# Stored data for newform 525.2.r.a, downloaded from the LMFDB on 25 April 2024. {"label": "525.2.r.a", "space_label": "525.2.r", "level": 525, "weight": 2, "hecke_orbit": 1, "hecke_orbit_code": 1168264659469, "dim": 4, "is_polredabs": true, "nf_label": "4.0.144.1", "trace_hash": 2026313674756163444, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[2, [4, 12, 14, 6, 1]], [11, [4, 4, 6, -2, 1]]], "qexp_display": "q+(-1+\\zeta_{12}-\\zeta_{12}^{2})q^{2}+(\\zeta_{12}-\\zeta_{12}^{3})q^{3}+\\cdots", "char_order": 6, "char_parity": 1, "char_degree": 2, "char_conductor": 35, "char_orbit_label": "r", "char_is_real": false, "Nk2": 2100, "analytic_conductor": 4.19214610611722, "hecke_ring_index": 1, "level_radical": 105, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 12, "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": [525, 6, [176, 127, 451], [6, 3, 4]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 2, "level_primes": [3, 5, 7], "conrey_indexes": [424, 499], "field_disc": 144, "field_disc_factorization": [[2, 4], [3, 2]], "field_poly": [1, 0, -1, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "4.058", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "58.922", "prec": 20}, {"__RealLiteral__": 0, "data": "14.174", "prec": 20}, {"__RealLiteral__": 0, "data": "1274.787", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "1.2.3.c6", "trace_display": [-6, 0, 0, 10], "traces": [0, 4, -6, 0, 4, 0, 4, 10, 0, 2, 0, 2, -12, 0, -18, 0, -16, 6, -6, 2, 0, 0, 0, 6, 12, 0, 2, 0, 16, -4, 0, -6, 48, 6, 8, 0, 8, -18, -18, -8, 0, 4, 10, 0, 8, 0, -12, 0, 0, 22, 0, 10, -36, 36, 2, 0, -12, 0, -12, 10, 0, -8, 0, 2, -64, 0, -4, 30, -48, -12, 0, 4, -12, 30, 14, 0, 56, 8, 0, 6, 0, -2, 0, 0, -36, 0, 14, -18, -24, 6, 0, -6, 0, -12, -4, 0, -16, 0, -48, 4, 0, 18, -24, 18, 72, 0, -80, 18, -12, 22, 0, -8, -16, 0, 14, 0, 32, -6, 0, 12, 0, 14, 24, 6, -12, 0, -12, 0, 48, 4, 0, -24, 0, 2, -84, 0, 48, -18, 24, 4, 0, -8, -24, 30, 16, 0, -76, 0, 0, -16, 0, 4, -84, 0, 0, 0, 4, -36, 18, -4, 0, 18, 0, -48, -8, 0, 48, 0, 48, -24, 0, -2, -12, 12, 32, 0, 16, 18, -60, -20, 0, -28, 2, 0, 48, 0, 6, 36, 0, 0, 0, 4, 48, 18, -40, 0, 52, 0, 0, 44, 0, -12, 0, -10, 16, 0, -26, 6, -48, -20, 0, 56, 96, -18, -12, 0, 24, -24, 0, -8, 0, -46, -6, 0, 96, 0, 28, 30, -36, -6, 0, 18, 0, -60, -2, 0, 16, 0, 20, -56, 0, -20, -54, 0, -32, 0, -8, 42, 36, -6, 0, -36, 20, 0, -2, 