# Stored data for newform 425.4.d.b, downloaded from the LMFDB on 05 January 2025. {"Nk2": 6800, "analytic_conductor": 25.075811752439762, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 17, "char_degree": 1, "char_is_minimal": true, "char_is_real": true, "char_orbit_index": 4, "char_orbit_label": "d", "char_order": 2, "char_parity": 1, "char_values": [425, 2, [52, 326], [2, 1]], "cm_discs": [], "conrey_index": 101, "dim": 4, "field_disc": 461777121, "field_disc_factorization": [[3, 2], [13, 2], [19, 2], [29, 2]], "field_poly": [77284, 0, 575, 0, 1], "field_poly_is_cyclotomic": false, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 0, "has_non_self_twist": 1, "hecke_cutters": [[2, [1, 1]], [3, [19, 0, 1]]], "hecke_orbit": 2, "hecke_orbit_code": 4503805852909993, "hecke_ring_generator_nbound": 17, "hecke_ring_index": 2, "hecke_ring_index_factorization": [[2, 1]], "hecke_ring_index_proved": true, "inner_twist_count": 2, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 17, 2, 1, 2, 0]], "is_cm": false, "is_largest": false, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": false, "is_self_twist": false, "is_twist_minimal": true, "label": "425.4.d.b", "level": 425, "level_is_powerful": false, "level_is_prime": false, "level_is_prime_power": false, "level_is_prime_square": false, "level_is_square": false, "level_is_squarefree": false, "level_primes": [5, 17], "level_radical": 85, "minimal_twist": "425.4.d.b", "nf_label": "4.0.461777121.6", "prim_orbit_index": 2, "qexp_display": "q-q^{2}-\\beta _{2}q^{3}-7q^{4}+\\beta _{2}q^{6}+(\\beta _{1}+\\cdots)q^{7}+\\cdots", "related_objects": [], "relative_dim": 4, "rm_discs": [], "sato_tate_group": "3.2.3.c2", "self_twist_discs": [], "self_twist_type": 0, "space_label": "425.4.d", "trace_display": [-4, 0, 0, 0], "trace_hash": 1205657846722009385, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.601", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "64.965", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1642.776", "prec": 27}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.513", "prec": 17}, "traces": [0, 4, -4, 0, -28, 0, 0, 0, 60, 32, 0, 0, 0, -14, 0, 0, 164, 35, -32, 14, 0, -266, 0, 0, 0, 0, 14, 0, 0, 0, 0, 0, -644, -266, -35, 0, -224, 0, -14, 0, 0, 0, 266, 592, 0, 0, 0, 896, 0, -690, 0, 95, 98, 630, 0, 0, 0, 0, 0, 1008, 0, 0, 0, 0, -668, 0, 266, -2082, -245, -1064, 0, 0, 480, 0, 0, 0, -98, 200, 0, 0, 0, -1796, 0, -2142, 1862, 0, -592, 0, 0, 1862, 0, 0, 0, 3002, -896, 0, 0, 0, 690, 0, 0, -1638, -95, -2016, -210, 0, -630, 0, 0, 0, 0, 3724, 0, 0, 0, 0, 0, -112, -1008, -3626, 0, 3262, 0, -3458, 0, 0, 0, -3308, 5820, 0, 0, 0, 1862, 0, 2082, 0, 525, 2632, 1064, 0, 0, 0, 0, 0, 1312, 0, 0, 0, 0, -6402, 0, -8628, 210, 280, -200, 0, 0, 854, 0, 0, 0, 5324, 1796, 0, 0, 0, 2142, 0, -3990, 12750, 0, 112, -4144, 0, 0, 0, 0, 0, -1862, 1582, 0, 0, 0, 532, 0, 0, -3002, 