# Stored data for newform 1225.2.b.i, downloaded from the LMFDB on 18 April 2024.
{"label": "1225.2.b.i", "space_label": "1225.2.b", "level": 1225, "weight": 2, "hecke_orbit": 9, "hecke_orbit_code": 36028865771996361, "dim": 4, "is_polredabs": true, "nf_label": "4.0.256.1", "trace_hash": 1179638703597775151, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[2, [2, 0, 1]], [19, [-6, 1]], [31, [18, 12, 1]]], "qexp_display": "q+\\zeta_{8}^{2}q^{2}+(\\zeta_{8}+\\zeta_{8}^{2})q^{3}+(-2-\\zeta_{8}^{3})q^{6}+\\cdots", "char_order": 2, "char_parity": 1, "char_degree": 1, "char_conductor": 5, "char_orbit_label": "b", "char_is_real": true, "Nk2": 4900, "analytic_conductor": 9.781674247606848, "hecke_ring_index": 2, "level_radical": 35, "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": "0.528", "prec": 17}, "analytic_rank_proved": true, "char_values": [1225, 2, [1177, 101], [1, 2]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 2, "level_primes": [5, 7], "conrey_indexes": [99], "field_disc": 256, "field_disc_factorization": [[2, 8]], "field_poly": [1, 0, 0, 0, 1], "hecke_ring_index_factorization": [[2, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.027", "prec": 17}, {"__RealLiteral__": 0, "data": "3.755", "prec": 17}, {"__RealLiteral__": 0, "data": "0.130", "prec": 17}, {"__RealLiteral__": 0, "data": "68.804", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1736.913", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "1.2.3.c2", "trace_display": [0, 0, 0, 0], "traces": [0, 4, 0, 0, 0, 0, -8, 0, 0, 0, 0, -12, 0, 0, 0, 0, -16, 0, 0, 24, 0, 0, 0, 0, -16, 0, 8, 0, 0, 12, 0, -24, 0, 0, -24, 0, 0, 0, 0, -4, 0, 8, 0, 0, 0, 0, -8, 0, 0, 0, 0, -28, 0, 0, -8, 0, 0, 0, 0, 8, 0, 0, 0, 0, -32, 0, 40, 0, 0, 16, 0, -24, 0, 0, 24, 0, 0, 0, 0, 28, 0, -4, 0, 0, 0, 0, 0, 0, 0, -32, 0, 0, 0, 0, 24, 0, 0, 0, 0, 32, 0, 24, 0, 0, 16, 0, -24, 0, 0, -20, 0, 32, 0, 0, -48, 0, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, 8, 0, -32, 0, 0, -24, 0, -48, 0, 0, 48, 0, 12, 0, 0, 0, 0, -48, 0, 0, 48, 0, 4, 0, 0, 0, 0, 0, 0, 0, -24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 8, 0, 48, 0, 0, 24, 0, 24, 0, 0, -16, 0, 24, 0, 0, 0, 0, -12, 0, 0, -24, 0, 0, 0, 0, -24, 0, -8, 0, 0, 0, 0, 24, 0, 0, -72, 0, 36, 0, 0, -48, 0, -16, 0, 0, -48, 0, 12, 0, 0, 0, 0, 40, 0, 0, -24, 0, 0, 0, 0, 48, 0, 0, 0, 0, 36, 0, -48, 0, 0, 0, 0, 8, 0, 0, 0, 0, 16, 0, 0, 24, 0, 0, 0, 0, 0, 0, 64, 0, 0, 80, 0, 0, 0, 0, -48, 0, 48, 0, 0, 0, 0, 0, 0, 0, -48, 0, -36, 0, 0, 0, 0, 24, 0, 0, -8, 0, 12, 0, 0, 0, 0, 48, 0, 0, 80, 0, 0, 0, 0, -96, 0, 16, 0, 0, -36, 0, 40, 0, 0, -16, 0, 0, 0, 0, 28, 0, -72, 