# Stored data for newform 525.2.t.f, downloaded from the LMFDB on 25 April 2024. {"label": "525.2.t.f", "space_label": "525.2.t", "level": 525, "weight": 2, "hecke_orbit": 6, "hecke_orbit_code": 22519303840465421, "dim": 8, "is_polredabs": true, "nf_label": "8.0.856615824.2", "trace_hash": 565059262940744130, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[2, [4, 24, 56, 48, 6, -12, -1, 3, 1]], [13, [36, 0, 135, 0, 123, 0, 21, 0, 1]], [37, [15376, -34100, 84925, 18889, 7426, 25, 124, 7, 1]]], "qexp_display": "q+(\\beta _{1}+\\beta _{3})q^{2}+(-1-\\beta _{1}-\\beta _{3}-\\beta _{7})q^{3}+\\cdots", "char_order": 6, "char_parity": 1, "char_degree": 2, "char_conductor": 21, "char_orbit_label": "t", "char_is_real": false, "Nk2": 2100, "analytic_conductor": 4.19214610611722, "hecke_ring_index": 1, "level_radical": 105, "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": "0.181", "prec": 17}, "analytic_rank_proved": true, "char_values": [525, 6, [176, 127, 451], [3, 6, 5]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 2, "level_primes": [3, 5, 7], "conrey_indexes": [26, 101], "field_disc": 856615824, "field_disc_factorization": [[2, 4], [3, 6], [271, 2]], "field_poly": [4, 0, 32, 0, 36, 0, 11, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "7.696", "prec": 17}, {"__RealLiteral__": 0, "data": "1.007", "prec": 17}, {"__RealLiteral__": 0, "data": "230.146", "prec": 24}, {"__RealLiteral__": 0, "data": "63.372", "prec": 20}, {"__RealLiteral__": 0, "data": "11218.555", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "1.2.3.c6", "trace_display": [-3, -2, 0, -2], "traces": [0, 8, -3, -2, 3, 0, -5, -2, 0, 4, 0, 0, 18, 0, 12, 0, 1, -12, -26, 9, 0, -22, 40, 27, -7, 0, 6, 4, -3, 0, 0, -21, 21, -4, 0, 0, 9, -7, -12, 15, 0, 30, 5, -16, 0, 0, -7, -6, -25, -4, 0, 12, -30, 24, 7, 0, 21, -6, 13, 12, 0, 15, 24, 44, 38, 0, -16, -4, 0, 13, 0, 0, -13, -15, -54, 0, 0, -36, 6, -29, 0, 28, -27, 30, -51, 0, -9, 29, 2, 3, 0, -3, 0, -45, -24, 0, -42, 0, -39, -34, 0, 3, -30, 48, 24, 0, -16, 15, 45, -20, 0, 16, -16, 0, -6, 0, -75, 9, 0, 12, 0, 12, -15, 3, -48, 0, 17, 26, -45, 4, 0, -6, -42, 21, 0, 0, 18, -48, -20, 0, 0, 0, -26, -18, 26, 0, -72, -2, -48, -69, 0, 22, -6, 42, 14, 0, -36, 18, -12, 64, 0, 24, -83, -4, 39, 0, -9, 30, 28, 62, 0, 51, 3, 6, 5, 0, 0, -42, 45, 42, 0, 0, 30, 51, 13, 0, 102, -54, -48, -10, 0, -6, 49, -13, 24, 0, -36, 0, 56, -42, 0, 19, 0, -45, -66, 0, 15, 58, 18, -72, 0, 16, 24, 2, -1, 0, -10, 42, 0, 27, 0, -24, 100, 0, -21, 0, -16, 0, -6, 3, 0, -20, 122, 60, 0, 0, 30, 32, -60, 0, 0, -12, 39, -2, 0, 0, -57, -15, 36, -45, 0, 48, -72, -32, 96, 0, 21, 60, 1, 61, 0, 41, -24, -33, 40, 0, -6, -117, -15, -51, 0, -66, 12, -60, 56, 0, 45, -13, -18, 30, 0, 0, 84, -75, 18, 0, 0, 15, 3, 8, 0, -84, -66, -84, 52, 0, 18, 38, 25, -42, 0, 28, 0, -30, 12, 0, 54, 0, 114, -45, 0, -36, 48, 33, -12, 0, 36, -48, -104, -22, 0, -101, 133, 0, 24, 0, 60, 35, 0, 30, 0, 31, -9, -23, -39, 0, 25, 38, 9, 64, 