# Stored data for newform 403.2.k.c, downloaded from the LMFDB on 20 April 2024.
{"label": "403.2.k.c", "space_label": "403.2.k", "level": 403, "weight": 2, "hecke_orbit": 3, "hecke_orbit_code": 9007886483063187, "dim": 4, "is_polredabs": true, "nf_label": "4.0.125.1", "trace_hash": 312746826060748092, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[2, [1, -4, 6, 1, 1]]], "qexp_display": "q+(-1+2\\zeta_{10}-\\zeta_{10}^{2})q^{2}+(1-\\zeta_{10}^{3})q^{3}+\\cdots", "char_order": 5, "char_parity": 1, "char_degree": 4, "char_conductor": 31, "char_orbit_label": "k", "char_is_real": false, "Nk2": 1612, "analytic_conductor": 3.2179712014575994, "hecke_ring_index": 1, "level_radical": 403, "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": [403, 5, [249, 313], [5, 3]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 2, "level_primes": [13, 31], "conrey_indexes": [66, 157, 287, 326], "field_disc": 125, "field_disc_factorization": [[5, 3]], "field_poly": [1, -1, 1, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.889", "prec": 17}, {"__RealLiteral__": 0, "data": "0.094", "prec": 17}, {"__RealLiteral__": 0, "data": "45.661", "prec": 20}, {"__RealLiteral__": 0, "data": "5.332", "prec": 17}, {"__RealLiteral__": 0, "data": "1003.927", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "1.2.3.c5", "trace_display": [-1, 3, 6, -9], "traces": [0, 4, -1, 3, -9, 6, -2, -9, 13, 4, 1, 3, -3, 1, 21, 7, 1, -1, 4, -10, -6, -3, -2, 12, 6, -6, 6, 9, 9, 10, 2, 4, -30, 11, -1, -6, -24, -26, 10, 2, 7, 5, 12, -2, 12, 1, 12, 1, -13, 16, 9, -2, -6, -28, -16, 7, -78, -20, 5, 0, -12, 44, 29, -24, 13, 4, 1, -18, 6, 4, 9, 2, 13, 11, 4, 3, -30, 12, 2, 9, -11, 16, -5, -14, -27, 1, 23, 20, 16, -11, 1, -6, -72, 23, 66, -30, -15, -12, -84, -2, 36, 5, 3, -25, -13, -12, -28, 24, 6, -18, -3, -22, 39, -13, -10, 8, 0, -4, 20, 6, -1, -18, -11, 10, -9, -24, 21, 10, 8, -4, 4, -4, 9, -30, 2, 11, -7, 12, -16, 29, -9, 17, 2, 7, 41, 25, -34, -13, 51, 40, 18, -5, -30, -1, 12, 16, -12, -27, 9, -1, -30, -72, 26, -28, 15, 29, -34, -41, -21, -1, 1, 0, -48, 39, 5, 36, -23, 5, 34, 15, -6, 68, -21, 33, 24, -44, 8, 8, -51, 6, 0, -72, 26, 40, 48, 3, 39, -38, -2, 32, -57, -16, 5, 0, -3, 15, 25, 12, 14, 20, 3, -28, 168, 14, 24, -13, 68, -9, 12, -13, 33, 1, 8, -56, 90, -21, 22, 27, 0, -22, 8, 9, 10, -5, 11, 19, -15, 8, -9, 46, -12, -3, 52, 20, -99, 19, 5, -20, -47, -28, 1, -41, 99, 24, 20, -3, 27, 11, -9, 51, -9, -5, -14, 3, 17, -27, -30, 13, 33, -15, -9, 42, -14, -12, -108, 3, -24, -17, -106, -26, -42, -25, 17, 10, -12, -60, 2, 15, -45, 