# Stored data for newform 825.2.m.b, downloaded from the LMFDB on 19 April 2024. {"label": "825.2.m.b", "space_label": "825.2.m", "level": 825, "weight": 2, "hecke_orbit": 2, "hecke_orbit_code": 4504424294646585, "dim": 4, "is_polredabs": true, "nf_label": "4.0.125.1", "trace_hash": 1931815309606308345, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[2, [0, 1]]], "qexp_display": "q-\\zeta_{10}q^{3}-2\\zeta_{10}^{2}q^{4}+(2-\\zeta_{10}+2\\zeta_{10}^{2}+\\cdots)q^{5}+\\cdots", "char_order": 5, "char_parity": 1, "char_degree": 4, "char_conductor": 275, "char_orbit_label": "m", "char_is_real": false, "Nk2": 3300, "analytic_conductor": 6.587658166755632, "hecke_ring_index": 1, "level_radical": 165, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 10, "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": "0.005", "prec": 17}, "analytic_rank_proved": true, "char_values": [825, 5, [551, 727, 376], [5, 1, 2]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 2, "level_primes": [3, 5, 11], "conrey_indexes": [16, 256, 361, 796], "field_disc": 125, "field_disc_factorization": [[5, 3]], "field_poly": [1, -1, 1, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.024", "prec": 17}, {"__RealLiteral__": 0, "data": "4.083", "prec": 17}, {"__RealLiteral__": 0, "data": "1.381", "prec": 17}, {"__RealLiteral__": 0, "data": "50.878", "prec": 20}, {"__RealLiteral__": 0, "data": "54.168", "prec": 20}, {"__RealLiteral__": 0, "data": "1231.989", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "1.2.3.c5", "trace_display": [0, -1, 5, 6], "traces": [0, 4, 0, -1, 2, 5, 0, 6, 0, -1, 0, 11, 2, 6, 0, -5, -4, 1, 0, -13, 10, 1, 0, -1, 0, -5, 0, -1, 28, -14, 0, -8, 0, 1, 0, -15, 2, 13, 0, 6, 0, 16, 0, 16, -2, -5, 0, 0, 16, 11, 0, 1, -2, -9, 0, 25, 0, 7, 0, 15, -10, 15, 0, -14, 8, 20, 0, -5, 18, -1, 0, -28, 0, -4, 0, -5, -24, 24, 0, 19, 0, -1, 0, -19, -2, -15, 0, -14, 0, -21, 0, 54, 12, 2, 0, 5, 0, 8, 0, 1, 10, -15, 0, -13, 0, -10, 0, 11, -8, -26, 0, 3, 24, 38, 0, -15, -32, 1, 0, -46, 0, 19, 0, -9, -4, -25, 0, -28, 0, -9, 0, -13, 8, -27, 0, 5, 0, -30, 0, -16, 30, -5, 0, -1, -4, -10, 0, -24, -6, -34, 0, -18, 0, -9, 0, -10, 28, 12, 0, -9, 0, -44, 0, -17, -2, -5, 0, 20, 0, 17, 0, 12, -2, 39, 0, -70, -36, 5, 0, -23, 0, 20, 0, -25, 0, 35, 0, 9, 10, 1, 0, -23, 8, 7, 0, -15, 48, 21, 0, -26, 0, 5, 0, -16, -32, 25, 0, -6, 4, -52, 0, 15, -72, 17, 0, 25, 0, -12, 0, 16, 