# Stored data for newform 925.2.a.f, downloaded from the LMFDB on 07 June 2026. {"Nk2": 3700, "analytic_conductor": 7.386162186968436, "analytic_rank": 1, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[5, 1], [37, 1]], "atkin_lehner_string": "++", "char_conductor": 1, "char_degree": 1, "char_is_minimal": true, "char_is_real": true, "char_orbit_index": 1, "char_orbit_label": "a", "char_order": 1, "char_parity": 1, "char_values": [925, 1, [852, 76], [1, 1]], "cm_discs": [], "conrey_index": 1, "dim": 5, "field_disc": 973904, "field_disc_factorization": [[2, 4], [60869, 1]], "field_poly": [6, 19, 6, -8, -2, 1], "field_poly_is_cyclotomic": false, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 0, "fricke_eigenval": 1, "has_non_self_twist": 0, "hecke_cutters": [[2, [12, 11, -14, -8, 2, 1]], [3, [22, 4, -20, -6, 3, 1]]], "hecke_orbit": 6, "hecke_orbit_code": 22517998170407837, "hecke_ring_generator_nbound": 3, "hecke_ring_index": 1, "hecke_ring_index_factorization": [], "hecke_ring_index_proved": true, "inner_twist_count": 1, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "is_cm": false, "is_largest": false, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": true, "is_self_twist": false, "is_twist_minimal": false, "label": "925.2.a.f", "level": 925, "level_is_powerful": false, "level_is_prime": false, "level_is_prime_power": false, "level_is_prime_square": false, "level_is_square": false, "level_is_squarefree": false, "level_primes": [5, 37], "level_radical": 185, "minimal_twist": "185.2.a.e", "nf_label": "5.5.973904.1", "prim_orbit_index": 1, "qexp_display": "q-\\beta _{4}q^{2}+(-1+\\beta _{1})q^{3}+(2+\\beta _{3})q^{4}+\\cdots", "related_objects": [], "relative_dim": 5, "rm_discs": [], "sato_tate_group": "1.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "925.2.a", "trace_display": [-2, -3, 0, -11], "trace_hash": 419512432857387497, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "4.539", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "56.154", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1099.109", "prec": 27}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.004", "prec": 17}, "traces": [0, 5, -2, -3, 10, 0, -6, -11, -6, 6, 0, -5, 2, -4, -8, 0, 16, 0, -2, -4, 0, 3, 8, -4, -42, 0, -4, -3, -28, -4, 0, 8, -14, -5, -32, 0, 16, -5, 2, 2, 0, -5, 52, -10, -46, 0, 0, -7, 20, 22, 0, -2, 32, 1, -10, 0, 8, 8, 16, -30, 0, -14, -24, -30, 20, 0, 48, -24, -20, 8, 0, -7, 10, -5, 2, 0, 12, 17, -58, 28, 0, -31, 8, -27, -18, 0, 44, -36, 28, 6, 0, -14, -56, 22, 4, 0, -42, 26, 18, -10, 0, -29, 34, -22, 0, 0, 56, -6, 16, 10, 0, 3, -82, 26, 16, 0, -24, 24, 16, 14, 0, -14, -32, -5, -10, 0, 10, -59, -30, -14, 0, -30, -10, 40, 50, 0, -28, 10, 24, -4, 0, -21, 32, -36, 56, 0, -52, -20, -10, -5, 0, 24, -6, 20, 0, 0, 26, -25, 60, 17, 0, -20, 18, -12, -46, 0, 54, 