16, 5, 36, -36, 34, -13, 5, -72, -37, -15, -12, -18, -48, 40, 15, 100, 66, -11, 37, -27, -50, 11, -52, -1, -26, -102, -6, -54, 17, 29, -15, 22, 13, 48, -10, -36, 6, -28, -6, 15, -51, 4, -48, 54, -21, -76, -32, 78, 17, -1, -21, -6, -27, 40, -3, -34, -4, -6, 56, -15, 12, -99, 11, -15, 46, 5, -12, 36, -3, -45, 2, 7, 39, -12, 4, 36, -1, -22, -28, 108, 0, -9, 168, -33, -50, 3, -23, -148, 10, 96, -15, -30, 10, 13, 32, 26, 33, -75, -7, 72, 65, 3, -8, 197, -48, 67, 1, -3, 12, 12, 0, -39, 38, 4, 1, -30, 34, 0, -22, -14, 24, 0, -21, -75, -15, 72, -26, 0, -12, 20, 8, -18, -51, 27, -49, -31, 9, -16, -99, -144, 14, 7, 0, -49, 2, -99, 50, 18, -40, -23, -12, 34, 71, -4, 61, 27, 1, 9, 25, -63, -65, -21, -10, -12, 55, -48, -9, 10, -30, 43, 4, -48, 25, 9, 8, -20, 47, 70, 12, 9, 33, 34, -54, -45, 11, -17, -30, -36, -28, 46, -4, -30, -9, -13, -24, -12, 12, -25, -14, 143, -21, -26, -12, 0, 10, 0, -8, 61, -12, 2, -35, 39, -82, 54, -23, -153, -10, 4, -2, -30, 62, 2, -36, 61, 40, 11, -75, -21, 37, -114, 18, -7, 76, 10, 47, -66, -18, 38, 19, -46, 39, -27, -15, 180, 10, 23, 11, -46, -15, 60, 22, 39, -27, 42, 56, 15, -42, 3, 2, 63, 44, 3, -30, 48, -54, -22, -53, 36, -32, 64, -18, 36, 11, -110, 136, -102, -17, -30, -36, 44, 49, -20, -9, 3, -59, 15, -48, -17, 47, -64, 50, 15, 54, 36, -106, 112, -1, 34, 73, 78, -30, 10, -56, 6, 63, -22, -6, -105, 19, 28, 54, -39, 47, -48, -13, 90, -32, -20, 51, 30, -15, 11, -16, 21, -63, 42, 30, -21, 33, -25, -78, 24, 72, -22, 36, 13, -16, 44, -30, 177, 4, 9, -28, 33, -1, -48, 30, 81, 29, -15, 2, 17, -11, -37, 49, 252, -26, -20, 20, -8, 10, -24, -33, 168, 5, -6, -26, -50, 46, -246, -21, 21, 20, -153, -3, 22, -30, -21, 20, 111, -47, -7, 33, 0, 4, -53, -21, 6, 42, 9, 72, -8, 54, -12, -96, -30, 3, 192, -44, 132, 28, -4, -20, -54, -3, 16, 46, 15, 5, 12, 15, -81, -1, 16, 80, -9, 18, 116, -30, -30, 16, -12, 9, -112, -28, -18, 18, -45, 32, -68, 70, 14, -75, -56, -41, -138, 15, 4, -29, 18, -53, -11, -2, -33, -13, 67, 3, -120, -16, -20, -54, 39, -20, -87, 112, 36, 50, -5, 16, -3, -144, 2, -20, 179, -7, 5, 25, -81, 16, -10, 28, -50, 3, 10, 18, 147, 1, -118, -5, 9, -128, 18, 7, 15, -55, 78, 24, -144, 27, 65, -10, -18, -76, -28, -15, -271, -38, -18, 49, -27, 11, 1, -12, 6, 11, -48, 26, -57, -74, 30, 16, 90, -46, 133, 27, 21, -48, -4, -30, 50, 47, 14, 80, 0, -11, 13, -7, 12, -10, -51, 9, 15, -78, -21, -19, -75, 21, -75, 55, -132, -29, -16, -34, -8, -29, -12, -84, -120, -21, 108, -53, -24, 49, -146, -50, 123, 1, 131, -12, -227, -10, 9, -68, 36, -37, 231, 10, 63, -27, 4, 34, -27, 0, -80, 70, -75, 96, -28, 