# Stored data for newform 225.4.a.b, downloaded from the LMFDB on 25 April 2024.
{"label": "225.4.a.b", "space_label": "225.4.a", "level": 225, "weight": 4, "hecke_orbit": 2, "hecke_orbit_code": 4503599694479585, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 2052512481258298677, "analytic_rank": 1, "is_twist_minimal": false, "hecke_cutters": [[2, [4, 1]], [7, [6, 1]]], "qexp_display": "q-4q^{2}+8q^{4}-6q^{7}-2^{5}q^{11}+38q^{13}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 3600, "fricke_eigenval": -1, "atkin_lehner_string": "-+", "analytic_conductor": 13.275429751291638, "hecke_ring_index": 1, "level_radical": 15, "field_poly_is_cyclotomic": false, "field_poly_root_of_unity": 0, "field_poly_is_real_cyclotomic": false, "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": "0.002", "prec": 17}, "analytic_rank_proved": true, "char_values": [225, 1, [101, 127], [1, 1]], "hecke_ring_generator_nbound": 1, "inner_twist_count": 1, "level_primes": [3, 5], "conrey_indexes": [1], "field_disc": 1, "field_disc_factorization": [], "field_poly": [0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "0.977", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.919", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "4.742", "prec": 17}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "3.2.3.c1", "atkin_lehner_eigenvals": [[3, -1], [5, 1]], "trace_display": [-4, 0, 0, -6], "traces": [0, 1, -4, 0, 8, 0, 0, -6, 0, 0, 0, -32, 0, 38, 24, 0, -64, 26, 0, 100, 0, 0, 128, -78, 0, 0, -152, 0, -48, 50, 0, -108, 256, 0, -104, 0, 0, -266, -400, 0, 0, -22, 0, -442, -256, 0, 312, -514, 0, -307, 0, 0, 304, 2, 0, 0, 0, 0, -200, -500, 0, -518, 432, 0, -512, 0, 0, -126, 208, 0, 0, -412, 0, 878, 1064, 0, 800, 192, 0, 600, 0, 0, 88, 282, 0, 0, 1768, 0, 0, 150, 0, -228, -624, 0, 2056, 0, 0, -386, 1228, 0, 0, -702, 0, 598, 0, 0, -8, -1194, 0, -550, 0, 0, 384, 1562, 0, 0, 400, 0, 2000, -156, 0, -307, 2072, 0, -864, 0, 0, -1846, 0, 0, 0, 2208, 0, -600, 504, 0, 0, -2334, 0, -700, 0, 0, 1648, -1216, 0, 0, -3512, 0, -2128, -2050, 0, 1852, 0, 0, -768, 0, 0, 2494, -2400, 0, 0, 468, 0, -2762, -176, 0, -1128, 3126, 0, -753, 0, 0, -3536, -78, 0, 0, 2048, 0, -600, 1300, 0, 1742, 912, 0, 0, 0, 0, -832, -4112, 0, 0, -3772, 0, 358, 1544, 0, -2456, -2214, 0, -2600, 0, 0, 2808, -300, 0, 0, -2392, 0, -2432, -3200, 0, -1168, 16, 0, 4776, 0, 0, 648, 2200, 0, 0, 988, 0, 6478, -1536, 0, -6248, 646, 0, 3750, 0, 0, 0, 1482, 0, 0, -4000, 0, 624, -1400, 0, 3022, 1228, 0, -4144, 0, 0, 3800, 0, 0, 0, 1248, 0, 2496, 7384, 0, 4096, 2106, 0, 1596, 0, 0, -8832, -3638, 0, 0, 2400, 0, -1008, 6550, 0, -4388, -1664, 0, 9336, 0, 0, -546, 2800, 0, 0, 6858, 0, -9282, -3296, 0, 4864, 132, 0, -4237, 0, 0, 7024, 4842, 0, 0, 0, 0, 8200, -2964, 0, 2652, -7408, 0, -6400, 0, 0, 2594, 1536, 0, 0, -7332, 0, -1562, -9976, 0, 4800, 1426, 0, -1600, 0, 0, -1872, 2600, 0, 0, 11048, 0, 0, 3084, 0, -4008, 2256, 0, -12504, 0, 0, -8866, 3012, 0, 0, 3456, 0, 3900, 0, 0, 312, -1714, 0, 1150, 0, 0, -8192, -4398, 0, 0, 1200, 0, -5200, -1800, 0, 3141, -6968, 0, -1824, 0, 0, 5874, 4992, 0, 0, -12, 0, 2078, 3328, 0, 0, 1900, 0, 7900, 0, 0, 15088, -7518, 0, 0, -1432, 0, -3088, 1950, 0, -2028, 0, 0, 8856, 0, 0, -13786, 10400, 0, 0, -6402, 0, -4104, -5616, 0, 1200, 8512, 0, 11150, 0, 0, 4784, 3000, 0, 0, 9728, 0, 12800, 13700, 0, -5438, 4672, 0, 0, 0, 0, 3108, -9552, 0, 0, -7692, 0, 1118, -2592, 0, -4400, -7800, 0, -2600, 0, 0, -3952, -11958, 0, 0, -25912, 0, 3072, 17050, 0, 704, 12496, 0, -2584, 0, 0, 9494, -15000, 0, 0, 11418, 0, -7962, -3200, 