, 0, 0, 0, 0, 0, 0, 0, 0, -4, -2, 0, 0, 0, 0, 0, 3, 0, 0, -6, 0, 0, 0, 0, -1, 0, 3, -2, 0, 0, -2, 2, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 6, 3, 0, -2, 6, 3, -8, 0, 0, 0, 0, 0, 2, 0, -2, 3, -2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -2, 1, 0, 0, 8, 0, 0, -1, 0, 0, -2, 0, 0, 0, 3, 0, -1, 0, -2, 3, 0, 0, 0, 0, 0, -4, 0, 0, -2, 0, 0, -3, 0, 1, 0, 0, -1, 0, 0, -1, 0, 1, 0, 0, 0, -4, 0, 0, 0, 0, -2, -3, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -6, 3, 0, -2, 0, 0, 2, 3, 0, -2, 0, 0, 0, -4, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, -2, -1, 0, -3, 0, 0, 0, 0, 3, 4, 0, 0, 0, 0, 0, 1, 0, 4, -2, 0, 0, 0, 0, 0, -4, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, -4, -1, 0, 0, 0, 0, -2, 0, -1, 0, 0, 0, -2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 3, 1, 0, 0, 6, 0, -2, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, -4, -6, 0, 0, 0, 0, -2, 0, 0, 4, 0, 0, -1, 2, 0, 0, -4, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, -2, 0, 0, 0, -2, 0, 0, 0, 0, 4, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 3, 0, -1, 1, 0, -1, -1, 1, 3, 0, 0, 0, 0, 0, 3, 0, -2, -3, -2, 0, 0, 0, 0, 1, 0, 0, 8, 0, 0, 4, 0, 0, 0, 2, 3, 0, 3, 0, 3, 1, 0, 0, 0, 4, 0, 0, 0, 1, -2, 0, 0, 0, 0, 0, -4, 0, 0, -1, 0, 0, 0, -3, 0, 0, 0, 2, 0, 0, 8, -1, 3, 0, 0, 0, 0, 0, 0, 0, 1, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 4, 4, 0, 6, 0, 0, -2, 2, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -2, 0, 0, 1, 0, 0, -1, 0, -2, 0, -2, 0, 0, -4, 0, 1, 3, 0, 0, 0, 0, 0, -2, 0, 0, 1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 2, 0, 0, -2, 0, 0, -4, 0, 0, 0, 0, 0, -4, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 4, 3, 0, 0, -1, 0, 1, 3, 0, 3, 0, 0, 0, 0, 0, 3, 0, 0, 1, -4, 0, 0, 0, 0, -3, 0, 0, -2, 0, 0, 0, -2, 0, 0, -2, 0, 0, -2, 1, -2, -1, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 3, 0, -2, 0, -1, 6, 0, 0, -2, 1, 0, 0, 0, 0, 6, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, -2, 0, 0, -2, -4, 0, -2, 4, -1, 6, 0, 0, 0, -4, 0, 4, 0, 1, -2, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, -3, 0, 1, 0, 2, 0, 0, 0, 0, 0, 0, -2, 0, 3, 0, 0, 0, 0, 0, 0, -1, 0, 0, -2, 0, 0, 1, -2, 4, 0, 0, 3, 0, 0, 6, -2, 0, 0, 0, 0, 2, 0, 0, 0, 0, -4, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -2, -4, 0, 3, 1, 0, 1, 3, 0, 0, 0, 0, 0, -2, 0, -3, 0, 0, -1, 3, 0, 0, 0, 0, 6, 0, 0, -2, 0, 0, -4, 0, 0, 0, -1, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, -3, 0, 0, 3, 4, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 3, 0, 1, 0, 0, 0, 0, -4, 3, 1, 0, 0, 0, 0, 3, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 2, 0, 1, -2, 0, 0, 1, 0, -2, 0, 0, 0, 3, 0, 6, 0, 0, 3, -4, 0, 0, 0, 0, 3, 0, 0, -3, 0, 0, 0, 0, 0, 0, -4, 0, 0, -1, 3, 0, 0, 0, 0, 0, 0, 0, -4, 0, -4, 1, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, -4, 0, 2, -1, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, -2, 2, 0, -4, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, -2, -3, -2, 0, 0, 0, 0, 4, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 3, 0, -4, 4, 0, 0, 0, -1, 0, -3, 0, 1, 4, 0, 0, 0, 0, 0, -2, 0, 0, 1, 0, 0, -2, -2, -2, 0, 0, 0, 0, 0, -2, -4, -2, 0, 0, 0, -2, 0, 0, 0, 3, 4, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 6, 0, -1, -2, 0, 0, 0, 0, 2, 0, 0, 