# Stored data for newform 275.2.a.d, downloaded from the LMFDB on 20 April 2024. {"label": "275.2.a.d", "space_label": "275.2.a", "level": 275, "weight": 2, "hecke_orbit": 4, "hecke_orbit_code": 13510798915666195, "dim": 2, "is_polredabs": true, "nf_label": "2.2.5.1", "trace_hash": 485543978146253645, "analytic_rank": 1, "is_twist_minimal": true, "hecke_cutters": [[2, [-1, 1, 1]]], "qexp_display": "q-\\beta q^{2}+(-1-\\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": 1100, "fricke_eigenval": 1, "atkin_lehner_string": "--", "analytic_conductor": 2.1958860555852104, "hecke_ring_index": 1, "level_radical": 55, "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": "0.012", "prec": 17}, "analytic_rank_proved": true, "char_values": [275, 1, [177, 101], [1, 1]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 1, "level_primes": [5, 11], "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": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.964", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "9.654", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "66.964", "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], [11, -1]], "trace_display": [-1, -3, 0, -1], "traces": [0, 2, -1, -3, -1, 0, 4, -1, 0, 1, 0, 2, -1, -8, -7, 0, -3, -1, -8, 0, 0, -6, -1, -3, -5, 0, 9, 0, 8, -5, 0, -6, 9, -3, -2, 0, 7, -16, 15, 17, 0, -6, 13, 12, -1, 0, -11, -6, 12, 9, 0, -1, -1, -3, 5, 0, 15, 15, 0, 10, 0, -11, 3, 22, 4, 0, 4, -16, 3, -8, 0, -6, 15, -23, 13, 0, -15, -1, -26, 5, 0, 2, 3, 27, -7, 0, -6, 5, 0, -25, 0, -11, 14, 9, 23, 0, -11, -1, 3, 1, 0, -1, 3, -13, -10, 0, 19, 4, -5, 5, 0, 29, -21, -8, -30, 0, 5, -19, 5, 8, 0, 2, -7, 9, 3, 0, -11, -1, -25, -18, 0, 9, -1, -45, 8, 0, 5, 9, 19, -20, 0, 29, -22, -8, -24, 0, 9, -6, 3, 0, 0, -6, -30, 7, -7, 0, 9, -16, -10, 22, 0, 39, 14, 7, 3, 0, -6, 24, -20, 16, 0, -45, -6, 2, -5, 0, -3, -5, 0, -25, 0, -1, 33, 4, 25, 0, -12, -1, -17, -15, 0, -31, -11, -8, 3, 0, -12, 29, -8, 5, 0, 24, 13, 10, -2, 0, 4, 36, 27, 0, 0, 34, -16, -16, -7, 0, -10, 3, 10, 32, 0, -1, -42, 2, -12, 0, -31, 19, 15, -5, 0, -6, 5, 7, 42, 0, -15, -15, 1, 15, 0, 9, -1, 12, 18, 0, -12, 30, 0, -33, 0, -21, -11, -3, -2, 0, 7, 4, 24, -7, 0, 5, -17, 42, -5, 0, 15, 25, 8, 45, 0, 4, -6, 44, 18, 0, -11, 14, -5, -3, 0, -6, -52, 17, 28, 0, 9, 3, -3, -31, 0, 4, 14, 12, 3, 0, -10, 0, 20, -13, 0, -6, 3, 14, 45, 0, -1, -11, 8, 17, 0, -16, 35, 2, -22, 0, 5, -31, -41, -5, 0, -11, -2, -15, -16, 0, -11, 5, 0, -57, 0, -16, -21, -23, 3, 0, 39, 24, -48, -23, 0, -6, 30, -20, 0, 0, -11, -21, 0, -10, 0, 10, 9, 2, 0, 0, 25, -7, 15, 0, 0, 52, 13, -3, -22, 0, 3, -21, -33, -3, 0, -51, 3, -28, -2, 0, -40, 15, 5, -40, 0, -1, 28, -28, 40, 0, 24, 6, -2, 20, 0, 14, -15, -26, -27, 0, 7, -41, 10, 60, 0, 24, -32, 24, -12, 0, 15, -16, -5, 0, 0, 9, 9, -35, -13, 0, -31, 15, 15, 20, 0, 9, -17, -63, -35, 0, 38, 43, 3, 17, 0, 24, 15, 2, 21, 0, -15, -75, -41, -35, 0, -18, 8, 42, 13, 0, 39, 20, 13, -15, 0, -6, 39, 9, -42, 0, 45, -31, -30, -5, 0, 4, 13, 22, 0, 0, 39, -66, -23, 8, 0, -6, -20, 12, 25, 0, -9, -54, -5, 30, 0, 