# Stored data for newform 38.4.e.a, downloaded from the LMFDB on 24 April 2024.
{"label": "38.4.e.a", "space_label": "38.4.e", "level": 38, "weight": 4, "hecke_orbit": 1, "hecke_orbit_code": 274945015846, "dim": 12, "is_polredabs": true, "trace_hash": 128134974053507401, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[3, [2289169, -3812760, 41991777, -7640667, -1524069, 455373, 104059, -12789, -3078, 18, 54, 9, 1]]], "qexp_display": "q-2\\beta _{3}q^{2}+(-1+2\\beta _{2}-\\beta _{4}+2\\beta _{6}+\\cdots)q^{3}+\\cdots", "char_order": 9, "char_parity": 1, "char_degree": 6, "char_conductor": 19, "char_orbit_label": "e", "char_is_real": false, "Nk2": 608, "analytic_conductor": 2.242072580218143, "hecke_ring_index": 1, "level_radical": 38, "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": "0.002", "prec": 17}, "analytic_rank_proved": true, "char_values": [38, 9, [21], [8]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 2, "level_primes": [2, 19], "conrey_indexes": [5, 9, 17, 23, 25, 35], "field_disc": 406399323195295048089, "field_disc_factorization": [[3, 18], [647, 2], [1583, 2]], "field_poly": [272110107, 62864118, -56759508, -11890401, 5157591, 918855, -262940, -36258, 7953, 730, -135, -6, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "11.583", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "365.543", "prec": 24}, {"__RealLiteral__": 0, "data": "30.194", "prec": 20}, {"__RealLiteral__": 0, "data": "16864.223", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "3.2.3.c9", "trace_display": [0, -9, 0, 21], "traces": [0, 12, 0, -9, 0, 0, -18, 21, -48, -27, 0, -9, 36, 39, -138, 423, 0, 69, 132, -462, -216, -279, 204, -66, -72, 342, 48, 189, 192, 159, 0, 72, 0, -1560, 408, -135, -108, 1116, -294, -1248, 0, 147, 414, -117, 408, 1296, 528, 783, 288, 1413, -354, -2301, -348, -249, -540, 2187, -336, -2670, -1932, -4248, 324, 3114, -438, 363, -384, 495, 822, 3060, 408, -237, -270, 1686, 432, 1626, 90, -1854, 0, -1416, -108, -327, 0, 3483, 294, 927, 204, -3294, 1188, 2892, -72, -6366, -5076, 840, -156, 870, 3432, 513, -576, -8052, 378, 4494, 1368, -1899, -2544, -3741, 384, 4014, 1524, -2307, -1080, -612, 1098, 5745, 768, 6114, 5130, -4104, 636, 2127, 4086, 732, 648, -867, 1254, -3072, -1632, 4671, 168, -8967, 0, 1389, -1440, 3648, -3096, -2766, -8112, -5202, -2184, -3153, -4764, -531, -540, -6054, -1938, 1194, -528, -2682, 3252, 3513, 1728, 13161, 11754, 6540, 2856, 2172, 3834, 8442, -576, 2100, -654, -1302, 864, -3309, -10368, 4323, 1584, -5058, -9312, -8124, 576, -4665, 1584, 7182, -16512, 8628, 1068, -2526, 1488, -6381, -2514, -2544, 9180, 2040, -2646, -9420, -312, -5823, 10110, 8298, 3132, 8844, 684, 12582, 1152, -7779, 5622, 7695, 756, 2157, -1134, -9498, -5472, -10461, 510, -1659, 4584, 1872, -5958, -9381, -768, -6126, -6408, 