0, -30, -36, 46, 0, 0, 60, -21, -96, 0, 0, -6, 42, 0, 18, 0, 126, 18, -20, 42, 0, -43, -57, -69, 18, 0, -66, -42, 57, 81, 0, -72, -102, 29, -42, 0, 36, -84, 44, 22, 0, -29, -62, -3, -53, 0, 0, 40, 138, 36, 0, 0, 9, 84, -10, 0, -54, -27, 156, -51, 0, -81, 25, -3, 27, 0, 32, 0, 0, -36, 0, -14, 0, 54, -191, 0, -18, 69, 54, 96, 0, -20, 6, -6, -32, 0, 8, 12, 0, 12, 0, 132, 29, 0, -90, 0, -15, 36, 90, -126, 0, -20, 12, -81, 84, 0, -18, -43, -89, 0, 0, -54, -120, 8, 0, 0, 36, 41, 18, -90, 0, -48, -116, 20, -3, 0, -46, 21, -6, 31, 0, 0, -96, -54, 2, 0, -30, -80, -74, 48, 0, 21, -108, -145, 30, 0, -38, -37, 51, -80, 0, 0, 78, -96, 42, 0, 0, 24, 39, -11, 0, -45, -108, 30, 85, 0, 240, -59, 0, -51, 0, 60, 0, -39, 0, 0, -36, 0, 30, -84, 0, -66, 8, -129, -192, 0, 2, 102, -74, 39, 0, 0, -60, 0, -60, 0, 15, 20, 0, -36, 0, -20, 30, 42, -102, 0, 60, 74, -66, 108, 0, 6, 71, 41, 0, 0, -60, -36, 60, 0, 0, 36, -20, 9, 24, 0, 0, 14, 8, 6, 0, 1, 6, 74, 78, 0, -23, -9, -81, 55, 0, 45, -102, 64, 12, 0, -36, 168, 9, 42, 0, 4, 16, 48, 92, 0, 0, -102, 96, -6, 0, 0, -30, -35, -30, 0, 81, -90, 0, -98, 0, 6, 66, 50, 39, 0, -110, 0, 60, -57, 0, 97, 0, -48, -30, 0, -18, 66, 126, 132, 0, 100, -126, 44, -70, 0, 96, 9, 0, -28, 0, -45, 100, 0, -63, 0, -12, 27, -31, -48, 0, 3, 216, 72, -13, 0, 21, 6, 12, 0, 0, -84, 84, -42, 0, 0, -92, -41, 9, 24, 0, -72, -99, 2, -180, 0, 21, 0, 100, -54, 0, 66, -78, -105, 30, 0, -147, -66, 7, -24, 0, -3, 0, 22, 182, 0, 19, -12, -33, 22, 0, 0, -12, 93, 102, 0, 0, 57, 24, 79, 0, -61, -3, -72, 48, 0, -78, 8, -56, 12, 0, 135, 0, 120, 33, 0, -24, 0, -60, 40, 0, 48, 9, -135, 186, 0, 54, 60, -186, 31, 0, -12, 112, 0, 66, 0, -192, 45, 0, 42, 0, -5, 0, -6, 114, 0, 9, 128, -78, -76, 0, 42, 16, -61, 0, 0, 231, 24, 24, 0, 0, -72, -42, 12, 10, 0, -108, 11, -140, 72, 0, 56, 48, -22, 1, 0, 144, 111, 72, 28, 0, 36, -26, -72, -48, 0, -12, -144, 102, 96, 0, 120, 55, -96, 27, 0, 0, 18, -75, -45, 0, 0, -3, 36, -68, 0, 42, 21, -174, -75, 0, -78, 100, 113, -45, 0, -60, 0, -21, 21, 0, 115, 0, -72, 42, 0, -6, -39, -120, -180, 0, -126, -111, 134, 36, 0, -48, -51, 0, 51, 0, -54, 78, 0, 183, 0, -101, -30, 24, -66, 0, -72, -20, 75, -33, 0, -36, -89, 24, 0, 0, -9, 93, 48, 0, 0, 30, 2, 6, 162, 0, 162, 91, -58, 90, 0, -55, -51, -64, -77, 0, -118, -30, 66, 68, 0, 150, -30, 115, -54, 0, -168, 240, 44, 88, 0, -112, 38, -66, -141, 0, 0, -12, -48, -144, 0, 0, 30, 0, -23, 0, 24, 24, 48, -72, 0, -195, 45, -117, 9, 0, 60, 0, -54, -249, 0, 12, 0, 39, -42, 0, 78, -138, 207, 24, 0, -44, -63, 42, -3, 0, 190, -30, 0, -8, 0, 150, -68, 0, 6, 0, 41, -30, -56, -84, 0, 71, -28, 63, -18, 0, -54, 105, 111, 0, 0, 63, 60, -188, 0, 0, -37, -2, -111, -9, 0, -24, -6, -24, -3, 0, 49, 18, 38, -40, 0, 30, -75, 48, -5, 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, 21, 7, 1, 6, 0]], "char_orbit_index": 20, "prim_orbit_index": 7, "minimal_twist": "105.2.s.c", "char_is_minimal": true, "conrey_index": 26, "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], [0, 