4291, -6272, -9310, 0, -2324, 0, 0, 0, 0, 4830, 0, 0, 0, 0, 0, 1638, -9048, -665, 0, 2016, 0, -574, 0, 0, 0, -4410, 13566, 0, 0, 0, 2590, 0, 7638, 0, 10622, -3724, 14840, 0, 0, 0, 0, 0, -9170, 0, 0, 0, 0, 112, 0, -7056, -2926, 3626, 3136, 0, 0, -3262, 0, 0, 0, 3458, 21440, 0, 0, 0, -6174, 0, -12772, 3308, 0, -476, -1162, 0, 6248, 0, 0, 0, -1452, -3990, 0, 0, 0, 14574, 0, 0, -7308, 1435, -20558, -2632, 0, 7448, 0, 0, 0, 0, -2846, 0, 0, 0, 0, 0, -20020, -5152, -8295, 0, 11096, 0, -9464, 0, 0, 0, -9310, 6402, 0, 0, 0, 8628, 0, 574, 0, -280, -14490, -1400, 0, 0, 0, 0, 0, -854, 0, 0, 0, 0, 9048, 0, -15960, -5324, 10867, 12572, 0, 0, 25004, 0, 0, 0, -10742, 14994, 0, 0, 0, -10906, 0, -12750, -15694, 0, 18424, -112, 0, 8880, 0, 0, 0, 0, 2674, 0, 0, 0, 39942, 0, 0, -13034, -13072, -1582, -29236, 0, -5898, 0, 0, 0, 0, -532, 0, 0, 0, 0, 0, -21014, -26498, -4291, 0, 13440, 0, 9310, 0, 0, 0, 2324, 5740, 0, 0, 0, 4736, 0, 5520, 0, 32998, -10350, 14098, 0, 0, 0, 0, 0, -22420, 0, 0, 0, 0, 11466, 0, 9048, 19820, 1425, 25228, 0, 0, 14112, 0, 0, 0, 2254, 30856, 0, 0, 0, -34450, 0, 7168, 9450, 0, -13566, -45640, 0, 22420, 0, 0, 0, -23002, -2590, 0, 0, 0, -7638, 0, 0, -5520, -10622, -17626, -26068, 0, -14840, 0, 0, 0, 0, -4186, 0, 0, 0, 0, 0, -13268, 9170, 3325, 0, -7252, 0, 20104, 0, 0, 0, -20440, 784, 0, 0, 0, 15120, 0, 2926, 0, 25382, 5040, -3136, 0, 0, 0, 0, 0, -22834, 0, 0, 0, 0, 29260, 0, -36872, 24206, -31668, -21440, 0, 0, 46350, 0, 0, 0, 23940, 6174, 0, 0, 0, 12772, 0, 23156, -462, 0, 50484, -46084, 0, 1162, 0, 0, 0, -6248, 20824, 0, 0, 0, 43722, 0, 0, 1452, -31462, -10906, -38612, 0, 8064, 0, 0, 0, 0, -31230, 0, 0, 0, 0, 0, 7308, 20140, -5635, 0, 20558, 0, -18424, 0, 0, 0, -15960, 4462, 0, 0, 0, 27114, 0, -2072, 0, 8417, 2846, -56840, 0, 0, 0, 0, 0, -25162, 0, 0, 0, 0, 20020, 0, -5344, 25494, 8295, -13566, 0, 0, -11096, 0, 0, 0, 9464, 94374, 0, 0, 0, -73948, 0, 29764, 9310, 0, 44814, -53732, 0, 46084, 0, 0, 0, -16656, 60396, 0, 0, 0, -2254, 0, 0, -3136, -1960, 10734, 14490, 0, 3000, 0, 0, 0, 0, -37240, 0, 0, 0, 0, 0, 20558, -5978, -28406, 0, 28444, 0, -10640, 0, 0, 0, -148008, -9048, 0, 0, 0, 15960, 0, -37268, 0, -10867, -36344, -26940, 0, 0, 0, 0, 0, -25004, 0, 0, 0, 0, -3514, 0, 42462, 10742, -75544, -32130, 0, 0, 72384, 0, 0, 0, 49364, 42826, 0, 0, 0, -89250, 0, 15694, 7168, 0, 64638, -18424, 0, -784, 0, 0, 0, 24272, 148218, 0, 0, 0, 1600, 0, 0, 0, -23387, -2674, -17024, 0, 15652, 0, 0, 0, 0, -39942, 0, 0, 0, 0, 0, 27930, 105364, 13072, 0, -11074, 0, 29236, 0, 0, 0, 5898, 43358, 0, 0, 0, 80416, 0, -86188, 0, 5180, -3724, -56798, 0, 0, 0, 0, 0, -8488, 0, 0, 0, 0, 45030, 0, 26498, -17136, -30037, -103362, 0, 0, 36736, 0, 0, 0, 65170, 112508, 0, 0, 0, -74088, 0, 62632, 16268, 0, -5740, -175440, 0, 22400, 0, 0, 0, -43974, -4736, 0, 0, 0, -5520, 0, 0, 48612, -32998, 0, -28290, 0, -14098, 0, 0, 0, 0, -119396, 0, 0, 0, 0, 0, -64554, 22420, 7840, 0, 14896, 