22, 172, 7, 0, -42, 16, 37, 28, 0, -76, 52, -56, -24, 0, -23, 34, 6, -8, 0, 48, 20, -44, 37, 0, 18, 100, 28, 0, 0, 108, -1, -8, -10, 0, -28, 28, 16, 118, 0, 8, 20, 84, -16, 0, -5, 30, 37, 36, 0, 22, 14, 12, -37, 0, 0, 6, -1, 100, 0, -4, -36, -80, 11, 0, 21, 96, -14, 8, 0, -74, -74, 118, 26, 0, -12, -14, 28, -8, 0, 48, -14, -84, 5, 0, -40, -96, 52, 38, 0, -20, -26, -20, 11, 0, 12, 26, -49, 108, 0, -72, 38, -24, 46, 0, 17, 16, 16, -16, 0, 116, -50, -88, -28, 0, -46, 112, 4, -54, 0, 4, 17, -82, 19, 0, 58, 18, 14, -144, 0, 6, -19, 8, -20, 0, 26, -148, -35, -56, 0, -68, -43, 154, 58, 0, -6, -86, -34, 76, 0, -2, -50, -92, 20, 0, -56, 124, -58, -102, 0, -12, -50, 28, 89, 0, -36, -130, -6, -24, 0, -52, -41, 42, -32, 0, 18, 48, -25, 92, 0, -8, 4, -96, -30, 0, 20, 68, 18, 16, 0, 0, -40, 38, -3, 0, -3, 48, 38, -166, 0, -12, 8, 0, -10, 0, -65, 76, 21, 60, 0, 60, 4, -48, 23, 0, 101, 36, -38, -74, 0, 28, -36, 112, 48, 0, 76, 14, 30, -172, 0, -96, 51, 42, -50, 0, -14, -56, -70, -22, 0, -88, 5, -2, -24, 0, -18, 64, 32, -84, 0, -108, 64, 4, -53, 0, -56, 52, -58, 20, 0, 56, 22, -50, -24, 0, 34, -26, 41, 60, 0, 52, -100, 36, 16, 0, 60, -32, -33, -2, 0, -70, 85, -134, 6, 0, 41, 20, -12, -84, 0, 108, 6, -96, -4, 0, 6, -224, -2, -72, 0, 36, 26, 84, -8, 0, 39, -28, -26, -20, 0, 102, -10, -26, -52, 0, 4, -72, 8, 32, 0, 130, 8, -16, 68, 0, -12, -10, 4, 38, 0, -22, 23, 92, -84, 0, 98, -6, 28, -22, 0, 8, 83, -162, -23, 0, 69, -134, 48, -12, 0, -228, 37, 8, -75, 0, 55, 60, -2, 52, 0, -58, 30, -128, 45, 0, -40, 56, -36, -40, 0, 154, -68, 112, -86, 0, -30, 36, -9, -104, 0, 176, -24, 60, 32, 0, -8, -8, -106, 48, 0, 80, -16, -66, 20, 0, -120, 8, -24, -150, 0, -60, 91, -28, -34, 0, 87, -100, 48, 0, 0, 52, 20, 98, -76, 0, 43, -68, -29, 32, 0, -40, 30, -62, 16, 0, 99, -16, 39, -12, 0, -90, -14, -92, 9, 0, 78, -208, 34, 88, 0, 18, 8, 138, 120, 0, -74, -88, 55, -12, 0, -76, -7, -200, -13, 0, -80, -20, -58, 102, 0, -24, 88, -150, 0, 0, 78, 152, -137, 20, 0, -110, 80, -112, -78, 0, 51, -8, 44, 80, 0, 42, 38, 42, 44, 0, -128, -64, 30, -8, 0, -76, 30, -136, -55, 0, -30, 118, 116, 98, 0, 2, -8, 200, 55, 0, -6, 120, -1, 80, 0, -42, -11, -10, -34, 0, -24, 108, -8, 2, 0, -50, 35, -84, 16, 0, -44, -70, 66, 188, 0, 100, 20, 64, -46, 0, 60, 88, 4, -64, 0, -12, 83, 88, -28, 0, 64, -144, 24, -144, 0, -100, 6, 72, 27, 0, -70, -78, 64, -54, 0, -90, 26, 30, -27, 0, -140, 140, 47, 114, 0, -112, 0, -8, 11, 0, -40, -112, -25, 12, 0, -120, -48, 4, -40, 0, 81, -202, -28, 124, 0, 42, 28, 92, -108, 0, 129, 84, 14, 166, 0, -136, 6, 176, -28, 0, 76, -64, -33, 144, 0, -168, -3, -172, -16, 0, 47, 52, 32, 188, 0, -156, 13, 146, 207, 0, -68, 80, 80, -148, 0, -52, 20, 22, -22, 0, 64, -148, -23, -116, 0, -102, -36, 156, 48, 0, -29, 92, 57, -8, 0, 138, 112, -56, -74, 0, 49, -160, -190, -64, 0, 148, -20, -76, -92, 0, 60, 56, -84, -12, 0, 60, -26, 