1, 0, 1, 0, 0, 0, 0], [-1, -1, 0, -1, 0, 0, 0, -1], [0, 0, -1, 0, 0, -1, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 2, 1, 0, 1, 1, 1], [0, -1, 0, 1, 0, -1, 1, 0], [0, 1, 0, 0, -1, 1, 0, 0], [0, 1, -1, 0, -1, -1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 0, 1, -1, 0], [1, -2, 1, -1, 0, 0, -1, 0], [0, 0, 0, 0, 0, 0, -1, 1], [-2, -1, 3, -1, -1, 0, -1, -2], [0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 0, 1, 0, -1, 1, -1], [-4, 0, 4, 0, -1, 0, -1, 1], [0, 1, -2, 0, 2, 1, 1, 1], [1, 0, 0, 0, -1, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0], [-3, 0, -1, -1, 0, 0, -2, 1], [3, 1, 0, 2, -2, -2, -1, -1], [2, 1, -2, 1, -2, -2, -2, 0], [-2, 1, 2, 1, 0, -1, 1, -1], [0, 0, 0, 0, 0, 0, 0, 0], [-1, 1, 1, -1, -1, 0, 0, -1], [-4, 1, 4, 0, -2, 0, -3, -1], [3, 0, 0, 3, 2, 1, 2, 0], [-1, -2, 2, 0, 2, -2, -1, 1], [0, 0, 0, 0, 0, 0, 0, 0], [1, 0, -3, 3, 1, -2, 3, 1], [4, 0, 2, 3, 1, 0, 1, 1], [3, -3, -1, -1, 3, 0, 4, 1], [-1, -3, 2, 0, 0, 0, 1, -1], [0, 0, 0, 0, 0, 0, 0, 0], [1, -4, -4, -5, 2, -1, 0, -2], [2, 1, -5, -1, 2, -2, 2, 0], [-2, 0, 2, 0, 1, 0, 1, -1], [3, -2, -1, -1, 2, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, -2, -2, -1, -1], [-1, 0, 1, -4, -1, 1, 1, 0], [-3, 0, 0, 0, -1, -1, 0, 0], [2, 6, 0, 6, -2, 0, 0, 2], [0, 0, 0, 0, 0, 0, 0, 0], [2, 8, -1, 4, 0, 1, 1, 0], [2, 0, -4, 0, 2, -2, 2, 0], [-4, 0, 0, -1, -1, 0, -1, 1], [1, 1, 4, -1, 2, 2, 2, 3], [0, 0, 0, 0, 0, 0, 0, 0], [4, 2, 0, -2, 2, 3, -1, 3], [0, 0, -3, 3, 1, -1, 2, 1], [0, 0, 4, -4, 0, 4, -4, 0], [6, 3, -2, 7, 0, 0, 2, 2], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -1, -3, 0, -3, 1], [-3, -1, 0, -2, 1, -1, -2, -2], [-5, 2, 5, -2, -5, 2, -2, -3], [4, 2, -1, 1, -2, 3, 1, 2], [0, 0, 0, 0, 0, 0, 0, 0], [-3, 0, -1, 0, -3, -4, -4, -1], [-4, -4, 0, -8, -1, -1, -4, -4], [8, 0, -1, 2, 2, -1, 0, 2], [0, -1, 0, -2, -1, -1, -4, -4], [0, 0, 0, 0, 0, 0, 0, 0], [-10, -6, 7, -7, -1, 1, -2, -3], [-1, 2, 0, 1, 0, -1, -1, 0], [-2, -2, 0, 2, -2, -2, 2, -4], [-6, -6, 6, -5, 0, -1, -3, -3], [0, 0, 0, 0, 0, 0, 0, 0], [-1, 1, 2, 0, 1, -1, 1, -1], [-2, 4, 4, 1, -3, 4, -1, 3], [1, 0, -3, -3, 2, 0, 2, 2], [-4, 0, -5, -7, 2, 3, -1, 2], [0, 0, 0, 0, 0, 0, 0, 0], [1, -3, -2, 0, 2, -2, 1, -1], [-8, -2, 4, -2, -3, 3, 0, -2], [-3, 3, 4, 0, -3, 1, -1, -1], [-3, 2, -6, -2, -3, 2, -2, -1], [0, 0, 0, 0, 0, 0, 0, 0], [3, -1, 5, -4, 1, 3, 2, 2], [1, 6, 1, 6, 1, 2, 2, 1], [6, 1, 0, 2, 0, 0, 2, 2], [0, -2, -3, 2, 2, 1, 5, 2], [0, 0, 0, 0, 0, 0, 0, 0], [-1, -2, 1, -2, 1, 1, 1, 0], [8, -3, -5, -4, 2, 4, -2, 3], [0, -4, -4, -2, 4, -4, 0, -4], [-1, -4, -1, 4, -1, -5, 5, -6], [0, 0, 0, 0, 0, 0, 0, 0], [4, 1, -2, 2, 1, 2, 3, 0], [8, -3, -16, 0, 5, -5, 0, 0], [-5, 2, 0, 4, -1, 0, -4, 3], [-4, 0, -2, -6, 0, 2, -2, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-2, -5, -2, -4, 3, 3, 2, 0], [-1, -3, 2, 0, -2, 2, 3, -3], [-6, -8, -2, -5, 2, -1, -1, -1], [-1, 3, -10, 2, -1, -1, -3, -1], [0, 0, 0, 0, 0, 0, 0, 0]]}