# Stored data for newform 275.2.a.e, downloaded from the LMFDB on 26 March 2023.
{"level_primes": [5, 11], "is_polredabs": true, "sato_tate_group": "1.2.3.c1", "rm_discs": [], "conrey_indexes": [1], "cm_discs": [], "trace_hash": 767742156726772763, "level_radical": 55, "hecke_ring_index_proved": true, "self_twist_type": 0, "related_objects": ["Genus2Curve/Q/75625/b"], "prim_orbit_index": 1, "is_cm": false, "hecke_orbit": 5, "analytic_conductor": 2.1958860555852104, "inner_twist_count": 1, "field_disc_factorization": [[13, 1]], "is_rm": false, "char_order": 1, "level_is_square": false, "weight_parity": 1, "label": "275.2.a.e", "field_poly_is_real_cyclotomic": false, "is_self_twist": false, "is_twist_minimal": true, "minimal_twist": "275.2.a.e", "field_poly_is_cyclotomic": false, "dim": 2, "trace_zratio": {"__RealLiteral__": 0, "data": "0.015", "prec": 17}, "traces": [0, 2, -1, -1, 3, 0, -6, -5, -6, 1, 0, -2, 5, -10, 9, 0, -3, -3, 6, -2, 0, -4, 1, 11, 3, 0, 5, -4, -14, -9, 0, 6, 7, 1, -18, 0, -5, -12, 1, 5, 0, -4, 15, 0, -3, 0, 1, 6, 8, 5, 0, 21, -15, -1, 15, 0, 15, 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19, -19, 0, -51, 0, -27, -20, 0, 24, -45, -8, -15, 0, 15, -6, -21, -9, 0, 5, 20, 90, -6, 0, 3, 40, -23, 7, 0, 41, -9, -27, 91, 0, 18, -5, -5, 11, 0, -53, 18, -7, 36, 0, -18, 6, -30, 90, 0, -18, -33, 32, -27, 0, 5, -73, 62, 11, 0, -40, -15, -20, -1, 0, -7, -40, -16, -18, 0, -15, 15, -40, -75, 0, 8, -44, 21, -68, 0, 14, -75, -6, -60, 0, -87, 60, -65, 51, 0, -18, 11, -52, 0, 0, 60, 8, -17, -24, 0, -64, -8, 11, -29, 0, 51, 3, 36, 68, 0, -31, 1, -10, 19, 0, 45, -17, -51, 100, 0, -5, -12, -33, 81, 0, 15, 4, 36, -28, 0, 112, 72, -35, 47, 0, 26, 30, -8, -25, 0, -15, 36, 12, -3, 0, -20, 15, -15, -18, 0, 60, -95, 3, -89, 0, 63, -19, -6, -21, 0, 15, 35, -31, -29, 0, 27, 68, 45, -7, 0, 35, 43, 40, -45, 0, 81, -12, 15, -26, 0, -23, -5, 31, 48, 0, -60, -61, 45, 50, 0], "hecke_ring_index_factorization": [], "nf_label": "2.2.13.1", "field_poly": [-3, -1, 1], "atkin_lehner_string": "++", "has_non_self_twist": 0, "atkin_lehner_eigenvals": [[5, 1], [11, 1]], "char_values": [275, 1, [177, 101], [1, 1]], "Nk2": 1100, "field_poly_root_of_unity": 0, "analytic_rank": 1, "char_orbit_label": "a", "weight": 2, "trace_display": [-1, -1, 0, -5], "analytic_rank_proved": true, "char_parity": 1, "level_is_squarefree": false, "hecke_ring_index": 1, "level_is_prime": false, "char_is_minimal": true, "qexp_display": "q-\\beta q^{2}+(-1+\\beta )q^{3}+(1+\\beta )q^{4}-3q^{6}+\\cdots", "self_twist_discs": [], "char_is_real": true, "field_disc": 13, "level_is_prime_power": false, "relative_dim": 2, "hecke_cutters": [[2, [-3, 1, 1]]], "space_label": "275.2.a", "level": 275, "is_self_dual": true, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "char_degree": 1, "char_conductor": 1, "char_orbit_index": 1, "hecke_ring_generator_nbound": 2, "hecke_orbit_code": 18014398543036691, "fricke_eigenval": 1, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.957", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "9.619", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "67.172", "prec": 20}], "id": null, "projective_field": null, "embedded_related_objects": null, "projective_image_type": null, "artin_image": null, "artin_field": null, "projective_image": null, "artin_field_label": null, "projective_field_label": null, "artin_degree": null, "qexp": [[0, 0], [1, 0], [0, -1], [-1, 1], [1, 1], [0, 0], [-3, 0], [-2, -1], [-3, 0], [1, -1], [0, 0], [-1, 0], [2, 1], [-5, 0], [3, 3], [0, 0], [-2, 1], [-3, 3], [3, 0], [-1, 0], [0, 0], [-1, -2], [0, 1], [6, -1], [3, -3], [0, 0], [0, 5], [-1, -2], [-5, -4], [-3, -3], [0, 0], [5, -4], [3, 1], [1, -1], [-9, 0], [0, 0], [-2, -1], [-5, -2], [0, 1], [5, -5], [0, 0], [-3, 2], [6, 3], [-2, 4], [-1, -1], [0, 0], [3, -5], [3, 0], [5, -2], [0, 5], [0, 0], [12, -3], [-5, -5], [0, -1], [6, 3], [0, 0], [6, 3], [1, -1], [9, 6], [-9, 4], [0, 0], [-4, 3], [12, -1], [1, 2], [1, -6], [0, 0], [3, 0], [4, 0], [6, 3], [-9, 6], [0, 0], [0, 2], [-3, 3], [4, -3], [6, 7], [0, 0], [-1, -1], [2, 1], [15, 0], [-7, 3], [0, 0], [-8, 2], [-6, 1], [-3, -5], [-7, -5], [0, 0], [-12, -2], [-6, -3], [3, 0], [3, 1], [0, 0], [10, 5], [3, 4], [-17, 5], [0, -3], [0, 0], [0, 3], [-14, 1], [-15, -5], [-1, 1], [0, 0]]}