# Stored data for newform 17.4.c.a, downloaded from the LMFDB on 19 April 2024. {"label": "17.4.c.a", "space_label": "17.4.c", "level": 17, "weight": 4, "hecke_orbit": 1, "hecke_orbit_code": 137506062353, "dim": 8, "is_polredabs": true, "trace_hash": 1599806077537756173, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [], "qexp_display": "q+(\\beta _{1}-\\beta _{3})q^{2}+\\beta _{4}q^{3}+(-5-\\beta _{2}+\\cdots)q^{4}+\\cdots", "char_order": 4, "char_parity": 1, "char_degree": 2, "char_conductor": 17, "char_orbit_label": "c", "char_is_real": false, "Nk2": 272, "analytic_conductor": 1.0030324700975903, "hecke_ring_index": 4, "level_radical": 17, "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": false, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.242", "prec": 17}, "analytic_rank_proved": true, "char_values": [17, 4, [3], [3]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 2, "level_primes": [17], "conrey_indexes": [4, 13], "field_disc": 186672103840000, "field_disc_factorization": [[2, 8], [5, 4], [34157, 2]], "field_poly": [256, 0, 836, 0, 561, 0, 46, 0, 1], "hecke_ring_index_factorization": [[2, 2]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.005", "prec": 17}, {"__RealLiteral__": 0, "data": "7.484", "prec": 17}, {"__RealLiteral__": 0, "data": "2.523", "prec": 17}, {"__RealLiteral__": 0, "data": "202.800", "prec": 24}, {"__RealLiteral__": 0, "data": "177.811", "prec": 24}, {"__RealLiteral__": 0, "data": "8601.328", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "3.2.3.c4", "trace_display": [0, 0, 14, 2], "traces": [0, 8, 0, 0, -36, 14, 22, 2, 0, 0, 78, -108, -174, -88, 108, 0, 420, -10, 428, 0, -306, -260, 30, -22, -862, 0, 0, 540, -764, 46, -120, 610, 0, 816, 1002, 1172, 0, -574, -768, -844, -342, -968, 0, 0, 550, -1154, -944, -368, 2494, 0, 468, 296, 2564, 0, -1592, -1996, 684, -300, 266, 0, 0, 1258, -2516, 122, -3044, 628, 0, 764, 1914, 1812, 0, 1266, 1404, -1732, 1538, 1292, 0, 0, -2836, 914, 498, 280, -280, 0, -2952, -2498, -4244, 0, 442, -2156, 2478, -1632, -1768, 0, 0, 1484, 3998, 1836, 6728, -2088, 0, 904, -290, -2016, 0, 1452, 9980, -3288, -1464, 2894, 0, 0, -3860, 6828, -232, -868, -11062, 0, -6988, -4050, -12088, 0, 2142, -1664, 7692, 2104, 4812, 0, 0, 1752, 992, 2156, 5636, -532, 0, 1848, -3322, -3272, 0, 4456, 5232, -4200, 7752, -508, 0, 0, -9364, 4600, -4726, -632, -5662, 0, 2896, -4710, -4760, 0, 3332, -7608, 10616, -6764, 9174, 0, 0, 4592, 1420, 6900, -1836, -6514, 0, -4360, -1790, 6668, 0, -378, 17048, -6670, 2666, 1280, 0, 0, -5214, 4490, -7272, -12420, 9992, 0, -18232, 1480, -4864, 0, -3528, -7312, -7550, -4216, -14232, 0, 0, 14842, -11490, 6694, 17012, 15804, 0, 22908, 21158, 4124, 0, 338, -11748, 1108, 560, 6612, 0, 0, -14834, 1140, 7832, -3340, -2134, 0, -3928, -8196, 22512, 0, -11564, -11260, -4304, -9604, -7624, 0, 0, 664, -28642, -6688, -3932, 12896, 0, -8060, 18516, 8624, 