# Stored data for newform 175.2.a.e, downloaded from the LMFDB on 23 April 2024.
{"label": "175.2.a.e", "space_label": "175.2.a", "level": 175, "weight": 2, "hecke_orbit": 5, "hecke_orbit_code": 18014398543036591, "dim": 2, "is_polredabs": true, "nf_label": "2.2.5.1", "trace_hash": 1106055822945171658, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[2, [-1, -1, 1]]], "qexp_display": "q+\\beta q^{2}+(-2+2\\beta )q^{3}+(-1+\\beta )q^{4}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 700, "fricke_eigenval": -1, "atkin_lehner_string": "+-", "analytic_conductor": 1.3973820353724067, "hecke_ring_index": 1, "level_radical": 35, "field_poly_is_cyclotomic": false, "field_poly_root_of_unity": 10, "field_poly_is_real_cyclotomic": true, "hecke_ring_index_proved": true, "self_twist_type": 0, "is_self_dual": true, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.024", "prec": 17}, "analytic_rank_proved": true, "char_values": [175, 1, [127, 101], [1, 1]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 1, "level_primes": [5, 7], "conrey_indexes": [1], "field_disc": 5, "field_disc_factorization": [[5, 1]], "field_poly": [-1, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.035", "prec": 17}, {"__RealLiteral__": 0, "data": "1.971", "prec": 17}, {"__RealLiteral__": 0, "data": "0.174", "prec": 17}, {"__RealLiteral__": 0, "data": "9.439", "prec": 17}, {"__RealLiteral__": 0, "data": "0.978", "prec": 17}, {"__RealLiteral__": 0, "data": "62.276", "prec": 20}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[5, 1], [7, -1]], "trace_display": [1, -2, 0, 2], "traces": [0, 2, 1, -2, -1, 0, 4, 2, 0, 6, 0, 4, 6, -2, 1, 0, -3, -4, -7, 0, 0, -2, 7, 8, -10, 0, -6, -20, -1, 10, 0, -6, -9, 6, -12, 0, -13, 6, 10, -8, 0, 14, 4, 8, 3, 0, -1, -4, -12, 2, 0, -16, -4, 8, 0, 0, 0, 20, 5, 10, 0, -6, -18, 6, 4, 0, 8, -4, -8, -18, 0, 4, 20, -22, 3, 0, 10, 4, -4, 0, 0, 22, 12, -2, 6, 0, 9, -10, -10, 30, 0, -2, -9, -24, -2, 0, 14, 6, 1, -8, 0, 14, -8, 8, 10, 0, -6, 16, 20, -10, 0, -6, -3, -2, 0, 0, -5, 14, -10, -4, 0, -4, 12, -4, -12, 0, -7, -4, 25, 2, 0, -16, 2, 0, 3, 0, 20, -4, 16, -10, 0, 4, -13, -14, 21, 0, -16, -2, -3, -10, 0, -36, -20, 28, 7, 0, 4, 6, 25, -28, 0, 8, -19, -12, -2, 0, 14, 6, -10, -14, 0, -40, 1, -32, 20, 0, -21, -40, 10, -20, 0, -6, -6, 36, 10, 0, -12, -28, 2, -20, 0, 4, 6, -2, -2, 0, -1, 6, -9, 10, 0, 14, 12, 10, 8, 0, -6, 44, 18, 20, 0, 24, -14, -34, 8, 0, -20, -6, -35, 12, 0, 24, 12, 18, -9, 0, 29, 16, -20, 0, 0, 6, 0, -2, 2, 0, -20, 50, -12, -20, 0, -16, 18, -22, 18, 0, 28, -20, 30, 32, 0, 4, -13, 6, -37, 0, 7, 6, 16, 6, 0, 30, 12, 28, -10, 0, 10, -40, 7, -10, 0, 34, 36, -8, 18, 0, 34, -4, -40, 42, 0, 14, -8, 8, -17, 0, -22, 14, -37, 14, 0, -16, 6, -22, 4, 0, 0, -20, -25, 2, 0, 8, -13, -4, -30, 0, 4, 36, 3, -28, 0, 4, 0, 48, 8, 0, 25, 6, 16, 20, 0, -16, -1, -40, -41, 0, -16, -50, -10, -4, 0, -36, 16, 18, -2, 0, -12, -24, 3, 62, 0, -42, 10, 2, -10, 0, -26, 36, 30, 0, 0, 0, -13, 18, 20, 0, -20, -16, 20, -20, 0, 2, -28, 44, -4, 0, -12, -34, 3, 22, 0, 8, 12, -22, -44, 0, 0, -10, 0, 0, 0, -66, -8, -62, -20, 0, -31, 4, -8, -30, 0, 4, 0, 56, 13, 0, -1, 36, 0, 20, 0, 14, -8, 36, -2, 0, 5, 12, 0, 40, 0, 44, -14, 10, -33, 0, 4, -60, 30, -30, 0, -26, 12, -12, 20, 0, 8, -6, -8, -16, 0, 44, 0, -12, -18, 0, -25, -20, -44, -30, 0, 6, 32, -12, 18, 0, -16, -30, 4, 50, 0, 38, 31, 46, -22, 