# Stored data for newform 294.4.e.l, downloaded from the LMFDB on 24 April 2024. {"label": "294.4.e.l", "space_label": "294.4.e", "level": 294, "weight": 4, "hecke_orbit": 12, "hecke_orbit_code": 49539870846091558, "dim": 4, "is_polredabs": true, "nf_label": "4.0.16281225.4", "trace_hash": 1411902178289108462, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[5, [108900, 1650, 355, -5, 1]], [11, [617796, 52662, 3703, 67, 1]]], "qexp_display": "q-2\\beta _{2}q^{2}+(3-3\\beta _{2})q^{3}+(-4+4\\beta _{2}+\\cdots)q^{4}+\\cdots", "char_order": 3, "char_parity": 1, "char_degree": 2, "char_conductor": 7, "char_orbit_label": "e", "char_is_real": false, "Nk2": 4704, "analytic_conductor": 17.34656154168774, "hecke_ring_index": 1, "level_radical": 42, "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": "0.000", "prec": 17}, "analytic_rank_proved": true, "char_values": [294, 3, [197, 199], [3, 2]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 2, "level_primes": [2, 3, 7], "conrey_indexes": [67, 79], "field_disc": 16281225, "field_disc_factorization": [[3, 2], [5, 2], [269, 2]], "field_poly": [112896, 336, 337, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.879", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "56.731", "prec": 20}, {"__RealLiteral__": 0, "data": "7.018", "prec": 17}, {"__RealLiteral__": 0, "data": "1432.538", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "3.2.3.c3", "trace_display": [-4, 6, 5, 0], "traces": [0, 4, -4, 6, -8, 5, -24, 0, 32, -18, 10, -67, 24, -82, 0, 30, -32, -92, -36, 43, -40, 0, 268, -148, 48, -435, 82, -108, 0, 154, -30, -520, -64, 201, 368, 0, 144, -7, 86, -123, 40, 852, 0, -214, -268, 45, -296, 576, -192, 0, 1740, 276, 164, 243, 108, 1010, 0, 258, -154, -7, -60, 224, 2080, 0, 256, 570, 402, -687, -368, -888, 0, 944, -144, -921, -14, 1305, -344, 0, 492, 526, 80, -162, -852, 442, 0, -5840, 214, 231, -536, 774, -180, 0, 1184, 1560, 1152, 1910, 192, -3906, 0, 1206, -1740, 704, 552, -2453, -656, 0, -972, -219, 216, 597, -1010, -42, 0, -3524, -258, -2320, -308, 369, 28, 0, 240, -255, 448, 1278, -2080, -7650, 0, -5708, -256, -321, 1140, 179, -1608, 0, 2748, -135, -736, 3370, 888, 3198, 0, 3456, -944, 2046, -288, -7205, 3684, 0, 56, -942, 2610, -933, 344, 1656, 0, 90, -492, -1274, 1052, -729, -320, 0, 648, -2188, -1704, 1515, -442, -5080, 0, -5762, 5840, 387, 428, 494, -924, 0, 2144, 21, 1548, -2646, 180, 5342, 0, 1344, -1184, 6070, 3120, -392, -4608, 0, -7640, 750, 384, 1400, 3906, 3420, 0, -5980, -1206, -5780, -3480, 2061, -2816, 0, -2208, 5100, -4906, -1332, 656, -6916, 0, 11132, 972, 1416, -438, 9820, -864, 0, -2388, 2763, -2020, -804, 42, 17938, 0, 7830, 3524, 6213, -516, 789, 9280, 0, 1232, -3826, 738, -9510, -28, 3156, 0, 11988, -240, 181, -510, 486, -1792, 0, -5112, -2899, -4160, 663, 7650, -186, 0, 15296, 5708, -8760, -512, -4692, 1284, 0, -4560, -693, 358, -10242, 1608, 5250, 0, 4644, -2748, 3635, -270, 4265, 2944, 0, -13480, -11210, 1776, 5711, -3198, 9360, 0, 9548, -3456, 5733, -1888, -5730, -8184, 0, 1152, -5166, -14410, -5859, -3684, 8046, 0, 33590, -56, 1809, -1884, 5724, -10440, 0, 3732, -2112, 688, 2130, -1656, -15330, 0, -14718, -90, -2218, -984, 5832, 5096, 0, -4208, -6753, -1458, -9977, 320, -1314, 0, 12184, -648, 5555, -4376, -1791, 6816, 0, -6060, -2917, -884, -63, 5080, 11360, 0, -4244, 5762, -5286, 