0, 0, 0, 0, 24, 0, 0, 0, 0, -8, 0, 0, 24, 0, 0, 0, 0, 16, 0, 24, 0, 0, 0, 0, -24, 0, 0, 24, 0, 20, 0, 0, -40, 0, 0, 0, 0, 0, 0, 68, 0, 0, 0, 0, 16, 0, 0, 48, 0, 0, 0, 0, 88, 0, 48, 0, 0, -8, 0, 8, 0, 0, 64, 0, 0, 0, 0, 84, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 36, 0, 0, 0, 0, 0, 0, 0, -24, 0, -48, 0, 0, -96, 0, 0, 0, 0, 24, 0, -76, 0, 0, -48, 0, 64, 0, 0, 44, 0, -36, 0, 0, 0, 0, 0, 0, 0, -48, 0, 0, 0, 0, 0, 0, -120, 0, 0, 108, 0, 24, 0, 0, -72, 0, -96, 0, 0, -20, 0, -80, 0, 0, -48, 0, -16, 0, 0, 0, 0, -88, 0, 0, -104, 0, 0, 0, 0, 64, 0, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, -36, 0, 0, 48, 0, 96, 0, 0, -12, 0, 44, 0, 0, 0, 0, -72, 0, 0, -16, 0, 0, 0, 0, -48, 0, 0, 0, 0, -12, 0, 8, 0, 0, 0, 0, 128, 0, 0, -60, 0, -48, 0, 0, 64, 0, -48, 0, 0, 0, 0, -20, 0, 0, 0, 0, 0, 0, 0, 32, 0, 72, 0, 0, 120, 0, 0, 0, 0, 24, 0, 148, 0, 0, 0, 0, 88, 0, 0, -48, 0, -104, 0, 0, 0, 0, 0, 0, 0, -64, 0, 0, 0, 0, -96, 0, 72, 0, 0, -144, 0, -40, 0, 0, 8, 0, 0, 0, 0, 60, 0, -24, 0, 0, 0, 0, -96, 0, 0, 0, 0, -60, 0, 0, -56, 0, 0, 0, 0, 96, 0, -32, 0, 0, 16, 0, -120, 0, 0, 80, 0, -68, 0, 0, 32, 0, 0, 0, 0, 32, 0, -48, 0, 0, 0, 0, -144, 0, 0, -72, 0, 0, 0, 0, 40, 0, -32, 0, 0, -12, 0, 48, 0, 0, 0, 0, -32, 0, 0, -108, 0, 32, 0, 0, 24, 0, 0, 0, 0, 0, 0, -60, 0, 0, 0, 0, 0, 0, 0, 24, 0, -48, 0, 0, 40, 0, 16, 0, 0, -64, 0, 84, 0, 0, 96, 0, -120, 0, 0, -68, 0, -96, 0, 0, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, -144, 0, 0, 84, 0, 8, 0, 0, 152, 0, 0, 0, 0, -52, 0, -24, 0, 0, 48, 0, 48, 0, 0, 0, 0, 84, 0, 0, 120, 0, 0, 0, 0, -128, 0, 0, 0, 0, 0, 0, 48, 0, 0, -24, 0, -120, 0, 0, -32, 0, -48, 0, 0, 48, 0, 104, 0, 0, 0, 0, 40, 0, 0, 152, 0, 0, 0, 0, 8, 0, 0, 0, 0, 60, 0, 0, 0, 0, 0, 0, -120, 0, 0, 36, 0, -48, 0, 0, -104, 0, 112, 0, 0, 0, 0, -60, 0, 0, 48, 0, 0, 0, 0, 120, 0, 144, 0, 0, -120, 0, 0, 0, 0, -144, 0, 48, 0, 0, 0, 0, 48, 0, 0, 52, 0, -24, 0, 0, 0, 0, -96, 0, 0, 48, 0, 0, 0, 0, 0, 0, 96, 0, 0, -180, 0, 72, 0, 0, -48, 0, 0, 0, 0, 20, 0, 144, 0, 0, 0, 0, 16, 0, 0, 0, 0, 108, 0, 0, -112, 0, 0, 0, 0, -168, 0, -72, 0, 0, 80, 0, -56, 0, 0, -96, 0, 0, 0, 0, 24, 0, 0, 0, 0, 52, 0, 28, 0, 0, 0, 0, 144, 0, 0, 168, 0, 0, 0, 0, 72, 0, 96, 0, 0, -132, 0, -48, 0, 0, -32, 0, -32, 0, 0, 48, 0, 56, 0, 0, 0, 0, 0, 0, 0, 0, 0, 92, 0, 0, 0, 0, 0, 0, 0, -168, 0, 120, 0, 0, 168, 0, 0, 0, 0, 96, 0, 0, 0, 0, 16, 0, -40, 0, 0, -48, 0, -56, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, -24, 0, 0, 68, 0, -48, 0, 0, -64, 0, 48, 0, 0, -120, 0, 120, 0, 0, 128, 0, -48, 0, 0, 0, 0, -84, 0, 0, -24, 0, 0, 0, 0, 24, 0, 16, 0, 0, 0, 0, 48, 0, 0, 16, 0, -4, 0, 0, 120, 0, 0, 0, 