0, 20, -34, 10, 0, 0, -6, 8, 8, -15, 0, -21, -4, -12, -4, 0, 4, 30, 26, 0, 0, -8, 64, -20, -30, 0, -6, -18, -18, 22, 0, 44, 16, -30, -8, 0, -16, 32, -20, -20, 0, 54, 4, -4, 40, 0, -16, -8, -52, 20, 0, 13, 34, -33, 50, 0, -22, -24, 40, 38, 0, 14, -8, 3, 12, 0, 44, -35, -12, 28, 0, 9, 72, -24, -4, 0, 90, 10, -24, 60, 0, -10, 80, 10, 4, 0, 14, 2, -44, 8, 0, -4, -24, 22, -78, 0, 0, -50, 0, 38, 0, -30, -54, 6, -18, 0, -32, 57, 8, -12, 0, -26, 22, 30, 10, 0, 24, -8, -24, 12, 0, -8, -4, 47, -58, 0, -2, 12, -4, 10, 0, 34, -54, 6, -60, 0, 14, -9, -12, -40, 0, -15, -20, -14, 0, 0, -56, 9, -32, 23, 0, 28, 26, 10, -10, 0, 4, -24, -62, 48, 0, -10, 6, 16, -10, 0, -100, -48, 30, 12, 0, 34, 20, 2, -12, 0, 24, -50, -24, -47, 0, 44, -2, 35, 72, 0, 34, 32, 28, -9, 0, -40, -4, 60, -10, 0, -24, -4, 68, -20, 0, -36, -46, -2, 0, 0, 4, -3, 16, -30, 0, -21, 40, -8, -68, 0, 18, 14, 48, -2, 0, 17, 16, -4, 6, 0, -76, -66, -12, 50, 0, 1, 20, -27, 12, 0, 14, 6, -8, 13, 0, -50, -48, -10, -38, 0, -76, 40, 0, 18, 0, 34, 14, 60, -60, 0, -100, 10, 6, -8, 0, 40, 0, 35, 10, 0, 8, 1, -4, -22, 0, -8, -24, 10, 66, 0, -36, -48, 8, 28, 0, -41, 2, -44, 20, 0, 0, -6, -12, 0, 0, 49, -66, -16, 16, 0, 24, 6, -24, -30, 0, 20, 66, 25, 14, 0, -16, -8, -10, -12, 0, -26, 20, 38, -10, 0, 64, -29, 78, -23, 0, 10, -6, -55, 20, 0, -22, -28, -100, -3, 0, -32, 86, 7, -38, 0, -2, 10, -24, 38, 0, -10, -44, 0, 8, 0, 110, 17, -54, -22, 0, 48, 40, -10, 50, 0, 4, -5, -64, 21, 0, 24, 20, 10, 14, 0, 4, -8, -32, 20, 0, -10, 16, -77, -60, 0, 84, -14, -4, -20, 0, 10, 0, 10, -30, 0, -8, -13, 86, -12, 0, 14, -4, 18, -68, 0, 24, 42, 28, 12, 0, 0, -54, -28, 0, 0, -4, 32, 68, 100, 0, 44, 66, -12, 50, 0, -6, 60, 38, 30, 0, -56, 16, -30, 112, 0, 34, -7, -52, 8, 0, 24, -74, -30, -4, 0, -16, -34, 0, -20, 0, 25, -32, 35, -30, 0, 24, 64, 2, -60, 0, -72, 16, -38, 22, 0, 24, 0, 26, -27, 0, 10, -16, 80, -60, 0, 24, 22, 26, 2, 0, 44, 64, -45, 90, 0, 0, -19, -104, -22, 0, 10, 66, 3, -28, 0, -6, 12, 46, 30, 0, 43, 16, -50, 32, 0, -106, 20, -2, -38, 0, 0, 30, 10, -4, 0, 46, -18, 48, -2, 0, 16, -64, -40, 0, 0, -36, 66, -10, 13, 0, -36, -14, -24, 50, 0, 90, -13, -2, -60, 0, -60, 4, 0, 22, 0, 4, 12, 66, -13, 0, -36, -64, 40, -60, 0], "weight_parity": 1, "has_non_self_twist": 0, "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]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "175.2.a.d", "char_is_minimal": true, "conrey_index": 1, "id": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0, 0], [1, 0], [0, 1], [-2, 2], [-1, 1], [0, 0], [2, 0], [1, 0], [1, -2], [5, -4], [0, 0], [1, 2], [4, -2], [0, -2], [0, 1], [0, 0], [0, -3], [0, -4], [-4, 1], [-2, 4], [0, 0], [-2, 2], [2, 3], [5, -2], [-6, 2], [0, 0], [-2, -2], [-12, 4], [-1, 1], [5, 0], [0, 0], [0, -6], [-5, 1], [2, 2], [-4, -4], [0, 0], [-9, 5], [3, 0], [4, 2], [-4, 0], [0, 0], [6, 2], [2, 0], [3, 2], [1, 1], [0, 0], [-2, 3], [-2, 0], [-6, 0], [1, 0], [0, 0], [-8, 0], [-2, 0], [6, -4], [4, -8], [0, 0], [1, -2], [12, -4], [0, 5], [8, -6], [0, 0], [-6, 6], [-6, -6], [5, -4], [1, 2], [0, 0], [2, 4], [-3, 2], [-4, 0], [-14, 10], [0, 0], [5, -6], [13, -6], [-10, -2], [0, 3], [0, 0], [6, -2], [1, 2], [0, -4], [-5, 10], [0, 0], [17, -12], [2, 8], [-4, 6], [4, -2], [0, 0], [2, 5], [-10, 10], [-3, -4], [16, -2], [0, 0], [0, -2], [-7, 5], [-12, 0], [0, -2], [0, 0], [12, -10], [4, -2], [0, 1], [-3, -2], [0, 0]]}