# Stored data for newform 225.4.a.i, downloaded from the LMFDB on 19 April 2024.
{"label": "225.4.a.i", "space_label": "225.4.a", "level": 225, "weight": 4, "hecke_orbit": 9, "hecke_orbit_code": 36028797086073057, "dim": 2, "is_polredabs": true, "nf_label": "2.2.41.1", "trace_hash": 1769862438549576550, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[2, [-8, 3, 1]], [7, [-360, -6, 1]]], "qexp_display": "q+(-1-\\beta )q^{2}+(3+3\\beta )q^{4}+(6-6\\beta )q^{7}+\\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": 2, "inner_twist_count": 1, "level_primes": [3, 5], "conrey_indexes": [1], "field_disc": 41, "field_disc_factorization": [[41, 1]], "field_poly": [-10, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.025", "prec": 17}, {"__RealLiteral__": 0, "data": "1.938", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "9.154", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "59.812", "prec": 20}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "3.2.3.c1", "atkin_lehner_eigenvals": [[3, -1], [5, -1]], "trace_display": [-3, 0, 0, 6], "traces": [0, 2, -3, 0, 9, 0, 0, 6, -51, 0, 0, 42, 0, 78, 114, 0, 25, -102, 0, 56, 0, 0, -186, 48, 0, 0, 6, 0, -342, 318, 0, 52, 309, 0, 358, 0, 0, 306, 408, 0, 0, 408, 0, 120, 558, 0, 92, -180, 0, 70, 0, 0, -18, -402, 0, 0, -30, 0, 384, 186, 0, 340, 168, 0, -479, 0, 0, 732, -1074, 0, 0, 36, 0, 1332, -1566, 0, -1224, -612, 0, 380, 0, 0, -858, 984, 0, 0, -2148, 0, -1194, -1116, 0, 972, -276, 0, -1616, 0, 0, -768, 633, 0, 0, 1122, 0, -3090, -1866, 0, -1078, 2160, 0, -664, 0, 0, -294, -306, 0, 0, -1152, 0, -402, 924, 0, -1042, -2478, 0, -504, 0, 0, -1818, 1629, 0, 0, 2910, 0, 3120, -2328, 0, 2806, 1302, 0, -76, 0, 0, 3636, 900, 0, 0, -4212, 0, 4698, 222, 0, 364, -936, 0, 3132, 0, 0, -42, -6720, 0, 0, 1128, 0, -2916, 2574, 0, -5740, 24, 0, -614, 0, 0, 6444, -2886, 0, 0, 894, 0, -1278, 5850, 0, 6712, 3708, 0, -1060, 0, 0, -3372, 4848, 0, 0, 4092, 0, 1356, 6072, 0, -1899, -5034, 0, 6908, 0, 0, -5496, 6120, 0, 0, 3282, 0, 606, -1776, 0, -2108, 3234, 0, -1436, 0, 0, 1632, 5178, 0, 0, -2748, 0, -5082, 2034, 0, 11570, 1464, 0, -16, 0, 0, -7248, -7830, 0, 0, 1206, 0, -7044, 1284, 0, -3692, -3603, 0, 7434, 0, 0, 5136, -1080, 0, 0, 486, 0, 24, 882, 0, -10071, -570, 0, -5724, 0, 0, -11622, -144, 0, 0, 240, 0, 6984, -4446, 0, 5668, -1890, 0, -8390, 0, 0, 11994, 852, 0, 0, -5556, 0, 6828, -10908, 0, -3564, -252, 0, -2574, 0, 0, 12636, -6954, 0, 0, -8910, 0, 9876, 2856, 0, -11448, 3144, 0, -776, 0, 0, -2880, -9396, 0, 0, -2148, 0, -1716, -11130, 0, 20160, -5790, 0, 1512, 0, 0, 1752, 2064, 0, 0, 8064, 0, -10650, -11856, 0, -1256, 17220, 0, 1276, 0, 0, -13956, 10515, 0, 0, -384, 0, 2580, -5028, 0, -12850, -9792, 0, -6388, 0, 0, 5382, 19242, 0, 0, 3834, 0, -6930, 216, 0, -342, -9822, 0, -11124, 0, 0, -1146, 108, 0, 0, -11292, 0, 2310, 15636, 0, 2704, 17568, 0, 2180, 0, 0, 2964, -564, 0, 0, 5100, 0, -18216, -19914, 0, -808, -1047, 0, 12922, 0, 0, 6930, -12576, 0, 0, -10680, 0, 3504, 16488, 0, 12960, 13068, 0, -7216, 0, 0, -9846, -180, 0, 0, 13158, 0, 9552, 14334, 0, -10784, -18732, 0, 8570, 0, 0, -10788, 4308, 0, 0, -6552, 0, -9396, 1488, 0, -15534, 5280, 0, 11900, 0, 0, 5844, -16368, 0, 0, 12666, 0, 18858, 1872, 0, 10044, -34710, 0, -884, 0, 0, -8184, -16458, 0, 0, -11514, 0, 12210, 1392, 0, 22118, -13440, 0, -5184, 0, 0, -4866, 14328, 0, 0, 21132, 0, 8652, 30540, 0, 5292, 19806, 0, 10809, 0, 0, 8802, -10638, 0, 0, 20910, 0, -7608, 14928, 0, -88, 22248, 0, 24896, 0, 0, 12186, -7548, 0, 0, 456, 0, -2646, -14034, 0, -9288, 8901, 0, 3274, 0, 0, 7536, 24084, 0, 0, -14832, 0, 9900, 34866, 0, 