0, -32, -30, 0, -54, 0, -2, 84, 36, 0, 0, -36, 0, 132, -32, 0, -20, 0, -32, 24, 0, -24, 30, 18, -12, 0, 0, 12, -42, 40, 0, -32, 10, 0, 22, 0, 16, 108, 0, 22, 0, -12, 6, 0, -18, 0, 18, 0, 6, 64, 0, 4, 0, 8, -16, 0, 6, -12, 30, 56, 0, -120, -102, 48, -20, 0, 12, -48, 0, 4, 0, 64, 0, 0, 0, 0, -30, -120, -18, 48, 0, -24, 0, -12, -4, 0, 18, 0, 40, 24, 0, 24, -24, -24, -88, 0, -16, 0, -42, -8, 0, 192, 10, 0, -6, 0, 12, 102, 0, -72, 0, -8, -18, -120, 2, 0, 72, 0, -78, -20, 0, 24, 0, 2, 44, 0, 20, -36, 60, -96, 0, -20, 18, 144, 42, 0, -48, -60, 0, -12, 0, -8, -18, 0, 12, 0, 12, 66, -66, -24, 0, -36, 0, -24, 34, 0, -6, 0, 40, -24, 0, 16, 24, 24, 128, 0, 28, -60, 0, -96, 0, 40, -8, 0, 14, 0, 0, -24, 0, 6, 0, -44, 42, 54, 8, 0, -4, 0, -12, 28, 0, -56, 0, -160, 88, 0, 8, -72, -24, -32, 0, 72, -30, 18, -10, 0, -36, -16, 0, -56, 0, 60, 48, 0, 60, 0, -8, -48, -30, -30, 0, -144, 0, 60, -24, 0, -34, 0, -30, 104, 0, -2, -54, 48, 32, 0, -56, 0, -96, -38, 0, 0, 10, 0, -34, 0, -18, 108, 0, -36, 0, -12, -48, 84, 16, 0, 60, 0, 12, 24, 0, 28, 0, 56, 72, 0, 4, -12, 6, -144, 0, -64, -78, -24, -22, 0, 20, 140, 0, 48, 0, -132, 0, 0, 26, 0, 30, 36, 60, -32, 0, 18, 0, 0, 8, 0, 34, 0, 6, -84, 0, -44, -72, 6, 68, 0, 32, -48, 0, -8, 0, 132, -8, 0, 6, 0, -58, -24, 0, 0, 0, -32, -30, -6, 8, 0, 42, 0, 24, -108, 0, 48, 0, -96, 36, 0, -18, 96, -114, -8, 0, 128, 0, 60, -28, 0, -28, 14, 0, -56, 0, 12, 18, 0, -36, 0, -16, -48, -24, 82, 0, -48, 0, 42, -74, 0, -6, 0, 6, 80, 0, -38, -6, -24, -76, 0, 112, 180, 24, 100, 0, -160, -30, 0, 2, 0, -18, 0, 0, 48, 0, 52, 114, -12, -28, 0, -36, 0, 54, 22, 0, 8, 0, -16, 16, 0, -14, 66, -54, 240, 0, 28, 48, -168, 20, 0, -16, -16, 0, -74, 0, 72, -42, 0, -24, 0, 14, -24, -66, 28, 0, -114, 0, -96, -20, 0, 10, 0, 10, -64, 0, 24, 36, 132, 0, 0, 28, 18, 6, 16, 0, 48, 72, 0, -16, 0, -6, -288, 0, -48, 0, 40, -24, 12, -48, 0, 54, 0, 12, -148, 0, 26, 0, 180, -4, 0, 38, 48, -30, 60, 0, 192, -6, 0, 14, 0, 8, -200, 0, 12, 0, 86, 42, 0, 54, 0, -50, -48, 54, 52, 0, -24, 0, -6, 0, 0, -90, 0, 88, 112, 0, -72, 102, 96, -140, 0, -12, -12, 78, -14, 0, -288, -20, 0, -10, 0, -16, 84, 0, 32, 0, -36, -12, -48, 4, 0, 24, 0, 24, 70, 0, -88, 0, 14, -40, 0, -6, -72, 6, -168, 0, 60, -12, 72, -4, 0, 0, 128, 0, -8, 0, 56, -6, 0, -18, 0, 6, 0, 108, 84, 0, -12, 0, 48, -30, 0, -12, 0, 18, -44, 0, -8, -12, -204, 44, 0, -4, -18, -48, 8, 0, -8, 14, 0, 24, 0, -6, -48, 0, 