0, -4, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, -3, 0, -1, 0, 3, 0, 0, -8, 0, 2, 0, 0, 0, 0, 0, 0, 3, 0, 0, -4, -2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 8, -3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -4, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 2, 3, 0, -2, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 3, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 3, 0, 0, 0, 0, 0, 3, -3, 3, 1, 0, 0, 0, 0, 0, 0, 0, 6, -4, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -6, 0, 1, 0, 0, -3, -2, 0, 4, 0, 0, 0, -3, 0, -2, 0, -1, -2, 1, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 1, 0, 0, 3, 1, 0, 0, 0, -4, 1, 0, 0, 0, -2, 0, -2, 0, 3, 4, 0, 0, 0, 0, 0, 6, 0, 0, -2, 0, 0, 2, -2, 0, 0, 0, -2, 0, 0, 0, -2, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, -4, 8, 0, 3, 0, 0, 0, 0, 0, -2, 0, 0, -3, 3, 0, 0, 0, 0, -3, 0, 0, -2, 0, 0, 0, -4, -4, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, -3, 0, 6, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 3, 0, 3, 0, 0, -3, 0, 0, 0, -4, 0, 0, 0, 0, -4, 0, 3, 0, -2, 0, 4, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 3, -2, 0, 2, -2, 0, -2, 4, 0, 0, 0, 0, 0, -4, 0, -2, 0, 0, 3, -3, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, -1, -2, 0, 0, 0, 0, 0, 8, 0, 0, 6, 0, 0, 0, 0, 0, 4, 0, 0, 1, 0, 0, -2, 0, 0, 0, -4, 1, 0, 0, -4, 3, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, -4, 0, 0, 6, 0, 0, 3, 0, 6, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 3, -2, 0, 0, -2, 0, 0, 0, 0, 8, -4, 0, 0, 0, 0, 0, 0], "projective_field": [-93, 310, -60, -15, 0, 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, 31, 2, -1, 2, -31], [1, 1, 25, 4, 1, 5, 0], [1, 1, 775, 23, -1, 10, 0]], "char_orbit_index": 23, "prim_orbit_index": 23, "minimal_twist": "775.1.w.a", "char_is_minimal": true, "conrey_index": 61, "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, 0], [-1, 1]], [], [[1, 0], [-1, 1], [1, 2]], [[1, 2]], [], [[-1, 1], [1, 4]], [[1, 0], [-1, 1], [1, 2], [-1, 3]], [[1, 2]], [[1, 2], [-1, 3]], [], [], [], [[1, 0], [-1, 1], [1, 2], [1, 4]], [], [[1, 0], [-1, 1], [1, 2], [-1, 3], [1, 4]], [], [[1, 2], [-1, 3]], [[1, 0], [-1, 3]], [[1, 2], [-1, 3], [1, 4]], [], [], [], [], [[1, 4]], [], [], [[1, 0], [-1, 1], [-1, 1], [1, 2], [-1, 3], [1, 4]], [], [], [[1, 4]], [[2, 0], [-1, 1], [1, 2], [-1, 3], [1, 4]], [], [], [[-1, 1], [-1, 3]], [[1, 2], [-1, 3], [1, 4]], [], [[1, 0], [-1, 1], [-1, 3], [1, 4]], [], [[1, 0], [1, 2], [-1, 3], [1, 4]], [[-1, 1], [-1, 3]], [], [], [], [[1, 4]], [], [[-1, 3], [1, 4]], [], [[1, 0], [1, 2], [-1, 3]], [[1, 0], [1, 4]], [], [], [], [], [], [[1, 0], [-1, 1], [-1, 1], [1, 2], [1, 2], [-1, 3], [2, 4]], [], [], [[-1, 1], [-1, 3]], [], [], [[1, 0], [1, 4]], [[-1, 1], [-1, 3]], [[3, 0], [-1, 0], [-2, 1], [1, 2], [-1, 3], [1, 4]], [], [], [[1, 0], [-1, 3]], [], [], [[-1, 1], [1, 2], [-1, 3], [1, 4]], [[-1, 1], [-1, 1]], [[1, 0], [1, 2], [-1, 3], [1, 4]], [], [], [], [[1, 0], [1, 0], [-1, 1], [1, 2], [-1, 3], [1, 4]], [], [], [], [[1, 0], [-1, 1], [1, 2], [-1, 3], [1, 4]], [[1, 4]], [[-1, 1], [1, 2], [-1, 3], [1, 4]], [], [], [], [], [], [], [], [[1, 0], [1, 4]], [], [], [], [[1, 0], [-1, 3], [2, 4]], [[1, 0], [1, 2]], [], [[-1, 3], [1, 4]], [[1, 0], [-1, 1], [1, 2], [-2, 3], [1, 4]], [], [[1, 0], [-1, 1], [1, 4]]]}