40, 19, 0, 25, 0, -5, 0, 54, -14, -22, 0, 29, 0, -12, 0, -15, -10, -6, 0, 40, 20, 53, 0, 4, -40, -50, 0, -62, 0, -19, 0, -2, -12, 6, 0, 25, -16, -34, 0, -23, 20, 16, 0, 3, 0, 45, 0, -21, -10, -28, 0, -14, -36, 4, 0, 5, -28, -17, 0, 2, 0, 28, 0, 21, 6, 40, 0, 4, 0, -44, 0, 3, 28, 12, 0, 45, 0, -4, 0, 11, -40, 4, 0, -10, -52, 45, 0, 0, 72, -13, 0, 17, 0, -52, 0, -15, 52, -20, 0, -16, 40, 11, 0, 8, 2, 5, 0, 14, 0, -5, 0, 9, -12, 3, 0, 5, 24, -2, 0, -12, 40, -22, 0, -53, 0, 20, 0, 36, 8, -40, 0, -14, 0, 78, 0, -45, -18, 19, 0, 9, 0, 50, 0, 4, 62, -20, 0, 17, -24, 1, 0, 9, -4, -44, 0, 25, 0, -46, 0, 24, -10, 32, 0, 36, 0, 5, 0, 1, 44, 80, 0, -44, 0, -23, 0, -20, 18, 20, 0, 58, -20, 18, 0, -12, 30, 0, 0, 17, 0, 68, 0, 30, 36, -25, 0, -45, 0, 9, 0, -9, -40, -65, 0, -5, 0, -45, 0, 65, -22, 24, 0, 90, -4, -1, 0, -20, -48, 22, 0, 5, 0, -24, 0, -30, -26, -45, 0, 16, -8, 16, 0, 49, 14, -18, 0, 50, 0, -51, 0, 16, 20, -31, 0, -11, 64, 10, 0, 63, -2, 15, 0, 12, 0, 49, 0, 60, -8, 36, 0, -24, 0, -28, 0, 11, -38, -25, 0, 78, 0, -17, 0, -88, -2, 84, 0, -20, 8, -2, 0, 88, 0, 30, 0, 9, 0, -70, 0, 2, 16, -26, 0, 54, 0, 7, 0, -75, -2, 15, 0, 4, 0, -13, 0, 13, 46, 5, 0, -2, 44, -8, 0, 5, -116, 4, 0, 55, 0, 37, 0, 94, -10, -38, 0, 20, 0, 10, 0, -12, 60, 20, 0, 108, 0, 31, 0, 35, 2, 7, 0, 4, 80, 4, 0, 25, 0, 50, 0, 6, 0, 30, 0, -44, -58, 12, 0, -30, 8, -39, 0, -13, -120, -116, 0, -36, 0, -10, 0, 18, -22, 26, 0, -74, -128, -56, 0, -65, -32, 44, 0, 8, 0, -27, 0, 5, 6, 80, 0, 55, 0, -46, 0, 25, 18, -24, 0, -15, 0, -7, 0, -37, -20, 14, 0, -114, 24, -25, 0, -17, 36, -23, 0, 44, 0, -20, 0, -40, 18, 109, 0, -3, 0, -142, 0, -62, -22, -15, 0, 39, 0, 15, 0, -2, -16, -16, 0, -95, -36, -14, 0, -46, -10, 14, 0, -46, 0, 120, 0, 66, 80, 50, 0, 60, 0, -23, 0, 20, -34, 25, 0, 2, 0, 4, 0, 25, 26, -90, 0, -12, -36, -126, 0, 59, -78, -36, 0, -25, 0, 19, 0, -7, -60, 16, 0, -51, -8, -15, 0, -85, -30, 58, 0, -26, 0, 2, 0, 80, -74, -10, 0, 66, -20, -212, 0, -37, -30, 80, 0, -55, 0, -1, 0, 19, 50, -79, 0, -50, 0, -25, 0, -82, 90, -27, 0, -69, 0, -20, 0, 6, 82, 154, 0, -22, 40, 48, 0, -60, -12, -59, 0, -4, 0, -5, 0, -54, -24, -20, 0, -40, -16, 41, 0, 6, 26, 68, 0, 10, 0, 102, 0, -27, 30, -87, 0, -4, 104, 0, 0, 30, -42, -27, 0, 47, 0, -30, 0, 0, 62, 0, 0, -5, 0, 9, 0, -26, 10, -55, 0, -28, 0, 23, 0, 57, -108, -14, 0, -35, 4, -27, 0, -31, 30, 25, 0, 26, 0, -20, 0, 3, 12, -24, 0, 8, -48, -46, 