48, 0, 0, -42, -12, 8, 0, 12, 0, -36, 16, 0, 38, 0, -12, 84, 0, 18, 132, -24, -120, 0, -152, 48, -12, -24, 0, -16, -18, 0, -16, 0, 24, 6, 0, 18, 0, 2, 192, 24, 32, 0, 144, 0, -180, 42, 0, 16, 0, 16, 144, 0, 28, -54, -24, 36, 0, -52, -120, -24, 46, 0, -24, -24, 0, -34, 0, -40, -36, 0, 0, 0, 54, 18, 96, -46, 0, -4, 0, 42, -20, 0, 36, 0, -210, -16, 0, 22, -12, -12, -16, 0, 16, -30, 36, 2, 0, -4, 192, 0, -40, 0, -8, -24, 0, -36, 0, 20, 18, 18, 64, 0, 72, 0, -156, 2, 0, 48, 0, 10, 44, 0, -64, 54, -96, -72, 0, 44, 168, -18, 0, 0, 136, -20, 0, -6, 0, -34, -48, 0, -72, 0, 96, 90, 90, -4, 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, 35, 10, 1, 6, 0]], "char_orbit_index": 18, "prim_orbit_index": 10, "minimal_twist": "105.2.i.d", "char_is_minimal": false, "conrey_index": 424, "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], [-1, 1, -1, 0], [0, 1, 0, -1], [0, -2, 2, -2], [0, 0, 0, 0], [1, -2, 0, 1], [3, 0, -1, 0], [2, 0, -4, 6], [1, 0, -1, 0], [0, 0, 0, 0], [0, 1, 1, 1], [-2, 2, -2, 0], [1, 0, -2, -4], [-4, 3, -1, -1], [0, 0, 0, 0], [-8, 4, 8, -8], [2, 5, -1, -5], [-2, 1, 1, -1], [1, -2, -1, 4], [0, 0, 0, 0], [0, 2, 0, -3], [0, 0, 0, -2], [1, -3, 1, 0], [0, -2, 6, -2], [0, 0, 0, 0], [1, -3, -1, 6], [0, 0, 0, -1], [2, -8, 4, -2], [-1, -6, 0, 3], [0, 0, 0, 0], [0, -2, -3, -2], [16, -8, -8, 8], [1, 1, 1, 0], [2, -8, 0, 4], [0, 0, 0, 0], [2, -4, 0, 2], [-3, -2, -3, 0], [-6, 7, 3, -7], [0, -1, -4, -1], [0, 0, 0, 0], [1, 2, 0, -1], [3, -5, -1, 4], [-3, 0, 6, 2], [4, 0, -4, 0], [0, 0, 0, 0], [0, 4, -6, 4], [0, -2, 0, 0], [4, 0, -8, 8], [8, 0, -5, 0], [0, 0, 0, 0], [5, 1, -5, -2], [-12, 2, 6, -2], [12, -2, -6, 2], [1, -1, -1, 2], [0, 0, 0, 0], [2, 6, -10, 12], [-2, 0, 4, -1], [-2, 8, -2, 0], [0, 3, 5, 3], [0, 0, 0, 0], [-4, 0, 4, 0], [-1, 0, 2, 3], [2, 0, -3, 0], [-16, 16, 0, -8], [0, 0, 0, 0], [0, 0, -2, 0], [10, -6, -5, 6], [-8, 4, -8, 0], [-3, 2, 0, -1], [0, 0, 0, 0], [1, -6, 0, 3], [-2, 6, -2, 0], [10, -4, -5, 4], [0, -1, 7, -1], [0, 0, 0, 0], [14, -12, 0, 6], [1, 4, 2, 1], [-3, 0, 6, -1], [3, 6, -3, -12], [0, 0, 0, 0], [0, 0, -1, 0], [0, -2, 0, 0], [-7, 0, 14, -3], [-8, 6, -2, -2], [0, 0, 0, 0], [7, -1, -7, 2], [-6, -1, 3, 1], [-8, 0, 4, 0], [3, -7, -3, 14], [0, 0, 0, 0], [1, -4, -5, -8], [-8, 0, 16, -12], [-2, -3, -2, 0], [0, 2, -2, 2], [0, 0, 0, 0], [-8, 8, 8, -16], [4, 0, -8, 8], [-13, 8, 2, -5], [1, 2, 0, -1], [0, 0, 0, 0]]}