74, -42, -41, -1, 0, -41, 34, 25, -18, 0, -36, 3, 5, -75, 0, 9, 78, 39, 35, 0, -21, 48, -18, 0, 0, -11, -64, 3, 35, 0, 19, 24, 30, -22, 0, -6, -6, 61, -13, 0, -26, 15, -28, 8, 0, -21, 3, 12, 21, 0, -25, 30, 24, -25, 0, 0, 40, -40, 9, 0, -51, -27, 14, -7, 0, -77, 49, -27, 32, 0, -15, -30, 20, -17, 0, 25, 24, 24, -48, 0, -1, 53, -3, 23, 0, -6, -46, 50, 55, 0, 39, -1, 59, 21, 0, 17, -11, 18, 32, 0, -36, -7, -3, 5, 0, -46, -21, 3, 0, 0, -56, 39, -18, 5, 0, -20, 5, 49, -15, 0, -11, -42, -8, 3, 0, -27, -16, 15, 5, 0, 64, -6, -33, 68, 0, 15, 54, -21, -10, 0, -25, 33, 50, -78, 0, -6, 15, 38, 3, 0, 39, 15, -51, 18, 0, 19, -21, 0, 72, 0, -6, 18, -48, -37, 0, 0, -56, -30, 10, 0, 18, 4, 27, -15, 0, 9, -4, 41, -15, 0, -76, 33, 9, -15, 0, 74, 20, -27, 37, 0, -11, -17, 22, 18, 0, 32, -26, 54, -7, 0, -61, 3, 42, 15, 0, 25, -25, -18, 47, 0, 49, 9, 22, 33, 0, 5, 3, -55, 32, 0, 44, -25, 30, 4, 0, 49, -37, 5, -20, 0, 25, 25, 9, 6, 0, 10, -20, 10, 0, 0, 14, -26, -51, -12, 0, 4, 49, -55, -59, 0, -6, -7, -38, 3, 0, -26, -16, 24, -65, 0, -105, 28, -53, 15, 0, -11, -9, 3, 13, 0, -11, 69, 69, -10, 0, 10, 34, 15, -8, 0, 24, 3, -40, 3, 0, -6, -20, -33, -10, 0, -26, -16, -43, -48, 0, -5, 68, 0, 0, 0, -6, 3, -5, 9, 0, 43, -56, -2, -63, 0, 109, 15, 19, 8, 0, -15, -31, -75, -17, 0, 25, -62, -23, 8, 0, -27, -85, -25, -60, 0, 34, -25, -31, 13, 0, 9, 0, -45, -88, 0, -36, -27, -28, 5, 0, -25, -6, -23, 15, 0, -31, -26, -12, -10, 0, -15, 0, -35, -5, 0, -43, 33, 59, -17, 0, 64, -1, 57, -23, 0, -1, -22, -93, 26, 0, 10, 84, -26, 10, 0, 18, 13, -48, 5, 0, -41, 49, -24, 5, 0, 64, -25, -8, 15, 0, 9, -36, -20, -58, 0, 9, -21, 32, -7, 0, -56, 14, 55, 8, 0, 2, -41, 120, -40, 0, 5, 62, 25, 15, 0, -16, 3, -36, 70, 0, -12, 24, 23, -38, 0, -36, -90, 27, -37, 0, 35, 33, 0, 20, 0, 79, 23, -26, -7, 0, 39, 1, -25, 60, 0, 45, -46, 49, 43, 0, -65, 24, 56, -8, 0, -6, 28, 9, 15, 0, -6, 34, -10, 87, 0, 49, -10, -8, 47, 0, -10, 5, -45, -72, 0, -44, -97, 17, 33, 0, 43, -41, 0, 15, 0, 59, 29, 55, -47, 0, -21, -56, 29, -25, 0, -35, -7, 12, 15, 0, 5, 98, 45, -18, 0, 9, -27, 49, -4, 0, -6, -71, -45, 10, 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": "275.2.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], [-1, -1], [-1, 1], [0, 0], [1, 2], [-2, 3], [-1, 2], [-1, 3], [0, 0], [1, 0], [0, -1], [-3, -2], [-3, -1], [0, 0], [0, -3], [-1, 1], [-3, -2], [3, -6], [0, 0], [-1, -4], [0, -1], [-4, 5], [-1, -3], [0, 0], [2, 5], [1, -2], [5, -2], [-3, 1], [0, 0], [-3, 0], [5, -1], [-1, -1], [-1, 0], [0, 0], [4, -1], [-7, -2], [6, 3], [5, 7], [0, 0], [-3, 0], [4, 5], [6, 0], [-1, 1], [0, 0], [-5, -1], [1, -8], [3, 6], [6, -3], [0, 0], [0, -1], [1, -3], [2, -7], [2, 1], [0, 0], [8, -1], [3, 9], [-1, 2], [7, -4], [0, 0], [-8, 5], [0, 3], [11, 0], [1, 2], [0, 0], [1, 2], [-8, 0], [2, -1], [-1, -6], [0, 0], [-8, 10], [7, 1], [-12, 1], [2, 9], [0, 0], [-9, 3], [-2, 3], [-7, -12], [1, 3], [0, 0], [4, -6], [0, 3], [15, -3], [-3, -1], [0, 0], [0, -6], [2, 1], [-1, 2], [-15, 5], [0, 0], [0, -11], [9, -4], [3, 3], [8, 7], [0, 0], [-4, -3], [0, -1], [3, -3], [-1, 3], [0, 0]]}