0, 2982, 0, 0, 0, -76152, -24570, 0, 0, 0, 63336, 0, -19820, 0, 3895, 2072, -25228, 0, 0, 0, 0, 0, -30240, 0, 0, 0, 0, 42070, 0, -18088, 2338, -81249, -30856, 0, 0, 105070, 0, 0, 0, 25172, 34450, 0, 0, 0, -7168, 0, 25830, 29450, 0, 106424, -94962, 0, 45640, 0, 0, 0, -22420, 148946, 0, 0, 0, -5568, 0, 0, 23002, -73549, -18130, -24944, 0, -143136, 0, 0, 0, 0, -53466, 0, 0, 0, 0, 0, 5520, 70514, -74354, 0, 17626, 0, 55860, 0, 0, 0, -103880, 3136, 0, 0, 0, 175636, 0, -63336, 0, 80724, 4186, -39368, 0, 0, 0, 0, 0, -13104, 0, 0, 0, 0, 13268, 0, 64190, 136430, -3325, -76332, 0, 0, 7252, 0, 0, 0, -20104, -16128, 0, 0, 0, -152838, 0, 69882, 20440, 0, -1680, -154952, 0, 21736, 0, 0, 0, 14924, 41328, 0, 0, 0, 20482, 0, 0, 32984, -54390, 39084, -5040, 0, -21952, 0, 0, 0, 0, -54834, 0, 0, 0, 0, 0, 36960, 48930, -74879, 0, 108066, 0, 92162, 0, 0, 0, -63752, -29260, 0, 0, 0, 36872, 0, -51870, 0, 31668, -59584, -150080, 0, 0, 0, 0, 0, -46350, 0, 0, 0, 0, 130340, 0], "weight": 4, "weight_parity": 1, "id": null, "artin_degree": null, "artin_field": null, "artin_field_label": null, "artin_image": null, "atkin_lehner_eigenvals": null, "atkin_lehner_string": null, "embedded_related_objects": null, "fricke_eigenval": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp": [[0, 0, 0, 0], [1, 0, 0, 0], [-1, 0, 0, 0], [0, 0, -1, 0], [-7, 0, 0, 0], [0, 0, 0, 0], [0, 0, 1, 0], [0, 1, -4, 0], [15, 0, 0, 0], [8, 0, 0, 0], [0, 0, 0, 0], [0, -1, -3, 0], [0, 0, 7, 0], [-3, -1, 1, 2], [0, -1, 4, 0], [0, 0, 0, 0], [41, 0, 0, 0], [9, 3, 0, 1], [-8, 0, 0, 0], [4, -1, 1, 2], [0, 0, 0, 0], [-67, 1, -1, -2], [0, 1, 3, 0], [0, -8, -10, 0], [0, 0, -15, 0], [0, 0, 0, 0], [3, 1, -1, -2], [0, 0, -35, 0], [0, -7, 28, 0], [0, 8, -4, 0], [0, 0, 0, 0], [0, 7, 36, 0], [-161, 0, 0, 0], [-66, -1, 1, 2], [-9, -3, 0, -1], [0, 0, 0, 0], [-56, 0, 0, 0], [0, 6, 46, 0], [-4, 1, -1, -2], [0, 19, -6, 0], [0, 0, 0, 0], [0, 7, -49, 0], [67, -1, 1, 2], [148, 0, 0, 0], [0, 7, 21, 0], [0, 0, 0, 0], [0, 8, 10, 0], [224, 0, 0, 0], [0, 0, -41, 0], [-176, 7, -7, -14], [0, 0, 0, 0], [22, 13, -17, -7], [21, 7, -7, -14], [161, -7, 7, 14], [0, 0, 35, 0], [0, 0, 0, 0], [0, 15, -60, 0], [0, 19, -13, 0], [0, -8, 4, 0], [248, 8, -8, -16], [0, 0, 0, 0], [0, 42, -14, 0], [0, -7, -36, 0], [0, 8, -32, 0], [-167, 0, 0, 0], [0, 0, 0, 0], [66, 1, -1, -2], [-524, 7, -7, -14], [-63, -21, 0, -7], [-262, -8, 8, 16], [0, 0, 0, 0], [0, 1, 178, 0], [120, 0, 0, 0], [0, -21, 111, 0], [0, -6, -46, 0], [0, 0, 0, 0], [-28, 7, -7, -14], [50, 0, 0, 0], [0, -19, 6, 0], [0, -13, -32, 0], [0, 0, 0, 0], [-449, 0, 0, 0], [0, -7, 49, 0], [-536, 1, -1, -2], [469, -7, 7, 14], [0, 0, 0, 0], [-148, 0, 0, 0], [-4, 8, -8, -16], [0, -15, -45, 0], [462, 7, -7, -14], [0, 0, 0, 0], [0, 63, -302, 0], [0, 56, 70, 0], [747, 7, -7, -14], [-224, 0, 0, 0], [0, 0, 0, 0], [0, 0, 161, 0], [0, 28, 132, 0], [176, -7, 7, 14], [0, -8, -24, 0], [0, 0, 0, 0]]}