0, -10, -46, 2, 0, 95, 0, -47, 0, 28, 40, 70, 0, 26, -36, 31, 0, -7, 6, 74, 0, 5, 0, -20, 0, 39, 30, 19, 0, -23, 0, 160, 0, 16, -56, 76, 0, -20, 0, -22, 0, -75, 28, 37, 0, 2, -20, -75, 0, 52, -38, 45, 0, -49, 0, -92, 0, -9, -50, 20, 0, 65, 0, -44, 0, 28, 10, 144, 0, 19, 0, 90, 0, 15, 62, -15, 0, -70, -52, -6, 0, -80, -136, 3, 0, -7, 0, 55, 0, -2, 32, 15, 0, -18, 0, -56, 0, 63, -26, 72, 0, -60, 0, -33, 0, 8, -20, -61, 0, 11, -160, 20, 0, -34, 12, 54, 0, -5, 0, -7, 0, -10, -80, -56, 0, -45, 40, -108, 0, 11, 64, -25, 0, -13, 0, 23, 0, 11, 2, -4, 0, -70, 60, 2, 0, -9, -30, 24, 0, -25, 0, 10, 0, -40, -116, 11, 0, 55, 0, -21, 0, -70, -52, -25, 0, 13, 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, 275, 7, 1, 5, 0]], "char_orbit_index": 13, "prim_orbit_index": 7, "minimal_twist": "825.2.m.b", "char_is_minimal": true, "conrey_index": 16, "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], [0, 0, 0, 0], [0, -1, 0, 0], [0, 0, -2, 0], [2, -1, 2, 0], [0, 0, 0, 0], [1, -1, 0, 3], [0, 0, 0, 0], [0, 0, 1, 0], [0, 0, 0, 0], [2, 2, -1, 0], [0, 0, 0, 2], [0, 1, -4, 1], [0, 0, 0, 0], [0, -2, 1, -2], [-4, 4, -4, 4], [0, 2, 3, 2], [0, 0, 0, 0], [-4, 4, 0, -1], [4, -4, 0, -2], [3, -4, 4, -3], [0, 0, 0, 0], [0, 1, 3, 1], [0, 0, 0, 0], [0, 0, 5, 0], [0, 0, 0, 0], [0, 0, 0, -1], [6, 0, -2, 2], [0, -6, 2, -6], [0, 0, 0, 0], [-2, 0, 0, 0], [0, 0, 0, 0], [0, -2, -2, 1], [0, 0, 0, 0], [-1, -6, 6, 1], [2, -2, 2, -2], [2, 7, 2, 0], [0, 0, 0, 0], [1, -1, 0, 3], [0, 0, 0, 0], [5, 0, 2, -2], [0, 0, 0, 0], [5, 0, 2, -2], [-2, 2, -6, -2], [-2, 2, 0, 1], [0, 0, 0, 0], [1, -3, 1, 0], [4, 0, 0, 0], [7, -10, 7, 0], [0, 0, 0, 0], [2, -2, 0, -5], [-6, 8, -8, 6], [0, 0, 0, -9], [0, 0, 0, 0], [6, 0, 2, 3], [0, 0, 0, 0], [-1, 5, -5, 1], [0, 0, 0, 0], [2, 9, 2, 0], [-2, -2, 2, 2], [8, -8, 0, -9], [0, 0, 0, 0], [-3, 0, 1, -1], [0, 8, 0, 0], [7, -7, 0, -1], [0, 0, 0, 0], [-2, 1, -2, 0], [10, -6, 6, -10], [1, -1, 0, -4], [0, 0, 0, 0], [-9, 0, -4, 4], [0, 0, 0, 0], [-4, 0, -6, 6], [0, 0, 0, 0], [0, 0, 0, -5], [-2, 0, 8, -8], [-1, 6, -9, 13], [0, 0, 0, 0], [5, -5, 0, 4], [-4, 0, -8, 8], [-1, 1, -1, 1], [0, 0, 0, 0], [0, -5, 9, -5], [2, -8, 2, 0], [-8, 8, 0, 9], [0, 0, 0, 0], [-6, 6, 0, 4], [0, 0, 0, 0], [0, -6, 9, -6], [0, 0, 0, 0], [10, 0, -7, 7], [8, -6, 6, -8], [0, 2, 0, 0], [0, 0, 0, 0], [-7, 13, -13, 7], [0, 0, 0, 0], [1, -1, 0, 5], [0, 0, 0, 0], [1, -1, 3, 1], [10, -10, 10, -10]]}