# Stored data for newform 605.2.g.i, downloaded from the LMFDB on 23 April 2024.
{"label": "605.2.g.i", "space_label": "605.2.g", "level": 605, "weight": 2, "hecke_orbit": 9, "hecke_orbit_code": 36029209369379421, "dim": 8, "is_polredabs": true, "nf_label": "8.0.324000000.3", "trace_hash": 540533559665697188, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[2, [81, 0, 27, 0, 9, 0, 3, 0, 1]], [3, [1, -1, 1, -1, 1]]], "qexp_display": "q+\\beta _{7}q^{2}-\\beta _{6}q^{3}+\\beta _{4}q^{4}+(1+\\beta _{2}+\\cdots)q^{5}+\\cdots", "char_order": 5, "char_parity": 1, "char_degree": 4, "char_conductor": 11, "char_orbit_label": "g", "char_is_real": false, "Nk2": 2420, "analytic_conductor": 4.830949322287463, "hecke_ring_index": 1, "level_radical": 55, "field_poly_is_cyclotomic": false, "field_poly_root_of_unity": 0, "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": "0.513", "prec": 17}, "analytic_rank_proved": true, "char_values": [605, 5, [122, 486], [5, 1]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 8, "level_primes": [5, 11], "conrey_indexes": [81, 251, 366, 511], "field_disc": 324000000, "field_disc_factorization": [[2, 8], [3, 4], [5, 6]], "field_poly": [81, 0, 27, 0, 9, 0, 3, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.078", "prec": 17}, {"__RealLiteral__": 0, "data": "8.279", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "866.913", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "132825.350", "prec": 34}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "1.2.3.c5", "trace_display": [0, 2, 2, 0], "traces": [0, 8, 0, 2, -2, 2, 0, 0, 0, 4, 0, 0, -8, 0, 6, -2, 10, 0, 0, 0, 2, 0, 0, 0, 0, -2, -12, -10, 0, 0, 0, 16, 0, 0, -96, 0, 4, 16, 12, 0, 0, 0, -6, 0, 0, 16, 0, -18, -10, 8, 0, 0, 0, -12, 0, 0, 24, 0, 0, 24, -2, 0, 0, 0, -2, 0, 0, -40, 0, 0, -6, 24, 0, 0, 0, 2, 0, 0, -48, 0, -10, -2, -42, 0, 0, 0, -30, 0, 0, 24, 0, 12, 0, -16, 0, 0, 0, 20, 0, 0, 8, 0, -24, 8, 12, 0, 0, 0, -10, 0, 0, 64, 0, 12, -12, 0, 0, 0, 0, -24, 0, 0, 120, 0, 16, 2, -12, 0, 0, 0, 12, 0, 0, 48, 0, 10, -24, -36, 0, 0, 0, 18, 0, 0, 80, 0, 0, -8, 16, 0, 0, 0, -12, 0, 0, 64, 0, -8, 36, 12, 0, 0, 0, 38, 0, 0, 48, 0, 6, 2, -24, 0, 0, 0, 0, 0, 0, 96, 0, 36, -4, -22, 0, 0, 0, -16, 0, 0, 72, 0, -12, 12, 2, 0, 0, 0, 8, 0, 0, -112, 0, -10, 6, 0, 0, 0, 0, 0, 0, 0, -24, 0, -12, -24, -6, 0, 0, 0, -6, 0, 0, -192, 0, 38, -18, 4, 0, 0, 0, -14, 0, 0, 0, 0, 24, 18, 24, 0, 0, 0, 10, 0, 0, -128, 0, -8, 42, 24, 0, 0, 0, 0, 0, 0, 24, 0, -38, -24, 30, 0, 0, 0, 12, 0, 0, -48, 0, 6, 10, 30, 0, 0, 0, -12, 0, 0, 0, 0, -48, -32, 6, 0, 0, 0, 24, 0, 0, -168, 0, -62, 0, -20, 0, 0, 0, -24, 0, 0, -264, 0, 2, 30, 72, 0, 0, 0, -48, 0, 0, 32, 0, 12, -12, -20, 0, 0, 