# Stored data for newform 325.2.m.c, downloaded from the LMFDB on 16 April 2024.
{"label": "325.2.m.c", "space_label": "325.2.m", "level": 325, "weight": 2, "hecke_orbit": 3, "hecke_orbit_code": 9008023922016581, "dim": 8, "is_polredabs": true, "nf_label": "8.0.22581504.2", "trace_hash": 2092650068701764225, "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}+\\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": "0.042", "prec": 17}, {"__RealLiteral__": 0, "data": "7.526", "prec": 17}, {"__RealLiteral__": 0, "data": "2.175", "prec": 17}, {"__RealLiteral__": 0, "data": "224.405", "prec": 24}, {"__RealLiteral__": 0, "data": "168.584", "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]]}