0, -180, 0, 132, 0, 0, 0, 0, 88, 0, 0, -48, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 96, 0, 0, 0, 0, 24, 0, 0, -192, 0, -96, 0, 0, -48, 0, 0, 0, 0, 0, 0, 164, 0, 0, -64, 0, 0, 0, 0, 160, 0, -168, 0, 0, -112, 0, 0, 0, 0, 16, 0, 48, 0, 0, 0, 0, -192, 0, 0, -20, 0, 52, 0, 0, 0, 0, 96, 0, 0, -56, 0, 0, 0, 0, 48, 0, 120, 0, 0, 64, 0, 0, 0, 0, -72, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 72, 0, 0, 0, 0, 20, 0, 0, 144, 0, 0, 0, 0, -48, 0, -40, 0, 0, 0, 0, 24, 0, 0, 120, 0, 20, 0, 0, 40, 0, 0, 0, 0, 60, 0, 124, 0, 0, 0, 0, -64, 0, 0, -24, 0, 0, 0, 0, -56, 0, -192, 0, 0, -24, 0, -176, 0, 0, 32, 0, 192, 0, 0, 96, 0, -24, 0, 0, -8, 0, 0, 0, 0, 0, 0, -144, 0, 0, 0, 0, 0, 0, 0, 24, 0, -48, 0, 0, 240, 0, -32, 0, 0, 184, 0, 132, 0, 0, -112, 0, -72, 0, 0, 36, 0, -120, 0, 0, 0, 0, 0, 0, 0, -144, 0, 0, 0, 0, 0, 0, -72, 0, 0, -144, 0, 0, 0, 0, -48, 0, 16, 0, 0, 120, 0, 32, 0, 0, 48, 0, -96, 0, 0, 0, 0, 96, 0, 0, 0, 0, 0, 0, 0, 24, 0, -96, 0, 0, 0, 0, 40, 0, 0, 88, 0, -132, 0, 0, -216, 0, 48, 0, 0, -204, 0, -32, 0, 0, 0, 0, 48, 0, 0, -144, 0, 0, 0, 0, -120, 0, 0, 0, 0, -96, 0, -168, 0, 0, 0, 0, -112, 0, 0, 60, 0, 88, 0, 0, 184, 0, 0, 0, 0, 0, 0, -8, 0, 0, -48, 0, 0, 0, 0, 160, 0, -24, 0, 0, -24, 0, 0, 0, 0, 24, 0, 100, 0, 0, 0, 0, 144, 0, 0, -132, 0, 0, 0, 0, 0, 0, -80, 0, 0, -56, 0, 0, 0, 0, 128, 0, 192, 0, 0, 24, 0, -24, 0, 0, -24, 0, 0, 0, 0, 36, 0, 48, 0, 0, 0, 0, 168, 0, 0, 0, 0, 168, 0, 0, -64, 0, 0, 0, 0, 72, 0, 176, 0, 0, 32, 0, 168, 0, 0, -112, 0, -72, 0, 0, 8, 0, 0, 0, 0, 44, 0, 36, 0, 0, 0, 0, 72, 0, 0, -216, 0, 0, 0, 0, 0, 0, 176, 0, 0, 132, 0, 168, 0, 0, 0, 0, -152, 0, 0, 124, 0, 96, 0, 0, 48, 0, 0, 0, 0, 0, 0, -96, 0, 0, 0, 0, 0, 0, 0, -192, 0, -96, 0, 0, -56, 0, 128, 0, 0, -24, 0, -120, 0, 0, 0, 0, -120, 0, 0, 32, 0, -36, 0, 0, 0, 0, 0, 0, 0, 136, 0, 0, 0, 0, 0, 0, -56, 0, 0, -48, 0, -8, 0, 0, 72, 0, 16, 0, 0, -156, 0, 72, 0, 0, -128, 0, 48, 0, 0, 0, 0, -16, 0, 0, 216, 0, 0, 0, 0, 40, 0, -40, 0, 0, 0, 0, 144, 0, 0, -144, 0, 96, 0, 0, 72, 0, -96, 0, 0, 108, 0, 32, 0, 0, 0, 0, -160, 0, 0, 144, 0, 0, 0, 0, 0, 0, 0, 0, 0, -176, 0, 16, 0, 0, 0, 0, -72, 0, 0, -36, 0, -72, 0, 0, 136, 0, -192, 0, 0, 0, 0, -108, 0, 0, -64, 0, 0, 0, 0, -120, 0, -160, 0, 0, 72, 0, 0, 0, 0, -48, 0, -76, 0, 0, 0, 0, 136, 0, 0, -200, 0, -192, 0, 0, 0, 0, 0, 0, 0, 96, 0, 0, 0, 0, 128, 0, 96, 0, 0, -36, 0, -72, 0, 0, 48, 0, 0, 0, 0, 192, 0, -120, 0, 0, 0, 0, -104, 0, 0, 0, 0, -60, 0, 0, 64, 0, 0, 0, 0, -48, 0, 120, 0, 0, 80, 0, -144, 0, 0, 120, 0, 12, 0, 0, -96, 0, 0, 0, 0, 296, 0, 96, 0, 0, 0, 0, 48, 0, 0, 64, 0, 0, 0, 0, -96, 0, -128, 0, 0, -36, 0, -144, 0, 0, -240, 0, 144, 0, 0, 