0, -5928, 6526, 0, 756, 0, 0, 0, 14144, 0, 0, -1248, 0, 5600, -17400, 0, -10108, -12088, 0, -2456, 0, 0, -1166, 0, 0, 0, -7072, 0, 1300, -15200, 0, 6912, 2472, 0, 100, 0, 0, -4992, 2602, 0, 0, -9984, 0, -14768, -11150, 0, -5268, -16384, 0, -8424, 0, 0, 16448, -6384, 0, 0, 3638, 0, 2078, 17664, 0, 14552, -2808, 0, -6083, 0, 0, -4800, -836, 0, 0, 0, 0, -26200, 9824, 0, 5622, 17552, 0, 6656, 0, 0, -16486, -18672, 0, 0, 5000, 0, -3600, 2184, 0, -5600, 11706, 0, -16796, 0, 0, -27432, -25038, 0, 0, 37128, 0, 0, -17550, 0, 10712, -9728, 0, -528, 0, 0, 13654, 16948, 0, 0, -1692, 0, -64, 0, 0, -19368, 14166, 0, -10800, 0, 0, 17024, 17842, 0, 0, -16400, 0, 11856, 17600, 0, 27302, -10608, 0, 14816, 0, 0, 3794, 25600, 0, 0, -19532, 0, 13238, -10376, 0, 0, -11574, 0, 8300, 0, 0, 29328, -900, 0, 0, 6248, 0, 19952, -6916, 0, -7508, 0, 0, -5704, 0, 0, -11666, 6400, 0, 0, 27378, 0, -1842, 3744, 0, -10400, -10114, 0, 16000, 0, 0, -22096, 10402, 0, 0, 1408, 0, -12336, -7100, 0, -7118, 16032, 0, 0, 0, 0, -3900, 25008, 0, 0, 16576, 0, 31278, 35464, 0, -6024, -30054, 0, 2316, 0, 0, -13824, -4518, 0, 0, -15600, 0, 28288, 76, 0, 29272, -624, 0, 6856, 0, 0, -572, -4600, 0, 0, 5798, 0, -26600, 16384, 0, 17592, 4212, 0, 8950, 0, 0, 0, 8424, 0, 0, 10400, 0, 7200, -7800, 0, -3588, -12564, 0, 13936, 0, 0, 8554, 0, 0, 0, -11492, 0, -2882, -23496, 0, -19968, 4032, 0, 18700, 0, 0, 48, 12242, 0, 0, -8312, 0, -6656, 7164, 0, -31148, 32896, 0, -7600, 0, 0, 7694, -31600, 0, 0, 4518, 0, 3300, -30176, 0, 30072, -19000, 0, -39550, 0, 0, 2864, 22122, 0, 0, 0, 0, -7800, -2200, 0, 13184, 8112, 0, 19648, 0, 0, 16634, -17712, 0, 0, -9372, 0, -19684, 55144, 0, -20800, 27586, 0, -13364, 0, 0, 25608, -28096, 0, 0, 16416, 0, 0, -3850, 0, 10032, -2400, 0, -34048, 0, 0, -44200, -44600, 0, 0, -20562, 0, -10322, 0, 0, -12000, 8846, 0, -25350, 0, 0, -19456, -7982, 0, 0, -25600, 0, -54800, -46000, 0, -21889, 21752, 0, -9344, 0, 0, 1842, -128, 0, 0, 20748, 0, 16998, -12432, 0, 0, -26494, 0, -21500, 0, 0, 30768, 25762, 0, 0, -4472, 0, 5184, -19200, 0, -4788, 0, 0, 31200, 0, 0, -30546, 10400, 0, 0, -32942, 0, 27118, 7904, 0, 47832, -38634, 0, 11076, 0, 0, 51824, -51400, 0, 0, 0, 0, -68200, -5400, 0, 52, -2816, 0, 0, 0, 0, 1794, 5168, 0, 0, -41732, 0, -9024, -37976, 0, 30000, -13248, 0, 29200, 0, 0, -45672, -15656, 0, 0, 31848, 0, 12800, 48650, 0, -30700, 11856, 0, -26104, 0, 0, 11334, -3024, 0, 0, 31178, 0, 1716, 32000, 0, -56576, 4686, 0, 33364, 0, 0, 0, -598, 0, 0, -11200, 0, 69600, 14004, 0, -18127, 40432, 0, 24176, 0, 0, -41726, 0, 0, 0, -24312, 0, 4200, 4664, 0, 33152, 40946, 0, -4800, 0, 0, 28288, 42282, 0, 0, -5200, 0, 30400, 34476, 0, 1172, -27648, 0, -9888, 0, 0, 31614, -400, 0, 0], "weight_parity": 1, "has_non_self_twist": 0, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": true, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "5.4.a.a", "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], [1], [-4], [0], [8], [0], [0], [-6], [0], [0], [0], [-32], [0], [38], [24], [0], [-64], [26], [0], [100], [0], [0], [128], [-78], [0], [0], [-152], [0], [-48], [50], [0], [-108], [256], [0], [-104], [0], [0], [-266], [-400], [0], [0], [-22], [0], [-442], [-256], [0], [312], [-514], [0], [-307], [0], [0], [304], [2], [0], [0], [0], [0], [-200], [-500], [0], [-518], [432], [0], [-512], [0], [0], [-126], [208], [0], [0], [-412], [0], [878], [1064], [0], [800], [192], [0], [600], [0], [0], [88], [282], [0], [0], [1768], [0], [0], [150], [0], [-228], [-624], [0], [2056], [0], [0], [-386], [1228], [0], [0]]}