0, -11012, 8020, -7920, 2394, -23054, 0, 0, 30956, -4720, -9400, -15740, 13756, 0, 32176, 12768, 30756, 0, -8900, -13292, 12496, 7214, 6242, 0, 0, 5304, -8592, -632, -23396, 5806, 0, 16624, -27034, -3272, 0, 2032, -17312, -6522, 3786, 6110, 0, 0, -4272, -3908, -34224, -2072, 14572, 0, 2756, 5540, 7572, 0, 15688, 4040, 3802, -8676, -30314, 0, 0, -1200, -11494, 9052, 31560, 3796, 0, 17788, -182, 24712, 0, -13000, -12400, 4286, 5700, -5036, 0, 0, -1808, 9506, 22908, -8212, -36082, 0, -18112, 4640, -25080, 0, -22526, -7420, -5328, 12888, 14136, 0, 0, 12274, 9028, -22680, 2792, -6940, 0, -21408, 12970, -21908, 0, 29988, 32836, 10524, -9542, -5972, 0, 0, 14572, 4216, 29574, 26820, 3748, 0, 39296, -9796, -35168, 0, 20298, 44224, -13994, -26492, 22696, 0, 0, -42858, 38392, 11512, -5348, -36696, 0, -61760, -38918, -1968, 0, -29036, -10496, 10672, 3064, 21588, 0, 0, -37342, 1316, -512, 11192, 12644, 0, -39408, -890, -40336, 0, 8298, 5484, -20870, 33442, 3360, 0, 0, 1460, 41300, 1192, 11620, 6310, 0, 45724, 12250, -41780, 0, 34532, 10392, 49948, -14176, 34908, 0, 0, 15080, 2392, 7760, 17984, -61910, 0, -74556, -15718, 46000, 0, 70138, 41552, -17632, 9890, 53144, 0, 0, -44316, 31382, -5268, -56140, -31486, 0, -72228, -22396, -44412, 0, -17412, -40552, -18904, -21996, -20828, 0, 0, 9292, -23700, 44006, -5616, 26472, 0, 63616, 15580, -30512, 0, -888, -4824, 41430, 54956, 35268, 0, 0, -5344, 21232, -8240, -13124, 1064, 0, 8140, -39980, -13516, 0, 16382, 12344, -15780, 908, 3648, 0, 0, -9754, -11858, -36054, 55048, 38978, 0, 7876, 12670, 23312, 0, -85532, 47748, -16524, -30200, -55960, 0, 0, -6234, 10956, -9756, 19104, -21792, 0, -22656, 2256, 60244, 0, -4800, -13708, 27032, -43460, -18792, 0, 0, 49920, -23060, 16106, 33500, -40874, 0, 36544, 38902, -40868, 0, 30416, 35208, -23376, 19752, -22096, 0, 0, 7940, 17486, -27028, -52640, 17098, 0, 78988, 60858, -20196, 0, 7972, -132340, 18118, -27466, 3956, 0, 0, 59514, -70068, 47678, 39240, 50404, 0, 59184, -30276, 73428, 0, -41136, 24172, -77466, -20330, -95728, 0, 0, -73328, -41316, -35136, -47720, 114, 0, -96096, -33344, 75056, 0, -82724, -54428, 23460, 90556, -44668, 0, 0, 97714, -30500, -11328, -44140, 92854, 0, 45488, 34388, 137472, 0, 50800, -17384, 25014, 47380, -25096, 0, 0, 28642, 6332, -35686, -19536, 43980, 0, 46288, 22934, -71416, 0, 24740, 5656, 59740, -26984, 25864, 0, 0, 3972, -42504, -53764, 47588, 13188, 0, 114736, -5334, 18784, 0, -44352, -65464, -49494, -60196, 77916, 0, 0, -34146, -57302, 4800, -110796, -26036, 0, -14136, 3592, 87728, 0, -34912, -6124, -56848, -101302, -78738, 0, 0, -31244, 892, -39808, -65776, 33128, 0, -1404, 87684, 86812, 0, -74422, 13092, 4964, 77684, -30896, 0, 0, 95120, -91860, 15068, 2124, 76162, 0, 59868, -2330, 32576, 0, 58212, -4016, 3588, 34728, 54944, 0, 0, 38592, 19428, 58874, 39996, 30670, 0, -134088, -46760, -103012, 0, 27916, 42248, 20336, 5676, 48214, 0, 0, -55184, 