# Stored data for newform 81.4.a.a, downloaded from the LMFDB on 24 April 2024.
{"label": "81.4.a.a", "space_label": "81.4.a", "level": 81, "weight": 4, "hecke_orbit": 1, "hecke_orbit_code": 67108945, "dim": 2, "is_polredabs": true, "nf_label": "2.2.33.1", "trace_hash": 2075052282591858344, "analytic_rank": 1, "is_twist_minimal": false, "hecke_cutters": [[2, [-6, 3, 1]]], "qexp_display": "q+(-1-\\beta )q^{2}+(1+3\\beta )q^{4}+(-8+\\beta )q^{5}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 1296, "fricke_eigenval": -1, "atkin_lehner_string": "-", "analytic_conductor": 4.77915471046499, "hecke_ring_index": 1, "level_radical": 3, "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": "0.000", "prec": 17}, "analytic_rank_proved": true, "char_values": [81, 1, [2], [1]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 1, "level_primes": [3], "conrey_indexes": [1], "field_disc": 33, "field_disc_factorization": [[3, 1], [11, 1]], "field_poly": [-8, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.929", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "9.086", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "59.019", "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]], "trace_display": [-3, 0, -15, 7], "traces": [0, 2, -3, 0, 5, -15, 0, 7, -33, 0, 6, -66, 0, -11, -60, 0, -7, -99, 0, -77, 12, 0, -33, -33, 0, -121, 264, 0, 166, 51, 0, 43, 423, 0, 297, -3, 0, -50, 561, 0, 264, -132, 0, 88, 231, 0, -264, -399, 0, -513, 429, 0, -770, -54, 0, 627, -66, 0, -60, -798, 0, 439, -114, 0, -727, -165, 0, 988, -693, 0, 318, -1368, 0, -455, -816, 0, -1529, 165, 0, -803, -96, 0, 1815, -813, 0, 594, -33, 0, 1221, 396, 0, -781, 858, 0, 2100, 132, 0, 736, 423, 0, -1045, 1653, 0, -2063, -66, 0, -2592, 1593, 0, 2002, 594, 0, -470, 2307, 0, 561, 78, 0, -1047, -792, 0, 572, 1074, 0, 256, 2535, 0, -2102, 231, 0, -1518, -627, 0, -1606, -2571, 0, 1485, 3912, 0, 1096, -948, 0, 4428, -1617, 0, -399, -3327, 0, 2548, 1947, 0, -209, 825, 0, 924, -273, 0, -1037, -3894, 0, -3024, 825, 0, 3136, -5181, 0, -546, -2607, 0, -621, -1188, 0, -77, -957, 0, -1166, -957, 0, 594, -4392, 0, -3560, 2310, 0, 858, 1266, 0, 2079, -5502, 0, -2904, -1083, 0, 880, -2787, 0, -243, 6606, 0, 922, 1749, 0, -978, 129, 0, -627, 2748, 0, 2266, -1023, 0, -1037, 7884, 0, -1053, -759, 0, 299, 1452, 0, -3036, 2772, 0, -2585, 1926, 0, -804, 2310, 0, -11, 1782, 0, -858, 2115, 0, 1491, 4737, 0, 4158, -7053, 0, 7216, 7854, 0, -4100, 4194, 0, 7106, -660, 0, -2598, -5841, 0, 3597, 2262, 0, -3127, 6942, 0, 2498, 4884, 0, 8646, -10659, 0, 3078, 5874, 0, 5737, -3186, 0, -4532, 1683, 0, -9861, 2013, 0, -11495, -2139, 0, -264, 231, 0, -7625, -10548, 