4316, -192, 0, -21870, 0, 0, -720, 14436, 0, 0, -19896, 0, -27648, -2958, 0, -5288, 24216, 0, -13914, 0, 0, 1896, 25170, 0, 0, 29568, 0, -35760, -12702, 0, -2556, -46602, 0, -7128, 0, 0, 4890, -9216, 0, 0, 10176, 0, 2772, -20256, 0, -10712, 10692, 0, 24732, 0, 0, -30528, -17049, 0, 0, -22632, 0, 1644, -36180, 0, -4534, 6720, 0, 7360, 0, 0, 7146, 12990, 0, 0, -29628, 0, 5064, 25512, 0, 6568, 18648, 0, -9432, 0, 0, 46362, 13080, 0, 0, -18336, 0, 20826, -38484, 0, 17820, 16602, 0, -12676, 0, 0, -36876, -21060, 0, 0, -6036, 0, 33390, -26676, 0, -7796, -15840, 0, -36866, 0, 0, 7158, -3744, 0, 0, 20688, 0, 9060, -5256, 0, -22448, -14412, 0, 4644, 0, 0, -24192, -31254, 0, 0, 5838, 0, 1056, -4290, 0, 21244, -49776, 0, -29356, 0, 0, 14520, -3828, 0, 0, 18948, 0, -348, 18228, 0, -31545, -21294, 0, 27216, 0, 0, 2544, -12264, 0, 0, -39540, 0, 7404, -25764, 0, 19168, 38550, 0, -4172, 0, 0, -23268, -1734, 0, 0, 32670, 0, -18000, -30354, 0, -12586, -19512, 0, -39784, 0, 0, 25506, 3216, 0, 0, 20790, 0, -34272, 34992, 0, -17388, 28065, 0, 29466, 0, 0, -24222, -19620, 0, 0, -25800, 0, -8310, -33582, 0, 8892, 22752, 0, -5416, 0, 0, -12828, 6660, 0, 0, -78618, 0, -46908, 17304, 0, 61468, 3408, 0, 26784, 0, 0, 37098, 64380, 0, 0, 264, 0, 23100, -8892, 0, -38104, 6516, 0, 36848, 0, 0, -15300, 45786, 0, 0, 24504, 0, 54348, 5520, 0, -21384, -2232, 0, -1339, 0, 0, -25980, -38766, 0, 0, 65748, 0, 1452, 29826, 0, 37728, 330, 0, -9680, 0, 0, 58578, 41256, 0, 0, 7536, 0, -32424, -13320, 0, -36716, -38880, 0, -61668, 0, 0, -43872, 9102, 0, 0, -5826, 0, -37614, 77442, 0, 11340, 26808, 0, -10480, 0, 0, 1614, 3810, 0, 0, -28656, 0, 35202, 35040, 0, 37946, -1290, 0, 56196, 0, 0, -34122, 18, 0, 0, -1512, 0, 19074, 31188, 0, -53276, 20850, 0, 69140, 0, 0, 67392, -39480, 0, 0, 84204, 0, -4464, 44880, 0, 21168, 21114, 0, 8480, 0, 0, 62886, -83040, 0, 0, 33444, 0, -31500, -17532, 0, 36524, 24360, 0, -16524, 0, 0, -37998, -50304, 0, 0, -63870, 0, 51066, 18600, 0, 3692, -45324, 0, 18914, 0, 0, 48480, 2652, 0, 0, 36096, 0, 46248, -22656, 0, 49374, -34812, 0, -1300, 0, 0, 14196, 23544, 0, 0, -15978, 0, 56880, 12144, 0, 19672, -66354, 0, 17044, 0, 0, -29736, 49104, 0, 0, 19038, 0, 7824, 2694, 0, -70200, 53232, 0, 38664, 0, 0, -29220, -26298, 0, 0, -25956, 0, -74100, -34716, 0, -55278, -32292, 0, -59418, 0, 0, -54258, 21405, 0, 0, -19962, 0, 4200, 40302, 0, 10154, 48258, 0, -5724, 0, 0, -53382, 74748, 0, 0, 96, 0, -44784, -12864, 0, -32276, 10248, 0, -20088, 0, 0, 25998, -44232, 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": "15.4.b.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, 0], [1, 0], [-1, -1], [0, 0], [3, 3], [0, 0], [0, 0], [6, -6], [-25, -1], [0, 0], [0, 0], [18, 6], [0, 0], [42, -6], [54, 6], [0, 0], [11, 3], [-46, -10], [0, 0], [40, -24], [0, 0], [0, 0], [-78, -30], [28, -8], [0, 0], [0, 0], [18, -30], [0, 0], [-162, -18], [180, -42], [0, 0], [32, -12], [159, -9], [0, 0], [146, 66], [0, 0], [0, 0], [126, 54], [200, 8], [0, 0], [0, 0], [198, 12], [0, 0], [12, 96], [234, 90], [0, 0], [52, -12], [-136, 92], [0, 0], [53, -36], [0, 0], [0, 0], [-54, 90], [-242, 82], [0, 0], [0, 0], [-90, 150], [0, 0], [240, -96], [90, 6], [0, 0], [122, 96], [88, -8], [0, 0], [-157, -165], [0, 0], [0, 0], [336, 60], [-438, -198], [0, 0], [0, 0], [108, -180], [0, 0], [612, 108], [-666, -234], [0, 0], [-600, -24], [-252, -108], [0, 0], [40, 300], [0, 0], [0, 0], [-318, -222], [388, 208], [0, 0], [0, 0], [-972, -204], [0, 0], [-510, -174], [-630, 144], [0, 0], [612, -252], [-156, 36], [0, 0], [-784, -48], [0, 0], [0, 0], [-264, -240], [307, 19], [0, 0], [0, 0]]}