6916, 34798, 94592, -44086, 0, -80396, -2904, -55344, 0, -75232, -52416, -3526, -12738, 10416, 0, 0, -109438, 78770, 80694, -74400, -30120, 0, -64004, 55492, 4912, 0, 29648, -12268, -49160, 43972, -42980, 0, 0, -26184, 77880, -41886, 129784, -24764, 0, 36856, 18750, -71204, 0, 68570, 10240, 31308, -23904, 3380, 0, 0, 64854, -30376, 312, -41440, -26032, 0, -26184, -24570, -27608, 0, 154046, 87936, -176, -109156, 24596, 0, 0, -17266, 95536, 28716, 32264, -25452, 0, -68204, 9856, -46600, 0, -49884, 141340, -34836, -28194, -21660, 0, 0, -71782, 12332, -3202, 2160, -156680, 0, -1856, -93680, -142388, 0, -92324, -30432, -3860, 6228, 159528, 0, 0, 15260, 51930, 47880, 3984, 1296, 0, 4548, -212470, -19192, 0, 61608, 89052, 8794, 138444, 54098, 0, 0, -100312, 163740, -44488, 142352, -42896, 0, 28004, 2170, -122852, 0, 21080, 43168, 201902, -108350, -26832, 0, 0, 78148, 14210, 37746, 20192, -41898, 0, -34432, 88042, 92844, 0, 76198, 92656, 19964, 210602, 25384, 0, 0, -67424, 49884, -92344, -204712, -160408, 0, -85592, -45460, -167664, 0, 109760, -181352, -71202, 53244, 6016, 0, 0, 34662, -153280, -33168, -11720, 87712, 0, 109580, -56472, -73272, 0, 28446, -2016, -13004, -35296, 20160, 0, 0, -101012, 23044, 55724, -520, -88008, 0, 22476, -136404, 40092, 0, -48488, -43524, 100680, -72444, 80782, 0, 0, -86942, 48104, 76816, 155280, -108892, 0, -67172, 125624, -10160, 0, -140280, 65636, -25128, -3176, 21462, 0, 0, 218722, 63176, -129712, 124468, 40104, 0, -87712, 55340, 120860, 0, 82808, -41864, 59216, -7486, -90452, 0, 0, 104112, 52164, 113452, 105536, 20416, 0, 178436, -29916, -174196, 0, 94232, 283336, -94828, -65736, 91952, 0, 0, -167080, 33828, -30936, -165764, -16144, 0, -224828, -18140, -70028, 0, -106782, -79172, -87992, 31828, -122970, 0, 0, 55328, -74434, 20594, -1872, 121890, 0, 78492, -48730, 66000, 0, -41788, -140776, -130678, -77164, -127424, 0, 0, -148588, -43270, -52882, -41736, 136184], "weight_parity": 1, "has_non_self_twist": 1, "level_is_prime": true, "level_is_prime_power": true, "level_is_square": false, "level_is_squarefree": true, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 17, 3, 1, 4, 0]], "char_orbit_index": 3, "prim_orbit_index": 3, "minimal_twist": "17.4.c.a", "char_is_minimal": true, "conrey_index": 4, "id": null, "nf_label": 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, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, -1, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0], [-5, 0, -1, 0, -1, -1, 1, 1], [2, -1, 1, 2, -1, 0, 0, -1], [3, 1, 1, -3, 0, 3, -1, 0], [1, -1, -1, -1, 0, 0, -3, 0], [0, -5, 0, 13, 4, -4, 2, -2], [0, -6, 0, 1, -3, 3, 0, 0], [10, 4, 4, -10, 0, -1, -1, 0], [-14, 0, 0, 14, 0, 3, 2, 0], [-23, 9, -9, -23, -3, 0, 0, 5], [-12, 0, 6, 0, -5, -5, 2, 2], [14, 10, -10, 14, 2, 0, 0, -2], [0, 2, 0, -30, 8, -8, 3, -3], [53, 0, 25, 0, 9, 9, -1, -1], [-2, -9, -15, 25, 1, 4, -1, 4], [55, 