# Stored data for newform 325.2.m.b, downloaded from the LMFDB on 07 May 2024. {"label": "325.2.m.b", "space_label": "325.2.m", "level": 325, "weight": 2, "hecke_orbit": 2, "hecke_orbit_code": 4504424294646085, "dim": 8, "is_polredabs": true, "nf_label": "8.0.22581504.2", "trace_hash": 775522680313230195, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[2, [1, -4, 19, 8, 16, 2, 7, 2, 1]]], "qexp_display": "q+(1-\\beta _{1}-\\beta _{3}-\\beta _{6})q^{2}+(2-\\beta _{3}-\\beta _{4}+\\cdots)q^{3}+\\cdots", "char_order": 6, "char_parity": 1, "char_degree": 2, "char_conductor": 65, "char_orbit_label": "m", "char_is_real": false, "Nk2": 1300, "analytic_conductor": 2.5951380656916125, "hecke_ring_index": 1, "level_radical": 65, "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": "0.184", "prec": 17}, "analytic_rank_proved": true, "char_values": [325, 6, [27, 301], [3, 5]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 2, "level_primes": [5, 13], "conrey_indexes": [49, 199], "field_disc": 22581504, "field_disc_factorization": [[2, 8], [3, 6], [11, 2]], "field_poly": [16, -32, 20, 4, -11, 2, 5, -4, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.049", "prec": 17}, {"__RealLiteral__": 0, "data": "7.526", "prec": 17}, {"__RealLiteral__": 0, "data": "4.543", "prec": 17}, {"__RealLiteral__": 0, "data": "224.405", "prec": 24}, {"__RealLiteral__": 0, "data": "296.965", "prec": 24}, {"__RealLiteral__": 0, "data": "10537.047", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "1.2.3.c6", "trace_display": [-2, 6, 0, 10], "traces": [0, 8, -2, 6, -2, 0, -18, 10, 12, 4, 0, 0, 0, 8, -4, 0, -2, 18, -40, -12, 0, 0, 6, 6, 12, 0, 10, 0, 8, 8, 0, 0, -4, -18, 0, 0, 20, -2, 0, 0, 0, 12, -42, -18, 0, 0, -42, -16, -6, -12, 0, -8, 16, 0, -18, 0, 12, -28, 22, 12, 0, -28, 12, -4, 8, 0, 12, -30, 12, 16, 0, 0, 12, -16, -10, 0, 54, 0, 18, 16, 0, 8, -6, 24, 30, 0, 0, 54, 42, -24, 0, 28, 0, 8, -32, 0, 0, -2, 24, 0, 0, -4, -10, 0, -36, 0, 24, 18, 24, 0, 0, -48, 44, -6, 34, 0, -92, -20, 0, 36, 0, 16, 4, 2, 12, 0, -56, -18, 18, 8, 0, 0, 36, -54, -18, 0, 24, -18, -76, 28, 0, 60, 0, -66, -64, 0, 28, -24, 8, -24, 0, 0, -90, -12, 18, 0, 60, 0, -52, 12, 0, 0, 22, -18, 0, 0, 0, -2, 0, 32, 0, -12, -12, 78, 0, 0, -78, 12, -54, -36, 0, -48, 56, 0, -12, 0, 28, 36, -56, -12, 0, -16, 30, -58, 20, 0, 0, 22, 12, -36, 0, -36, -50, 52, -22, 0, -12, 0, -2, 0, 0, 24, -60, 148, 6, 0, 0, 48, -12, -12, 0, 48, 0, 34, 22, 0, 0, -30, 64, 0, 0, 36, 54, 0, 32, 0, -18, 108, 30, 0, 0, -60, -16, 72, 10, 0, -20, 6, 0, 12, 0, 24, 64, 6, 30, 0, 26, 18, 10, -64, 0, 88, 12, 78, 48, 0, -42, -6, 24, 40, 0, -24, 0, 12, 132, 0, 50, -90, -124, 24, 0, 0, -96, -6, -102, 0, 30, 0, 16, -28, 0, 0, -8, -54, 0, 0, 36, -42, 0, -48, 0, -36, 96, -126, 0, 0, -48, -40, 36, -20, 0, -16, -162, 0, -48, 0, -40, -8, 36, -12, 0, -20, -150, -10, 52, 0, 156, -8, -18, -20, 0, -48, 36, -40, -34, 0, -18, 0, 58, -128, 0, 0, 156, -52, -24, 0, 0, -90, -180, 120, 0, -60, 0, 6, -6, 0, 0, 14, -42, 