0, -5016, -5313, 0, -3589, 54, 0, 10891, -10509, 0, 8229, 1716, 0, -16896, -4521, 0, 11, 9768, 0, 4279, -5025, 0, 2893, -3102, 0, 426, -14253, 0, -3476, -13938, 0, 13288, 627, 0, -1815, 2928, 0, -1518, 7821, 0, 4378, -8268, 0, 561, -5901, 0, -12791, 3264, 0, 7458, -6321, 0, -14186, -1791, 0, 2376, -1023, 0, -3157, -1551, 0, 16896, 9120, 0, 15235, 5610, 0, -12771, 1914, 0, 7884, -2574, 0, 1836, -2790, 0, 1275, 17814, 0, -5368, 7422, 0, -1667, -2706, 0, 5196, 7830, 0, 5929, -1485, 0, 5082, -33, 0, -6017, 8448, 0, -15288, 9813, 0, -2409, 8877, 0, 6889, -2469, 0, -1188, 8811, 0, -6048, 11121, 0, -5018, -12966, 0, 2651, 7608, 0, -979, -372, 0, -1398, 8778, 0, 12760, -10098, 0, -4118, 3939, 0, 7863, -4554, 0, -8085, 3621, 0, 2923, 14574, 0, 3564, 8217, 0, -3661, -27, 0, -330, -5778, 0, 1111, -1686, 0, -8360, -7194, 0, -12359, -11880, 0, -17226, 18780, 0, -4158, -3300, 0, -10118, 441, 0, -8580, -2202, 0, 7095, 4719, 0, 11428, -24684, 0, -6468, -19497, 0, 6523, -30, 0, 22815, 26019, 0, 6725, -10206, 0, 15411, -3696, 0, 11341, -10890, 0, 22740, -11199, 0, -13090, -27951, 0, -24706, -3837, 0, 21442, -8976, 0, 540, 9948, 0, -2376, -22638, 0, -596, -11916, 0, 1150, 2724, 0, 15741, -8604, 0, -13899, 7128, 0, -2582, -5379, 0, 10436, -2553, 0, -9687, 15819, 0, 1155, -5628, 0, 4488, -13887, 0, -14036, -24684, 0, 22836, -2574, 0, -17833, 15876, 0, -14410, 24981, 0, -13284, -15213, 0, -21060, 19701, 0, 21442, 1452, 0, -22275, -19470, 0, -2396, 21759, 0, -3201, -1518, 0, 12485, 32340, 0, 4225, -12060, 0, 1001, 2832, 0, -29436, 26400, 0, -19959, 7230, 0, 20196, -5916, 0, 21994, 18282, 0, 16896, -2706, 0, -5207, -9318, 0, 636, 2451, 0, 23166, 11517, 0, 6540, 15504, 0, -2992, 11070, 0, -7844, -2052, 0, 2970, 46794, 0, 4422, -4983, 0, 1870, -1848, 0, -28886, -13002, 0, 5335, -20295, 0, -9078, 24717, 0, -43142, 23727, 0, -3894, -2814, 0, -2720, -732, 0, 21660, -2178, 0, -5092, 23133, 0, 43888, -5544, 0, 4648, 18348, 0, 44220, 16656, 0, -2376, -1188, 0, 6864, -42708, 0, -49610, 2904, 0, -39501, -25434, 0, 44286, -22902, 0, 18532, -4065, 0, -3003, 15015, 0, 23982, 31119, 0, -11405, 426, 0, 15180, 8580, 0, -1155, -17160, 0, 9498, -28347, 0, -803, 33555, 0, 6615, -42879, 0, 7625, -9504, 0, 330, 1989, 0, -25347, 33198, 0, 583, -39798, 0, -12143, -48774, 0, -34041, -7725, 0, 21087, 3234, 0, -14498, -33264, 0, -22132, 3795, 0, -32703, 1281, 0, 35647, -18360, 0, -7722, 231, 0, 19569, 3276, 0, 15174, -18540, 0, -6181, -36216, 0, -46322, -2838, 0, -38117, 11748, 0, 22692, -3465, 0, 18025, -19230, 0, -4158, -23892, 0, 20119, -18120, 0, -19764, -11769, 0, -627, 1452, 0, 297, 1566, 0, -4925, 14910, 0, 6270, -7887, 0, 