0, -5, 0, -3, -3, -3, -3], [0, 10, 0, 6, 2, -2, -1, 1], [-38, 4, -4, -38, -13, 0, 0, -1], [-30, 0, 4, 0, 2, 2, -5, -5], [3, -17, 17, 3, -9, 0, 0, 3], [-3, 9, 9, 3, 0, 6, 1, 0], [-111, -33, -33, 111, 0, -3, 13, 0], [0, -10, 0, -21, -9, 9, -7, 7], [0, -34, 0, -34, 9, -9, -1, 1], [66, 12, 12, -66, 0, -4, 6, 0], [-94, 14, 14, 94, 0, -14, -6, 0], [12, 1, -1, 12, 21, 0, 0, -25], [-12, 0, 4, 0, 22, 22, -6, -6], [73, 31, -31, 73, -16, 0, 0, 13], [0, 37, 0, -301, -20, 20, -18, 18], [100, 0, 14, 0, -25, -25, 4, 4], [129, -6, 7, 164, 12, -3, 5, -20], [138, 0, -10, 0, 2, 2, 17, 17], [0, 19, 0, 37, -10, 10, 8, -8], [-72, -15, 15, -72, 33, 0, 0, 1], [-100, 0, 4, 0, -4, -4, 8, 8], [-106, 28, -28, -106, 26, 0, 0, 2], [-46, -16, -16, 46, 0, -55, 13, 0], [-119, 16, 16, 119, 0, -8, -8, 0], [0, 4, 0, -20, -10, 10, -6, 6], [0, 36, 0, -92, -3, 3, 4, -4], [71, -15, -15, -71, 0, 31, -9, 0], [-140, -25, -25, 140, 0, 49, -17, 0], [-124, 0, 0, -124, -36, 0, 0, 24], [-40, 0, 52, 0, -20, -20, -12, -12], [319, -81, 81, 319, 51, 0, 0, -29], [0, -96, 0, -91, -20, 20, 31, -31], [59, 0, -81, 0, -17, -17, -1, -1], [32, 8, 2, 42, -50, -47, -1, 21], [334, 0, 26, 0, 21, 21, -27, -27], [0, -86, 0, 134, 15, -15, -21, 21], [-204, 44, -44, -204, -12, 0, 0, 20], [-246, 0, -30, 0, 36, 36, -7, -7], [86, -10, 10, 86, 30, 0, 0, -2], [-34, 0, 0, 34, 0, 28, -14, 0], [38, 108, 108, -38, 0, 61, -19, 0], [0, 80, 0, 44, 15, -15, 40, -40], [0, 84, 0, -396, -6, 6, -2, 2], [160, -25, -25, -160, 0, -47, -11, 0], [-334, 18, 18, 334, 0, -110, 78, 0], [1, -53, 53, 1, -24, 0, 0, 57], [-405, 0, -249, 0, -25, -25, 49, 49], [74, -20, 20, 74, -72, 0, 0, 18], [0, 26, 0, -126, 61, -61, 11, -11], [98, 0, -90, 0, 81, 81, -5, -5], [240, 111, 134, -25, 16, 81, -33, 30], [230, 0, 52, 0, -4, -4, -7, -7], [0, 40, 0, -64, 4, -4, 8, -8], [173, -71, 71, 173, 14, 0, 0, -59], [173, 0, 25, 0, -73, -73, 5, 5], [-209, 70, -70, -209, -46, 0, 0, -30], [208, -42, -42, -208, 0, 129, -63, 0], [166, 58, 58, -166, 0, -39, -18, 0], [0, -76, 0, 108, 24, -24, -8, 8], [0, 88, 0, 386, 6, -6, 1, -1], [-362, -86, -86, 362, 0, 22, 30, 0], [125, -123, -123, -125, 0, 2, -43, 0], [86, -108, 108, 86, 93, 0, 0, -95], [35, 0, 150, 0, 15, 15, 0, 0], [-41, -103, 103, -41, -8, 0, 0, 24], [0, 24, 0, -100, -1, 1, -76, 76], [-356, 0, -44, 0, -18, -18, -26, -26], [-316, -11, -109, -232, 39, 54, 46, -31], [-550, 0, -74, 0, -45, -45, 39, 39], [0, -174, 0, 382, -28, 28, 49, -49], [49, -7, 7, 49, -135, 0, 0, 25], [-290, 0, 0, 0, -16, -16, 41, 41], [310, -40, 40, 310, -97, 0, 0, -1], [-220, 106, 106, 220, 0, -56, 64, 0], [-232, -160, -160, 232, 0, -60, 44, 0], [0, 184, 0, -530, 46, -46, -57, 57], [0, -8, 0, -440, 8, -8, -32, 32], [178, 26, 26, -178, 0, -24, 30, 0], [527, 193, 193, -527, 0, 291, -109, 0], [233, 168, -168, 233, -24, 0, 0, -14], [879, 0, 55, 0, 36, 36, -76, -76], [-248, 144, -144, -248, 189, 0, 0, -52], [0, -49, 0, 849, 60, -60, 42, -42]]}