0, 0, 0, -24, 0, 2, 0, 78, -102, -90, 0, 0, -12, -56, -42, 6, 0, 72, -22, 0, 12, 0, -36, 52, -34, 78, 0, -50, 12, 20, -32, 0, -8, 0, -24, -10, 0, 60, 26, 204, -8, 0, 36, 0, 24, 172, 0, -34, 138, -12, 96, 0, 0, 168, 78, -48, 0, -22, 0, 42, 84, 0, 0, 18, 64, 0, 0, -94, 46, 0, -48, 0, 96, -90, -18, 0, 0, -48, 68, 72, 4, 0, 96, 12, 0, -66, 0, 14, -92, 58, -144, 0, 0, 108, 76, 12, 0, -216, -10, -48, 32, 0, 60, 42, -32, 34, 0, -48, 0, -16, -120, 0, -44, 42, -36, -168, 0, 0, 48, 132, 12, 0, 40, 0, -58, -88, 0, 0, 18, -42, 0, 0, 40, 4, 0, 48, 0, 12, 42, 0, 0, 0, -12, -36, -78, 12, 0, 60, 162, 0, 96, 0, 28, -140, -26, 78, 0, 22, -24, 34, 64, 0, -160, -124, 126, -24, 0, 6, -40, -36, -4, 0, -36, 0, 18, -84, 0, -48, -30, 92, 156, 0, 0, 66, -36, 6, 0, 18, 0, -48, 4, 0, 0, 30, 20, 0, 0, 62, 18, 0, -48, 0, -96, 0, 30, 0, 0, 126, -20, -18, 0, 0, -32, -72, 0, -30, 0, -20, -32, -56, -84, 0, 36, 6, 24, 24, 0, 132, 58, -120, -8, 0, 24, 50, -32, -18, 0, 78, 0, -42, 16, 0, 52, -30, -72, -156, 0, 0, -42, 36, 84, 0, -136, 0, -34, 16, 0, 0, -10, -40, 0, 0, -28, -20, 0, 114, 0, -144, -114, 24, 0, 0, 144, -24, 30, 44, 0, -168, -24, 0, 180, 0, -12, 44, 50, 30, 0, 22, 6, -54, -48, 0, 112, -24, -114, 56, 0, -6, -56, -160, 12, 0, 12, 0, -8, -120, 0, 16, 30, 104, 24, 0, 0, 60, -54, -120, 0, -134, 0, 62, 20, 0, 0, -36, 46, 0, 0, -122, -16, 0, 24, 0, -24, -132, 36, 0, 0, 264, 44, -18, -76, 0, 0, 114, 0, -168, 0, -18, -68, 0, 24, 0, 104, 150, 32, -44, 0, -84, 68, -12, -84, 0, 12, 0, 36, -36, 0, 24, 0, -90, 112, 0, -40, -156, 24, 126, 0, 0, -42, -12, 12, 0, 140, 0, -10, -24, 0, 0, 0, 48, 0, 0, -40, -56, 0, -146, 0, 90, -18, 114, 0, 0, 156, 84, 96, 34, 0, 28, 42, 0, 96, 0, 0, -8, 6, 48, 0, 72, -114, -16, 40, 0, -216, -46, 66, 132, 0, 0, 22, -40, 0, 0, -144, 0, 62, 148, 0, -66, -78, 116, -108, 0, 0, -90, -72, 210, 0, 12, 0, -54, 0, 0, 0, -76, 38, 0, 0, 26, 10, 0, 68, 0, -84, 234, -6, 0, 0, 102, 56, 144, -56, 0, 56, 128, 0, -270, 0, 42, 64, 30, -60, 0, 16, 48, -48, -60, 0, -160, 8, 84, -88, 0, -24, -64, 24, -10, 0, -120, 0, 144, -16, 0, -32, -162, -72, -6, 0, 0, -168, -12, -120, 0, -84, 0, 20, 106, 0, 0, 26, -34, 0, 0, 36, 48, 0, -6, 0, 12, 42, 114, 0, 0, -12, -160, -72, 110, 0, 156, 22, 0, 0, 0, 12, 60, -14, -36, 0, 140, 198, -60, -200, 0, 256, 118, -84, 22, 0, -72, 0, 4, 4, 0, -84, 0, -114, 84, 0, -40, -24, -64, 96, 0, 0, 144, 0, 36, 0, -228, 0, 30, -148, 0, 0, -4, 26, 0, 0, -6, 18, 0, 56, 0, -60, 66, 66, 0, 0, -36, 108, -114, -60, 0, 120, -70, 0, 138, 0, -86, 184, -120, -36, 0, 48, -72, -10, 204, 0, 76, -14, 234, 132, 0, -24, -82, 16, -36, 0, 18, 0, -168, 8, 0, -16, -12, -148, -258, 0, 0, -66, -132, 84, 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, 65, 12, 1, 6, 0]], "char_orbit_index": 13, "prim_orbit_index": 12, "minimal_twist": "65.2.m.a", "char_is_minimal": false, "conrey_index": 49, "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], [1, -1, 0, -1, 0, 0, -1, 0], [2, 0, 0, -1, -1, 1, -1, 0], [-2, 1, 2, 1, 