0, 12, 0, 0, -8, 0, 0, -48, -2, 0, 0, 0, 42, 0, 0, -272, 0, -32, 18, -10, 0, 0, 0, -12, 0, 0, 96, 0, 30, 0, -36, 0, 0, 0, 6, 0, 0, 192, 0, -24, -6, 24, 0, 0, 0, 14, 0, 0, -48, 0, 30, -34, 0, 0, 0, 0, -16, 0, 0, 8, 0, 0, 30, 68, 0, 0, 0, -48, 0, 0, -48, 0, 20, -6, -12, 0, 0, 0, 36, 0, 0, 160, 0, 12, 10, -54, 0, 0, 0, 2, 0, 0, -96, 0, 42, 36, 8, 0, 0, 0, 36, 0, 0, 144, 0, 34, 0, 36, 0, 0, 0, 30, 0, 0, -120, 0, 50, -64, -48, 0, 0, 0, 0, 0, 0, 64, 0, 30, -16, 6, 0, 0, 0, 30, 0, 0, -48, 0, -66, -12, 12, 0, 0, 0, 0, 0, 0, 328, 0, 16, 12, -6, 0, 0, 0, 8, 0, 0, 144, 0, -24, 24, -12, 0, 0, 0, 66, 0, 0, 80, 0, 40, 30, -38, 0, 0, 0, 0, 0, 0, 320, 0, 12, 76, 2, 0, 0, 0, 12, 0, 0, 8, 0, -30, 24, 0, 0, 0, 0, -8, 0, 0, 192, 0, -12, -30, 0, 0, 0, 0, -84, 0, 0, -184, 0, -48, -12, -84, 0, 0, 0, -36, 0, 0, -40, 0, 48, 22, -72, 0, 0, 0, -36, 0, 0, 0, 0, -36, -36, 16, 0, 0, 0, -60, 0, 0, -96, 0, 18, -12, 18, 0, 0, 0, 12, 0, 0, 48, 0, 0, 4, 40, 0, 0, 0, 12, 0, 0, 0, 0, 24, -42, -8, 0, 0, 0, -80, 0, 0, -96, 0, -28, 0, -60, 0, 0, 0, -20, 0, 0, 24, 0, -36, 0, 30, 0, 0, 0, 36, 0, 0, -288, 0, -40, -16, 0, 0, 0, 0, -2, 0, 0, 32, 0, 12, -56, -36, 0, 0, 0, 12, 0, 0, 192, 0, -60, 6, 62, 0, 0, 0, -66, 0, 0, 48, 0, 38, 60, 6, 0, 0, 0, 54, 0, 0, 296, 0, -48, 12, 12, 0, 0, 0, -38, 0, 0, -72, 0, -36, -10, 2, 0, 0, 0, 24, 0, 0, -168, 0, 36, -66, 14, 0, 0, 0, 20, 0, 0, -168, 0, 0, 168, -120, 0, 0, 0, -60, 0, 0, 72, 0, -6, -24, -50, 0, 0, 0, 0, 0, 0, -144, 0, 12, -12, 20, 0, 0, 0, -22, 0, 0, 8, 0, -26, 0, 120, 0, 0, 0, 8, 0, 0, -336, 0, -16, -24, 36, 0, 0, 0, 48, 0, 0, -24, 0, 28, 90, 0, 0, 0, 0, 4, 0, 0, -48, 0, 6, 6, 12, 0, 0, 0, 38, 0, 0, -96, 0, 0, 60, 16, 0, 0, 0, 84, 0, 0, 0, 0, -40, 8, -12, 0, 0, 0, -36, 0, 0, 240, 0, -12, 28, 24, 0, 0, 0, 12, 0, 0, 40, 0, 96, -30, -6, 0, 0, 0, 0, 0, 0, 152, 0, 60, -18, -24, 0, 0, 0, -34, 0, 0, 288, 0, 0, -58, 12, 0, 0, 0, 48, 0, 0, -320, 0, 84, -6, 58, 0, 0, 0, -2, 0, 0, -240, 0, 24, 0, -24, 0, 0, 0, 6, 0, 0, 112, 0, -42, -132, -42, 0, 0, 0, 62, 0, 0, 0, 0, 6, -40, 0, 0, 0, 0, 96, 0, 0, -168, 0, 112, 48, 24, 0, 0, 0, 6, 0, 0, -152, 0, -66, -36, 42, 0, 0, 0, 4, 0, 0, 120, 0, 22, -72, -34, 0, 0, 0, -12, 0, 0, 288, 0, -14, -12, 120, 0, 0, 0, 42, 0, 0, -64, 0, -16, 0, -36, 0, 0, 0, -12, 0, 0, 96, 0, -30, 20, 18, 0, 0, 0, -120, 0, 0, -96, 0, 0, 12, -12, 0, 0, 0, -12, 0, 0, 144, 0, -2, -66, 96, 0, 0, 0, 0, 0, 0, -192, 0, 0, 32, 48, 0, 0, 0, 48, 0, 0, 32, 0, -84, 6, -42, 0, 0, 0, 24, 0, 0, -16, 0, -68, -72, -28, 0, 0, 0, 80, 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, 11, 2, -1, 2, 0], [1, 3, 11, 3, 1, 5, 0], [1, 3, 11, 4, -1, 10, 0]], "char_orbit_index": 7, "prim_orbit_index": 3, "minimal_twist": "605.2.a.e", "char_is_minimal": false, "conrey_index": 