32, 189, -12, 15, -7, -36, -72, 80, 39, 33, 97, 8, 43, -57, 80, -184, -30, -6, 5, 61, -41, -29, -30, 11, -18, 111, -140, -30, 0, 27, -4, 150, -10, 126, 27, -10, -21, -96, 112, 35, -48, 123, 5, -9, 52, 70, 12, -30, 77, -108, -66, 9, -41, -4, 29, -10, -2, -54, 24, 118, 0, -45, 132, 12, 40, -45, -74, 72, 22, -38, 13, -72, -2, -54, -12, 16, 20, 55, 39, 11, -11, -3, -1, -60, -11, 57, -31, -143, -118, -276, 25, -4, 63, 44, -76, -34, 24, -57, 45, 96, 32, -126, -10, 12, 31, -105, 36, -14, -3, 11, 59, 49, -27, -9, -18, -32, 33, -5, -47, 0, -102, 30, -36, -3, 54, 0, -96, 48, 83, 48, 40, 30, -56, -53], "weight_parity": 1, "has_non_self_twist": 1, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": false, "level_is_squarefree": true, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 31, 4, 1, 5, 0]], "char_orbit_index": 11, "prim_orbit_index": 4, "minimal_twist": "403.2.k.c", "char_is_minimal": true, "conrey_index": 66, "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], [-1, 2, -1, 0], [1, 0, 0, -1], [0, -3, 3, -3], [2, 0, 1, -1], [0, 0, 1, -1], [0, -3, 3, -3], [4, -4, 0, 1], [1, -1, 0, 1], [0, 1, 0, 0], [0, 2, 1, 2], [0, -3, 0, 0], [1, -1, 1, -1], [6, -6, 0, 3], [3, -1, 1, -3], [-5, 8, -8, 5], [0, 0, 0, -1], [-2, 5, -5, 2], [-2, -4, -2, 0], [0, -3, 0, -3], [0, -3, 0, 0], [-1, 1, 0, 1], [4, -4, 0, 0], [0, 1, -4, 1], [0, 0, 3, -3], [1, 0, -1, 1], [0, 4, -1, 4], [-9, 18, -18, 9], [3, 1, 3, 0], [1, 0, 1, -1], [3, -2, 6, 0], [-6, 0, 3, -3], [3, 2, 3, 0], [1, -2, 2, -1], [0, -3, 0, -3], [-3, 0, 6, -6], [-7, 0, -1, 1], [0, 2, -6, 2], [1, -1, 0, -1], [3, -3, 0, -2], [1, 2, 1, 0], [0, 3, -6, 3], [1, -5, 1, 0], [6, -3, 3, -6], [0, 0, 0, 1], [-4, 12, -12, 4], [7, -10, 10, -7], [-5, 5, 0, 2], [-2, 11, -11, 2], [6, -9, 6, 0], [0, -1, 0, -1], [-3, 3, -3, 0], [-11, 11, 0, 5], [-5, 5, 0, -1], [0, 5, 3, 5], [-12, 0, 15, -15], [-8, 0, -6, 6], [0, 2, -1, 2], [2, -3, 3, -2], [-3, -3, -3, 0], [11, 0, 0, 0], [3, 2, -7, 8], [-3, 0, 6, -6], [6, -5, 6, 0], [2, -1, 1, -2], [0, 1, 1, 1], [-5, 0, -1, 1], [0, 0, -3, 3], [0, 0, -4, 0], [3, -3, 0, 0], [-2, 2, 0, 8], [9, -14, 9, 0], [0, 2, -7, 2], [5, -11, 5, 0], [3, -3, 3, -3], [-12, 12, 0, 6], [6, -3, 3, -6], [0, 1, -1, 0], [2, -2, 0, 3], [-7, 5, -5, 7], [6, -2, 6, 0], [0, -1, 3, -1], [-6, 4, -6, 0], [-9, 9, 0, 0], [1, -1, 0, -2], [0, 6, -11, 6], [7, 0, 4, -4], [5, 0, 2, -2], [0, -2, 7, -2], [-1, 2, -2, 1], [-3, 3, -3, 0], [-12, 0, 12, -12], [7, 0, 4, -1], [10, 0, -13, 13], [-8, -6, -8, 0], [-3, -3, 3, 3], [0, 0, 12, 0], [-11, 0, 20, -20], [-1, 0, -1, 1], [0, 9, -18, 9]]}