1977, 4836, -4170, -8634, -5373, 1512, -1599, 810, -5070, 4428, 6000, 11490, 18072, -2208, 1530, 7788, -9288, 5352, 4974, 7434, 792, 1272, -2199, 4254, 8406, 1572, 15711, -4710, -10392, 0, 10527, -3246, -8469, -10908, -4815, -4716, -16755, -1152, -14739, -9234, -10650, -528, 3429, -3138, 7317, 0, 19005, -4920, 477, -2880, 5136, 19716, -5268, 3288, 342, -252, 38148, 12240, -13674, 2466, 4623, -4368, -1992, 9372, -23865, -3372, 5760, -1680, 5379, -576, -31779, -27306, -28470, -10272, 10431, 2748, 12744, -864, -8385, -24624, 3237, 10752, 5574, -8778, 18693, -4464, 18009, 26322, 17916, -20988, -10431, -7062, -23754, 2688, 43506, 14106, 3660, -468, 6618, 16884, 1008, 4992, 34317, 7332, -17631, 3876, 35880, -15414, 22398, 0, -26715, 6912, -18798, -11184, -16080, 4260, -19098, 7728, 22227, -24066, 9846, 9996, -41751, -3558, 945, 1152, 5028, 9228, -46905, -13176, -42048, -2292, 15960, 4752, -11421, -19878, -31143, 2136, 2919, 7440, 15840, -6240, -12384, 17700, 16200, 12480, -8922, -4128, 975, -20736, -26094, 19368, 41565, 444, 8298, 18132, 102, 4224, 12528, 33192, 6216, 5472, 29265, 16596, 28548, -14112, -2727, -4752, -30222, 17100, 20340, -20766, 21048, -1152, 15849, -15558, 13215, -9612, -25395, -9252, 16857, 11304, -13683, -8334, -15894, 4728, -13998, 11256, 18948, 5664, -15756, 8628, -19398, -468, -19926, -9978, -32055, 9240, 4524, -20520, -8538, -11916, -28326, 15510, -23166, 1536, 45894, -22248, -1446, 16056, -39600, -11076, -2430, 9672, 6375, 4362, 8499, 5304, -4317, -16974, 4836, -4320, -7221, 11244, 6687, -16392, 57408, 24936, 52032, -21888, -26703, -5406, 14142, 17352, -2025, -38880, -30648, 1344, -11142, 3060, 16800, -25932, 23619, -21768, 28710, 22848, -54804, 2604, 53382, 7884, 3825, 1584, 2718, 7728, 3699, -2364, -5442, -9336, -1089, 11232, 46629, 17640, 83487, 14424, -49419, -12600, -6351, -26310, 42777, 13536, -17718, 498, -15507, 1464, 9693, -3636, -19098, -21816, 474, 2790, 56877, -12288, -4674, -960, -81000, -6528, 3597, 12012, -44688, -18468, -55470, -18960, -73089, -1848, 4086, -25332, 6990, 26952, 5085, 45018, -31209, 6144, 58056, 27300, -4293, 31368, -7170, 1722, -15378, 3960, 36237, -35682, 17487, 2460, -30882, -10536, -8037, -24960, 23142, 5562, 24504, 1884, -27390, -23430, -38709, -3096, 17436, -27348, 3369, -33696, 37089, 37056, 8007, 3264, -20619, 13086, 44880, 17844, 110106, 83916, 23037, 3792, 9750, 35406, 97488, 12528, -8079, -7236, -17808, 3312, -93195, 36048, -46182, -54612, -80208, 5736, -33126, -7752, 7812, -49932, -80496, 4776, -18822, -9414, -38046, -1728, 5760, 60, -22503, 41364, -28644, -6936, -5472, -14136, -9909, 14940, 73122, 16968, -57474, 45576, -36639, -7632, 52296, 11028, -23553, 18240, 3435, -17034, -7980, 7416, 77664, -20862, -10683, -3360, 25425, 35190, 90192, 0, 16320, -88740, 60045, -15528, 