1, -1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0], [-1, -1, 0, -1, 1, -1, -2, -1], [2, 1, 0, 0, 1, 0, -3, 0], [2, -1, -2, 1, 0, 1, 0, 2], [4, -2, 0, -2, -2, 2, -2, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -2, -2, 2, 0, 0, 1, 0], [-5, 3, 4, 3, 3, 0, 4, 4], [0, 1, 0, -1, 0, -3, 0, -2], [-2, 0, -1, 0, 3, -3, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0], [1, -1, -1, -3, -2, -2, 0, -2], [2, -1, 0, 0, 1, 0, 1, 0], [-6, 0, 2, 0, 2, -2, 0, -2], [-1, 0, 0, 0, 0, 0, -1, -4], [0, 0, 0, 0, 0, 0, 0, 0], [5, -2, 2, -2, 0, 2, -6, 2], [0, 1, 0, -1, -1, -1, 1, -4], [4, -2, 2, -1, -3, 3, -1, 0], [6, -4, -8, 0, -4, 4, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-1, 1, 5, 1, 2, 0, 2, 6], [2, -1, -2, -1, -2, -1, -2, -2], [-1, 1, 2, 2, 1, 1, 2, 4], [-2, 2, 2, 2, 0, 0, 3, 4], [0, 0, 0, 0, 0, 0, 0, 0], [-2, 0, -2, 0, 0, 0, 4, -2], [-2, 0, 0, 1, 0, -1, 2, 0], [-4, -1, -8, 0, -1, 0, 5, -4], [2, -2, 1, -2, -1, 1, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0], [-4, 4, 4, 6, 2, 2, 6, 8], [2, -2, 2, 1, 3, 3, -3, 4], [-7, 6, 4, 6, 5, -1, 2, 4], [-2, 2, 4, -2, 2, -2, 1, -4], [0, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 0, -1, 0], [-11, 1, 0, 3, 4, -4, 5, 0], [-2, 1, 0, 0, -1, 0, -1, 0], [-3, 2, 1, 2, -1, -3, 2, 1], [0, 0, 0, 0, 0, 0, 0, 0], [-3, -1, 0, 1, 1, 1, -4, -3], [0, 0, -2, 0, -4, 4, 0, 2], [0, -1, 0, -3, 1, -3, -1, -8], [-2, 2, 0, 6, 4, 4, -4, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-1, 2, 0, -2, -2, 0, 0, 0], [8, -2, -4, -3, -6, 3, -4, 0], [-2, 2, 4, 2, 2, 0, 0, 4], [-7, 3, 5, 1, 4, -4, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0], [1, 0, -12, 2, 0, -2, -1, -6], [-6, 3, 4, -3, 2, -5, 0, -4], [14, -7, -8, -5, -7, 5, -7, -4], [1, 0, 0, -2, 0, -2, 1, 2], [0, 0, 0, 0, 0, 0, 0, 0], [-5, 0, 0, -2, 0, 2, 5, 0], [4, 0, 2, -2, -2, 2, -2, 0], [6, -6, 2, -6, 0, 0, -4, 4], [-1, 4, 2, -4, 0, -4, 0, -2], [0, 0, 0, 0, 0, 0, 0, 0], [0, 4, 5, -4, -1, -3, 0, -5], [0, 0, 0, -1, -1, -1, -7, 0], [1, -1, 2, 2, 1, -1, 0, 0], [9, -2, 0, -4, -2, 4, -7, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-3, 6, 0, 0, -6, 0, 3, -2], [14, -10, -12, -6, -10, 6, -4, -6], [-4, 2, -2, -2, 2, -4, 0, 2], [-3, -1, -6, 1, -1, -1, 4, -3], [0, 0, 0, 0, 0, 0, 0, 0], [15, -5, -7, -1, -6, 6, -5, 0], [-4, -1, -8, -1, -4, -3, 10, -8], [-2, 3, 6, 7, 3, 5, 3, 14], [4, 2, 2, -2, -6, 4, 0, -2], [0, 0, 0, 0, 0, 0, 0, 0], [-2, 2, -4, 2, 0, 0, 3, -8], [0, -1, 0, 1, 1, 1, -1, 2], [2, 2, 4, -2, 0, -2, 0, -4], [2, 1, 0, 5, -1, 5, 3, 9], [0, 0, 0, 0, 0, 0, 0, 0], [-2, 2, -1, 2, 1, -1, 0, -1], [4, 1, 0, 6, -1, 6, 5, 8], [10, 0, 6, -3, -3, 3, -5, 0], [2, -8, -8, 2, -6, 6, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-1, 8, 4, 2, 6, -4, -5, -2], [-7, 5, 6, 5, 3, -2, 4, 6], [-4, 4, -2, 0, -4, -4, 6, -4], [2, -2, -6, -4, -2, -2, -8, -12], [0, 0, 0, 0, 0, 0, 0, 0], [-5, 2, -1, 2, 1, -1, 6, -1], [-2, -1, -8, 2, -1, -2, 3, -4], [0, 4, -12, 4, 4, -4, -4, -6], [-2, 0, -8, 0, -2, -2, 4, -8], [0, 0, 0, 0, 0, 0, 0, 0]]}