144, 0, -16, 0, 0, -88, 0, 0, 0, 0, 0, 0, -164, 0, 0, 0, 0, 0, 0, 0, -40, 0, -56, 0, 0, -216, 0, -144, 0, 0, -168, 0, -116, 0, 0, 0, 0, 0, 0, 0, 24, 0, 132, 0, 0, 0, 0, 0, 0, 0, 232, 0, 0, 0, 0, 0, 0, 0, 0, 0, 156, 0, -32, 0, 0, 240, 0, -96, 0, 0, -120, 0, 48, 0, 0, -32, 0, -80, 0, 0, 0, 0, -84, 0, 0, 88, 0, 0, 0, 0, 72, 0, 192, 0, 0, 0, 0, -160, 0, 0, 136, 0, -48, 0, 0, -24, 0, -208, 0, 0, 0, 0, 60, 0, 0, 0, 0, -232, 0, 0, 0, 0, 0, 0, 0, -104, 0, 0, 0, 0, 144, 0, 96, 0, 0, 0, 0, 96, 0, 0, -132, 0, -120, 0, 0, -240, 0, -96, 0, 0, 0, 0, -128, 0, 0, 64, 0, 0, 0, 0, -184, 0, 144, 0, 0, 208, 0, 0, 0, 0, -24, 0, 72, 0, 0, 0, 0, 120, 0, 0, 24, 0, -48, 0, 0, 0, 0, 96, 0, 0, -32, 0, 0, 0, 0, 192, 0, -128, 0, 0, 128, 0, 72, 0, 0, 72, 0, 0, 0, 0, 20, 0], "weight_parity": 1, "has_non_self_twist": 1, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": true, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 5, 2, 1, 2, 0]], "char_orbit_index": 2, "prim_orbit_index": 2, "minimal_twist": "245.2.a.e", "char_is_minimal": false, "conrey_index": 99, "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, 1, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-2, 0, 0, -1], [0, 0, 0, 0], [0, 0, 2, 0], [0, 0, 0, -2], [0, 0, 0, 0], [-3, 0, 0, -2], [0, 0, 0, 0], [0, 3, -1, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-4, 0, 0, 0], [0, 1, 3, 0], [0, -4, 0, 0], [6, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -4, -3, 0], [0, -6, 1, 0], [-4, 0, 0, -2], [0, 0, 0, 0], [2, 0, 0, -3], [0, -1, 1, 0], [0, 0, 0, 0], [3, 0, 0, -4], [0, 0, 0, 0], [-6, 0, 0, 3], [0, 0, 0, 0], [0, -7, -5, 0], [-6, 0, 0, -1], [0, 0, 0, 0], [0, 0, 0, 0], [0, -2, -3, 0], [0, 0, 6, 0], [-1, 0, 0, -2], [0, 0, 0, 0], [2, 0, 0, -3], [0, 0, 0, 0], [0, -2, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-2, 0, 0, 6], [0, 3, -3, 0], [0, -4, -4, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-7, 0, 0, -4], [0, 0, 0, 0], [0, 0, 3, 0], [-2, 0, 0, 1], [0, 0, 0, 0], [0, 0, 0, 0], [0, 6, 6, 0], [0, -8, 3, 0], [2, 0, 0, 3], [0, 0, 0, 0], [0, 0, 0, -2], [0, 6, -6, 0], [0, 0, 0, 0], [-8, 0, 0, 0], [0, 0, 0, 0], [10, 0, 0, 7], [0, -4, 3, 0], [0, 0, 0, 0], [4, 0, 0, 5], [0, 0, 0, 0], [-6, 0, 0, -2], [0, -8, 0, 0], [0, 0, 6, 0], [6, 0, 0, 2], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -4, -1, 0], [7, 0, 0, 6], [0, 0, 0, 0], [-1, 0, 0, -6], [0, -6, 2, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 2], [0, -5, -1, 0], [0, -8, -6, 0], [-8, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, -3, 0], [6, 0, 0, -3], [0, 0, 0, 0], [0, 0, 0, 0], [0, -9, 3, 0], [0, 0, 0, 0], [8, 0, 0, 6], [0, 0, 0, 0]]}