45972, 7320, -30024, 5664, 3483, 40794, 90351, -19008, -64050, 18006, 18939, 3168, -29754, -63480, 67050, -43176, -43749, 6912, 19020, 24240, 23244, 25248, -37503, -22980, 12558, 9714, -60087, 0, -102417, 9930, 1275, -13236, -10764, -77928, -117150, -41472, -89799, 27240, 40380, 8520, -11598, -59976, 124767, -17808, 11139, -1650, -114258, 64152, 54954, 41592, -33594, -14832, 82593, 59940, -32862, 26292, -51135, 14202, 40869, 1632, 83103, -35412, 77814, 32760, 23151, -93810, -56880, -12672, 77268, -19584, -16488, -28632, -41202, -39756, 165741, -1872, 20388, -22842, -11433, 13992, 42075, 65730, 9666, 23136, 86382, 33270, 40575, -5640, 72513, 13380, -58011, 1152, -34101, -34038, -465, -2196, 73857, 27072, -19740, 25968, -20925, 13914, 50904, -8256, -113916, -38442, -99912, 36720, -14880, 6192, -224052, 8160, -23646, -7500, -105501, 888, -6810, -306, -68262, -8736, 73998, 4266, -18288, -2112, -118959, 14496, -62409, -68832, 41943, 3492, 90036, -47400, 117504, 35658, -9804, 39552, -8595, -57420, 111699, -13728, 41421, -5454, 68265, 7344, -129231, -27408, 10506, 13680, 9954, -53238, -516, 26436, 74178, 42096, 9141, 2304, 50079, -42840, 10038, -4524, -24441, -28764, 97539, 41928, -50547, 96672, -63198, 41472, -71487, 48354, -83283, 7200, 85626, 38046, 33579, 11376, -26259, 9630, -30330, 9456, -76266, -8484, -104814, -37992, -103086, 33570, 124968, -21888, -74901, 45816, -76245, 17256, -3654, -3018, -25584, 16128, -27954, -7992, 110049, 25908, 42051, 19938, 105435, 40704, -34794, -5940, 77880, 5148, 67755, -16950, -88896, -29928, 127467, 74712, -1626, 732, 71346, -46332, 83394, -5568, 71625, 5208, -76338, -53988, 61344, -26238, 106536, -11952, -47817, -79200, 7644, -6492, -52488, 54666, -3174, 12192, -41037, 4530, -23814, -52644, -51705, -92064, -148770, 36912, -79548, -25014, -29043, 10656, -22572, -2922, -70497, 17280, -135108, -666, -122769, 22488, 18903, -27234, -534, 3240, 9036, -58128, 53892, -20280, -158625, -69744, 21042, -43776, 15564, 27954, 130236, -19128, -175608, 43458, 125121, -62040, 78, -3762, 7689, 22440, 83790, 105036, 12402, 2688, -25809, 29430, 118620, -51360, 85527, 27552, 103836, -24456, -45315, 47238, 149655, 61476, 36027, -64476, 225456, -27360, -14520, 84582, 146133, -39072, 70734, 106764, 11262, 16416, -96855, -23958, -25431, -40632, 161199, 12072, 41337, -10176, 48960, 14364, -59463, 47400, 228534, -122364, -39825, 27888, -138027, -21588, -96567, -69912, -61188, -91452, 17997, 35280, -84087, -98598, -130518, 62844, 50364, 166296, 29190, -18840, -126423, 4380, -240273, -52620, 6123, 3600, -54516, -32256, -4842, -37404, -34071, 15504, -60399, 10722, -200898, 13872, 98562, -166896, 46866, 67212, -7467, -119298, -21411, 10032, -81816, -47202, 18720, -44676, 9825, 113754, 42213, 7608, 16497, -40218, -135354, -41532, 282432, 