19768, 14817, 0, 528, 5547, 0, -6358, 48030, 0, -48594, -29271, 0, 13921, -6534, 0, -28391, 9108, 0, -3344, -10461, 0, 8472, 48741, 0, 26136, 14850, 0, -1323, 23271, 0, -1793, 4932, 0, 28182, 105, 0, 23573, 38712, 0, 37054, -29319, 0, 33264, -27819, 0, 25251, 47091, 0, -5907, 7062, 0, -28776, 30537, 0, 4189, 3936, 0, 19536, -19956, 0, -715, -16071, 0, 31548, 27555, 0, -16049, 34386, 0, 5988, 43560, 0, 16528, 8154, 0, 41866, 22275, 0, 16005, 26301, 0, -45246, -27489, 0, -47461, -2058, 0, -41648, 7380, 0, -24134, -23868, 0, -33561, 17754, 0, -38279, 690, 0, -27621, -10929, 0, 7306, 2508, 0, 48762, 38016, 0, -8283, -1221, 0, 4460, 67287, 0, -21769, -37488, 0, 15510, 5259, 0, 475, -10914, 0, 11616, -1692, 0, 53545, 46134, 0, -34539, -63591, 0, -4684, -5940, 0, 15070, 55902, 0, 37692, 26598, 0, -41499, 1047, 0, -21384, -31779, 0, -40722, 14226, 0, 55330, -25905, 0, -9174, -33177, 0, 40953, -25359, 0, 74074, -25311, 0, -84722, -11880, 0, 6096, 43164, 0, -10340, 4422, 0, 10638, 49155, 0, 10395, -72675, 0, -62343, -17226, 0, -20732, -38352, 0, 27636, -21363, 0, -28545, -17403, 0, -3531, -18768, 0, -57640, -53493, 0, 10098, 40113, 0, 25035, -54114, 0, -6648, 25671, 0, -58509, 18348, 0, 69421, -16797, 0, -13079, -18150, 0, 12306, -32076, 0, 5321, -43746, 0, 14056, -23100, 0, -22572, -10008, 0, 46095, -36273, 0, -53406, 6534, 0, 53702, -3333, 0, 51304, 9540, 0, 60048, 4668, 0, 71071, -60729, 0, -43032], "weight_parity": 1, "has_non_self_twist": 0, "level_is_prime": false, "level_is_prime_power": true, "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": "9.4.c.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], [1, 3], [-8, 1], [0, 0], [2, 3], [-17, 1], [0, 0], [0, 6], [-37, 8], [0, 0], [2, -15], [-26, -8], [0, 0], [1, -9], [-45, -9], [0, 0], [-25, -27], [16, -20], [0, 0], [-27, 21], [-26, 19], [0, 0], [-53, -15], [118, 28], [0, 0], [74, 18], [26, -1], [0, 0], [20, 3], [207, 9], [0, 0], [117, 63], [8, -19], [0, 0], [-52, 54], [241, 79], [0, 0], [144, -24], [-17, -98], [0, 0], [47, -6], [155, -79], [0, 0], [-126, -12], [-154, -91], [0, 0], [-267, 21], [173, 83], [0, 0], [-358, -54], [-108, 162], [0, 0], [360, -93], [-10, -46], [0, 0], [-18, -24], [-467, 136], [0, 0], [272, -105], [-44, -26], [0, 0], [-287, -153], [-136, 107], [0, 0], [461, 66], [-261, -171], [0, 0], [144, 30], [-612, -144], [0, 0], [-349, 243], [-380, -56], [0, 0], [-673, -183], [118, -71], [0, 0], [-556, 309], [-80, 64], [0, 0], [801, 213], [-460, 107], [0, 0], [288, 18], [1, -35], [0, 0], [693, -165], [234, -72], [0, 0], [-356, -69], [430, -2], [0, 0], [882, 336], [-16, 164], [0, 0], [317, 102], [99, 225], [0, 0], [-413, -219]]}