# Stored data for newform 578.2.c.e, downloaded from the LMFDB on 19 April 2024. {"label": "578.2.c.e", "space_label": "578.2.c", "level": 578, "weight": 2, "hecke_orbit": 5, "hecke_orbit_code": 18014535981990466, "dim": 4, "is_polredabs": true, "nf_label": "4.0.256.1", "trace_hash": 1079658691890994427, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[3, [16, 0, 0, 0, 1]]], "qexp_display": "q-\\zeta_{8}^{2}q^{2}+\\zeta_{8}q^{3}-q^{4}-\\zeta_{8}^{3}q^{6}+\\cdots", "char_order": 4, "char_parity": 1, "char_degree": 2, "char_conductor": 17, "char_orbit_label": "c", "char_is_real": false, "Nk2": 2312, "analytic_conductor": 4.615353236830006, "hecke_ring_index": 4, "level_radical": 34, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 8, "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": "0.761", "prec": 17}, "analytic_rank_proved": true, "char_values": [578, 4, [3], [1]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 4, "level_primes": [2, 17], "conrey_indexes": [251, 327], "field_disc": 256, "field_disc_factorization": [[2, 8]], "field_poly": [1, 0, 0, 0, 1], "hecke_ring_index_factorization": [[2, 2]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.822", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "126.213", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "5280.242", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "1.2.3.c4", "trace_display": [0, 0, 0, 0], "traces": [0, 4, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 4, 0, 4, 0, 0, -32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -48, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -20, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 32, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 44, 0, 0, 32, 0, 32, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, 0, -36, 0, 0, 72, 0, -64, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 48, 0, 0, 0, 0, 0, 0, 0, 0, 48, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -24, 0, 0, -16, 0, -96, 0, 0, -56, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -36, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -32, 0, 0, 32, 0, 0, 0, 0, 96, 0, 0, 0, 0, 0, 0, 0, 0, 20, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, -64, 0, 0, 0, 0, 32, 0, 0, 20, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, -64, 0, 96, 0, 0, -100, 0, 0, 0, 0, 0, 0, 0, 0, 96, 0, 0, -64, 0, 4, 0, 0, -64, 0, 0, 0, 0, 0, 0, 0, 0, -32, 0, 0, 32, 0, 64, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, -24, 0, 0, 0, 0, 0, 0, 0, 0, 64, 0, 0, 0, 0, 80, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -44, 0, 0, -128, 0, 0, 0, 0, 0, 0, 0, 0, -32, 0, 0, 48, 0, -96, 0, 0, -32, 0, 0, 0, 0, 0, 0, 0, 0, -24, 0, 0, -24, 0, 48, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -88, 0, 0, 0, 0, 64, 0, 0, 0, 0, 0, 0, 0, 0, -32, 0, 0, 0, 0, 36, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -72, 0, 0, -96, 0, -40, 0, 0, 64, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, -24, 0, 0, 0, 0, 96, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 36, 0, -96, 0, 0, -32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 56, 0, 0, 0, 0, 64, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 80, 0, -24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, -48, 0, -32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 120, 0, -32, 0, 0, -24, 0, 0, 0, 0, 0, 0, 0, 0, 64, 0, 0, 96, 0, -48, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, -24, 0, 0, 0, 0, 0, 0, 0, 0, 120, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 96, 0, 0, 56, 0, 80, 0, 0, 112, 0, 0, 0, 0, 0, 0, 0, 0, -96, 0, 0, 96, 0, 24, 0, 0, 96, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 56, 0, 0, 96, 0, 0, 0, 0, 0, 0, 0, 0, -100, 0, 0, 56, 0, 0, 0, 0, -80, 0, 0, 0, 0, 0, 0, 0, 0, -48, 0, 0, 0, 0, -192, 0, 0, 40, 0, 0, 0, 0, 0, 0, 0, 0, 48, 0, 0, -64, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 36, 0, 0, -224, 0, 48, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 96, 0, 0, 0, 0, 104, 0, 0, -72, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -96, 0, 0, 0, 0, 0, 0, 0, 0, -32, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -32, 0, 0, 0, 0, 96, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -24, 0, 0, -96, 0, -96, 0, 0, -56, 0, 0, 0, 0, 0, 0, 0, 0, -120, 0, 0, 0, 0, 0, 0, 0, -48, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -128, 0, -20, 0, 0, -48, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -128, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 40, 0, 0, 8, 0, -16, 0, 0, 64, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -112, 0, 0, 0, 0, -64, 0, 0, 0, 0, 0, 0, 0, 0, -192, 0, 0, 8, 0, 64, 0, 0, -64, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -64, 0, 0, 0, 0, -32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -20, 0, 144, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -104, 0, 0, 96, 0, 224, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, 0, 144, 0, 0, 48, 0, 8, 0, 0, -272, 0, 0, 0, 0, 0, 0, 0, 0, 64, 0, 0, 96, 0, -120, 0, 0, -96, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 100, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, 0, 0, 0, 48, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 64, 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, 17, 2, 1, 2, 0], [1, 2, 17, 3, 1, 4, 0]], "char_orbit_index": 3, "prim_orbit_index": 3, "minimal_twist": "34.2.a.a", "char_is_minimal": false, "conrey_index": 251, "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], [1, 0, 0, 0], [0, 0, -1, 0], [0, 1, 0, 0], [-1, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, -1], [0, 0, 0, 2], [0, 0, 1, 0], [0, 0, 1, 0], [0, 0, 0, 0], [0, 0, 0, 3], [0, -1, 0, 0], [-2, 0, 0, 0], [0, 2, 0, 0], [0, 0, 0, 0], [1, 0, 0, 0], [0, 0, 0, 0], [1, 0, 0, 0], [0, 0, 4, 0], [0, 0, 0, 0], [-8, 0, 0, 0], [0, 3, 0, 0], [0, 0, 0, 0], [0, 0, 0, 1], [0, 0, -5, 0], [0, 0, 2, 0], [0, 0, 0, -2], [0, 0, 0, -2], [0, 0, 0, 0], [0, 0, 0, 0], [0, 2, 0, 0], [0, 0, -1, 0], [-12, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, -1, 0], [0, 2, 0, 0], [4, 0, 0, 0], [0, -2, 0, 0], [0, 0, 0, 0], [0, 0, 0, -3], [0, 0, 8, 0], [0, 0, 8, 0], [0, 0, 0, -3], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 1, 0, 0], [0, 0, -9, 0], [-5, 0, 0, 0], [0, 0, 0, 0], [2, 0, 0, 0], [0, 0, 6, 0], [0, -2, 0, 0], [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, 0, 2], [0, 0, 0, -2], [0, -2, 0, 0], [-1, 0, 0, 0], [0, 0, 0, 0], [0, 0, 12, 0], [8, 0, 0, 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, -2], [0, 0, 0, -5], [0, 0, -4, 0], [0, 0, -24, 0], [0, 0, 0, 2], [0, 0, 0, 4], [0, 0, 0, 0], [11, 0, 0, 0], [0, -3, 0, 0], [0, 0, 0, 0], [8, 0, 0, 0], [0, 0, 0, 0], [8, 0, 0, 0], [0, 0, 0, 0], [0, -3, 0, 0], [6, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, -4], [0, 0, 0, 0], [0, 0, 8, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, -1], [0, 7, 0, 0], [-9, 0, 0, 0], [0, -3, 0, 0], [0, 0, 5, 0]]}