241542, -65823, -7008, 138813, 7194, 14769, -27072, 116151, -8178, 41841, 37368], "weight_parity": 1, "has_non_self_twist": 1, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": false, "level_is_squarefree": true, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 19, 5, 1, 9, 0]], "char_orbit_index": 5, "prim_orbit_index": 5, "minimal_twist": "38.4.e.a", "char_is_minimal": true, "conrey_index": 5, "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, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 2, 0, -1, 0, 2, -1, -2, 0, 0, 0], [0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0], [1, -2, 0, -3, 0, 1, 1, 0, 3, 1, 1, 0], [0, 0, -2, 0, 0, 2, -2, 4, 2, 0, 0, 0], [0, -1, 6, 2, 0, 0, 2, -4, -7, 1, 0, 0], [-8, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0], [0, -3, -7, -3, 3, 0, 0, 3, 0, 0, 3, 3], [2, 4, 12, 0, -2, 0, -2, 2, 0, -2, 0, -4], [-6, 0, -4, -3, 2, -3, 16, -4, -13, 0, -2, 5], [0, 4, 8, 4, 0, 0, 4, -4, -4, -4, 0, 0], [9, 1, -5, -7, -2, -5, -7, 7, 10, -2, 0, -1], [-8, 0, -12, -6, -2, 0, -10, 4, 6, 0, 0, -2], [44, 3, 0, 28, 3, 9, 3, 34, 19, 3, -9, -3], [0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0], [-6, -6, -33, 22, 0, -6, -21, -33, 0, 7, -1, -5], [8, 6, 0, 6, 0, 0, -12, 0, -6, 0, -6, -6], [-29, 3, 18, 0, -7, -13, 9, 10, 0, 2, 4, 1], [-20, 0, 0, 0, 4, -4, 0, -4, 0, 0, 8, 8], [-23, 0, -5, 10, 0, 0, 18, -5, 0, -5, 5, 2], [30, -10, -40, 0, 0, 6, -26, 32, 2, 6, -10, 0], [-23, 13, 0, -17, 13, 1, 38, -12, 7, -4, -1, 4], [-8, 0, -16, -16, 8, 0, 0, 8, 16, 0, 0, 8], [18, 9, 43, 0, -18, 0, 25, -39, -57, -18, 0, -9], [-2, -10, 10, 6, 4, 2, 6, -14, -20, 10, 2, 2], [31, 0, 0, 0, 9, 18, -49, 40, 49, -8, -9, -9], [8, 0, 16, 28, 0, 0, 0, -20, -8, 0, 4, 0], [39, -1, 91, 13, 4, 0, -3, 26, -36, -3, 26, 1], [12, 0, 38, -38, -6, -12, 94, 6, -56, -18, 6, 6], [-13, -9, -15, -72, -12, 13, -34, -4, 6, 9, -25, 13], [0, 0, 32, 0, 0, 0, 32, 0, 0, 0, 0, 0], [-141, -25, -111, -43, 3, 4, -138, -51, 43, 21, 21, 3], [34, -14, 0, -20, -14, -10, 36, -42, 40, 12, 10, -12], [-34, 0, 19, 0, 15, 15, 23, -23, 15, 15, 0, 0], [-12, -12, -24, -16, 0, -12, 0, -24, 0, 0, 12, 12], [96, 21, -1, 11, -27, 27, -33, 27, -68, 0, -19, -19], [-20, -18, 0, 96, -4, 16, 26, 18, -50, 26, -2, 6], [-98, -8, 17, -1, -4, 4, 26, 4, 12, 0, 6, 6], [-16, 8, 0, 24, 0, 8, 8, 0, 0, 8, -16, 0], [82, 7, -72, 0, -3, -21, -135, 117, -50, -21, 7, 0], [42, 10, 0, 32, 10, 4, 14, 36, 20, 0, -4, 0], [25, 4, -36, -337, -7, -15, 18, 50, 337, 11, 11, -7], [28, -8, 8, 12, -12, 0, -4, -52, -64, -12, 0, -20], [28, 27, 282, 114, -29, -28, 87, -202, -255, -27, -1, -28], [68, 0, -20, -14, 8, -18, -20, 76, 34, -2, -8, 26], [-29, -5, -178, 126, 34, 0, -29, -155, 58, -29, -31, 5], [16, 0, 16, 16, 0, 0, 0, 0, -16, 0, -16, 0], [234, 0, 18, -11, 3, 13, 64, 237, -53, 7, -3, -10], [-18, 0, -114, -114, 