81, "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, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, -1, 0], [0, 0, 0, 0, 1, 0, 0, 0], [1, 0, 1, 0, 1, 0, 1, 0], [0, 0, 0, -1, 0, 0, 0, 0], [0, 1, 0, 1, 0, 1, 0, 1], [0, -1, 0, 0, 0, 0, 0, 0], [0, 0, -2, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, -1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 2], [0, 0, 0, 0, 0, 0, -3, 0], [0, 0, 0, 0, 1, 0, 0, 0], [5, 0, 5, 0, 5, 0, 5, 0], [0, 0, 0, -4, 0, 0, 0, 0], [0, 2, 0, 2, 0, 2, 0, 2], [0, -2, 0, 0, 0, 0, 0, 0], [0, 0, -1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 6, 0, 0, 0], [-5, 0, -5, 0, -5, 0, -5, 0], [0, 0, 0, -1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0], [0, 0, -8, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, -3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-12, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, -2, 0], [0, 0, 0, 0, -8, 0, 0, 0], [6, 0, 6, 0, 6, 0, 6, 0], [0, 0, 0, -2, 0, 0, 0, 0], [0, -1, 0, -1, 0, -1, 0, -1], [0, 7, 0, 0, 0, 0, 0, 0], [0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 5, 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, 0, 0, 0, 0, 0, 9, 0], [0, 0, 0, 0, 5, 0, 0, 0], [4, 0, 4, 0, 4, 0, 4, 0], [0, 0, 0, 1, 0, 0, 0, 0], [0, -4, 0, -4, 0, -4, 0, -4], [0, 2, 0, 0, 0, 0, 0, 0], [0, 0, 6, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 5, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [3, 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, -12, 0, 0, 0], [-1, 0, -1, 0, -1, 0, -1, 0], [0, 0, 0, 5, 0, 0, 0, 0], [0, 8, 0, 8, 0, 8, 0, 8], [0, 2, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, -2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-5, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, -4], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 3, 0, 0, 0], [12, 0, 12, 0, 12, 0, 12, 0], [0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -8, 0, 0, 0, 0, 0, 0], [0, 0, -1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, -2, 0, 0], [0, 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, 5, 0], [0, 0, 0, 0, 1, 0, 0, 0], [-21, 0, -21, 0, -21, 0, -21, 0], [0, 0, 0, 2, 0, 0, 0, 0], [0, -1, 0, -1, 0, -1, 0, -1], [0, 4, 0, 0, 0, 0, 0, 0], [0, 0, 15, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [3, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 2], [0, 0, 0, 0, 0, 0, -6, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-8, 0, -8, 0, -8, 0, -8, 0], [0, 0, 0, 9, 0, 0, 0, 0], [0, -2, 0, -2, 0, -2, 0, -2], [0, 3, 0, 0, 0, 0, 0, 0], [0, 0, -10, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, -4, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0]]}