80, -32, 0, -65, 20, 38, -86, 0, 74, -16, 44, 168, 0, 4, -62, 36, 168, 0, 160, 114, 144, 38, 0, 21, -112, 48, 74, 0, -56, -145, 128, 30, 0, 106, 92, -76, 136, 0, 30, 54, -78, -22, 0, -6, 62, 44, -32, 0, -108, -29, 42, 99, 0, 71, 122, 100, 6, 0, 216, 28, 44, -60, 0, -152, -36, 90, 8, 0, 4, 38, -112, -18, 0, 156, -44, 103, 112, 0, 250, -14, 24, 154, 0, 55, -156, -104, 58, 0, 184, 48, 112, 14, 0, -14, 104, 92, -88, 0, -92, -23, -68, 46, 0, 70, 84, 52, -50, 0, -136, 28, -184, 68, 0, -26, 170, 13, 60, 0, -76, 60, -106, -130, 0, -31, 4, 72, 32, 0, -260, -90, -62, 120, 0, -64, -88, 80, -96, 0, 68, -88, 52, 6, 0, 4, -124, -11, 108, 0, -4, -1, -94, -152, 0, 66, 0, 0, -48, 0, -86, 0, 108, 3, 0], "weight": 2, "weight_parity": 1, "id": null, "artin_degree": null, "artin_field": null, "artin_field_label": null, "artin_image": null, "embedded_related_objects": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp": [[0, 0, 0, 0, 0], [1, 0, 0, 0, 0], [0, 0, 0, 0, -1], [-1, 1, 0, 0, 0], [2, 0, 0, 1, 0], [0, 0, 0, 0, 0], [-1, -1, -1, -1, 1], [-2, -1, -1, 0, 1], [0, -2, 0, 0, -1], [1, 0, 1, 0, 0], [0, 0, 0, 0, 0], [-1, 0, 0, -1, 0], [-2, 3, 2, -1, 2], [-1, 0, 1, 1, 0], [-4, 3, 2, -1, 2], [0, 0, 0, 0, 0], [2, 2, 2, 1, 0], [-1, 0, 1, -1, 2], [1, -2, -1, 1, -1], [0, -1, -2, 1, 0], [0, 0, 0, 0, 0], [2, -2, 1, 0, -2], [0, 2, 0, 0, 2], [-2, 2, 2, -2, 0], [-7, -3, -3, -1, 1], [0, 0, 0, 0, 0], [1, -4, -1, 1, 0], [0, -2, -1, 1, 1], [-5, -3, -3, -3, 3], [0, -2, 0, 0, 0], [0, 0, 0, 0, 0], [1, 1, -1, -1, 1], [0, -4, -4, 0, -1], [1, -2, -2, 1, -2], [-7, 0, -1, -1, 2], [0, 0, 0, 0, 0], [3, 2, 1, 2, -2], [-1, 0, 0, 0, 0], [-1, 3, 3, -1, -1], [-1, 0, 1, 0, 3], [0, 0, 0, 0, 0], [-1, 0, 0, -1, 0], [11, 0, 1, 5, -2], [0, -2, -2, 2, -2], [-8, -2, -2, -2, 0], [0, 0, 0, 0, 0], [0, -2, -4, 0, 4], [0, -3, -3, 0, 1], [0, 5, 2, 1, 4], [5, 0, 1, 2, -2], [0, 0, 0, 0, 0], [1, 0, -1, 4, -3], [5, 4, 3, 1, -2], [1, 2, 0, 1, -4], [-3, 2, 3, 0, -1], [0, 0, 0, 0, 0], [-4, 9, 2, -1, 4], [1, 0, 3, -3, 0], [2, 2, 2, 2, 0], [-7, 3, 1, -1, -1], [0, 0, 0, 0, 0], [-4, 0, 2, 0, 2], [-6, 3, 0, -3, 0], [-6, 1, -2, -1, 0], [0, 8, 4, -1, 0], [0, 0, 0, 0, 0], [8, 4, 4, 2, -2], [-4, -1, 2, 1, -2], [-7, 4, -1, -1, 4], [4, -2, -4, 4, -2], [0, 0, 0, 0, 0], [-1, 2, -2, -1, -2], [5, -4, -1, -1, -3], [-1, -4, 0, 1, 4], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0], [4, -5, -2, -1, 2], [3, 2, 2, 3, -2], [-11, -2, -1, -2, 1], [7, -1, 1, -1, -3], [0, 0, 0, 0, 0], [-6, 0, -1, -1, 0], [0, 2, 0, 0, 2], [-5, 1, 0, -2, -2], [5, -8, -3, 3, -12], [0, 0, 0, 0, 0], [8, 2, 4, 2, -2], [-6, -2, -2, 0, 0], [0, 6, 4, 0, 6], [-2, 4, 4, -2, 2], [0, 0, 0, 0, 0], [-3, 2, -1, -4, -1], [-14, 6, 2, -2, 0], [5, 2, 1, 1, -4], [-4, 9, 6, -1, 0], [0, 0, 0, 0, 0], [-5, -5, -1, -5, -3], [6, 2, -4, 2, -2], [9, -6, -1, 3, -7], [-2, -2, 0, -2, 2], [0, 0, 0, 0, 0]]}