36, 18, -114, 50, 114, 0, 18, 18], [-215, 28, 219, 165, -3, -17, 216, -5, 9, -3, 0, 25], [-12, 8, -20, -12, -20, -4, -32, 12, 12, -4, -4, -20], [6, 43, 0, 92, 43, -19, 96, 106, -43, -33, 19, 33], [-80, 18, 82, 0, 16, -36, 46, -98, -28, -36, 18, 0], [66, 8, -199, 180, 0, 8, -273, -199, 0, 41, -49, -48], [-32, 8, -8, -56, 0, 0, 40, 0, 40, 0, 0, 0], [-132, -39, -266, 132, 42, 3, -64, 153, -102, -7, 21, 13], [-190, 52, -34, -26, 6, -6, -60, -6, -46, 0, -2, -2], [-385, -12, -15, 48, 0, -12, 382, -15, 0, 36, -24, 23], [100, -12, -148, 0, 36, 24, -200, 188, 0, 24, -12, 0], [271, -46, 0, -81, -46, -61, 97, -133, 306, -9, 61, 9], [-64, -24, 30, -16, -18, 50, -82, -68, 16, -26, -26, -18], [-10, -30, -37, -20, 45, 29, 8, -36, -20, 45, 0, 15], [0, 0, 0, 0, 0, 0, 0, 64, 0, 0, 0, 0], [100, 0, -53, 74, -14, -7, -247, 86, 173, 0, 14, -7], [-60, 50, 172, 216, -42, 0, -8, -276, 68, -8, -6, -50], [298, -24, 315, 183, 5, 0, 19, 115, -317, 19, -17, 24], [96, 0, 132, -80, -24, 4, 40, 72, 40, 20, 24, -28], [7, -35, 68, -211, -19, -7, -206, 28, -103, 35, -12, -7], [8, 30, 60, -8, -30, -30, 30, 46, 46, -30, 0, 0], [145, 47, 165, -254, -35, 21, 110, 48, 254, -68, -68, -35], [24, 0, 0, 0, 0, 24, -32, 0, 24, 24, -24, -24], [73, -18, -81, 0, -10, 29, 140, -101, -473, 29, -18, 0], [-26, 16, -66, -196, 0, 16, -56, -66, 0, -54, 38, 42], [-133, -70, -368, -583, 27, -27, 285, -27, 228, 0, 111, 111], [40, 28, -12, 68, -52, 20, 128, 52, -56, -32, -12, -36], [-93, -40, -222, -93, -10, 10, -89, 10, -98, 0, -11, -11], [6, 20, 52, 200, 0, 20, 26, 52, 0, -8, -12, -16], [139, 18, -90, 0, -31, 17, -286, 334, -203, 17, 18, 0], [16, -16, 0, 0, -16, 0, 80, 16, 0, -16, 0, 16], [75, 6, 471, -236, 21, -27, 96, -417, 236, 21, 21, 21], [-126, -28, -164, 98, 42, 6, -122, -270, -234, 42, 0, 14], [17, 15, 405, 35, 13, -17, -12, -162, -390, -15, 30, -17], [28, 0, 20, -40, 0, -20, 104, 28, -64, -8, 0, 20], [-479, -50, -69, -95, -44, 0, 94, -384, 385, 94, 0, 50], [122, -8, 702, 86, -22, 0, 30, 36, -152, 30, 14, 8], [499, 0, 37, -23, 14, 42, 132, 513, -109, -34, -14, -28], [16, 0, -128, -104, 24, -16, -160, -8, 128, 0, 40, -16], [-472, -91, 216, 606, 24, 128, 240, 47, -57, 24, 0, -67], [-334, -58, -564, -402, 54, 2, -280, 174, 402, 56, 56, 54], [152, -32, 0, 84, -32, -41, -225, 66, 36, -23, 41, 23], [-52, -52, -4, 0, 4, 36, 72, -40, -184, 36, -52, 0], [-219, 53, -551, 209, 0, 53, -385, -551, 0, -65, 12, -3], [288, -62, -72, -252, 58, -58, 242, -58, 368, 0, -10, -10], [57, 95, -247, 665, 38, 0, -456, 209, 95, -19, -57, 19], [-32, -32, -64, -32, 0, 0, 0, 0, 0, 0, 0, 0], [-473, 4, 173, -306, 0, 4, 642, 173, 0, -72, 68, -125], [112, 20, -78, 0, -14, -26, -140, 128, -462, -26, 20, 0], [443, 53, 0, 313, 53, 138, -52, 396, 183, 55, -138, -55], [-36, 72, 228, 64, 0, -36, -36, -228, -64, -36, -36, 0]]}