11680, -18765, -1548, 0, -1712, 6960, 988, 6288, 924, -21912, 0, 2214, -2144, -3090, 42, 14630, -6192, 0, 10584, 3538, 360, 6741, -5342, -1530, 0, -51680, -1344, 10108, -2368, -3834, -24280, 0, -12480, 18717, -784, -11475, 4608, -17952, 0, -20070, 7640, -8562, 1500, -2354, -1536, 0, -5600, 963, 7812, 23800, -3420, -7904, 0, 1074, 5980, 4065, -2412, -5257, 23120, 0, 13920, -15288, 4122, 12005, 2816, -810, 0, -11636, 2208, 652, 10200, -10110, 19624, 0, 5328, 17365, 1312, 4797, 6916, -6564, 0, 26014, -11132, 5184, 1944, -33460, -5664, 0, 1752, -6138, 19640, -4962, 864, 16054, 0, -43230, 2388, 11252, 5526, 17321, 8080, 0, 3216, 9179, 84, 26310, -17938, -5652, 0, -43748, -7830, -10236, 7048, 2799, -24852, 0, 2064, 7212, 1578, 2484, -9280, 30476, 0, 1914, -1232, 135, -7652, 12770, -2952, 0, 38040, 3822, -56, 13672, -3156, 1470, 0, -4374, -11988, -24902, -480, -5909, -724, 0, 2040, 18655, 972, -2320, 1792, -13128, 0, 9282, 5112, 26048, -5798, -4545, 16640, 0, -2652, 4191, 15300, -7620, 186, 10452, 0, -23380, -15296, -8643, 11416, 147, 35040, 0, 2048, -1161, -9384, -7990, -1284, -22452, 0, 2964, 4560, -27438, -1386, -8939, -1432, 0, 40968, -18540, 3216, 2622, -5250, 126, 0, -9396, -4644, -29715, -5496, 7938, -14540, 0, 1080, -13499, 8530, 8013, -2944, -62920, 0, 19384, 13480, 2016, -22420, 23848, -7104, 0, -22844, -18210, -6396, -34025, -9360, 24562, 0, -2352, -9548, 41467, -6912, 50740, -22932, 0, 7552, 16470, -11460, -36965, 8184, 4500, 0, 37480, -1152, -15042, -10332, -4200, 57640, 0, 23436, 6123, -7368, 5130, -8046, -28574, 0, -30430, -33590, -8970, -112, 15522, -7236, 0, 7536, 17340, 11448, -9342, 10440, -75764, 0, 12366, -3732, -44420, -4224, -14056, -2752, 0, -8520, -3738, -3312, 7414, 15330, 30600, 0, 632, 14718, 207, -180, 3996, 8872, 0, 3936, -25800, 11664, -10374, -5096, 49064, 0, -15562, 4208, 16698, -13506, 38595, 5832, 0, 39908, -4248, 640, -61222, 1314, 55798, 0, 58920, -12184, -312, -1296, -17047, -22220, 0, 17504, 24411, -3582, -5155, -6816, 16578, 0, 53120, 6060, 24105, -5834, 2412, 3536, 0, 252, -35288, 10160, 26907, -11360, -20388, 0, 39992, 4244, 11745, 11524, -7293, 21144, 0, -46720, -18639, -37530, 37557, 1548, 84100, 0, 4734, 1712, -2964, 13920, -6803, -3952, 0, -25152, 71920, 1848, -35736, 21912, -22956, 0, 13258, -2214, -18007, -4288, 28530, 12360, 0, -168, 19628, 29260, 4734, 6192, 87720, 0, -62400, -10584, 17982, 7076, -7236, -1440, 0, -26964, -543, -10684, 20240, 1530, 10908, 0, 2916, 51680, -35428, -2688, -20125, -40432, 0, 9472, -30412, -7668, 28483, 24280, -17394, 0, 29928, 12480, 6390, 37434, -1989, 3136, 0, 45900, -44258, 9216, -279, 17952, 74690, 0, -41312, 20070, 22944, 15280, 6328, 34248, 0, -6000, 26280, -4708, 16956, 1536, -66360, 0, -28152, 5600, 13388, 1926, -106375, -31248, 0, -95200, -2946, -6840, -2362, 7904, -4158, 0, 17840, -1074, -6418, 11960, 30726, -16260, 0, 9648, -7282, -10514, 7875, -23120, -101526, 0, -117552, -13920, 6966, -30576, -7316, -16488, 0, -48020, -10905, 5632, -12002, 810, -22620, 0, 25590, 11636, 94240, 4416, -32563, -2608, 0, -40800, -7747, -20220, 39936, -19624, -67260, 0, 78990, -5328, -17319, 34730, -17133, -5248, 0, -19188, -970, 13832, 14040, 6564, 17080, 0, 71118, -26014, 14322, -22264, -34775, -20736, 0, -7776, -17199, -66920, 23692, 5664, 121366, 0, -34380, -1752, -22626, -12276, -26138, -78560, 0, 19848, 39664, 1728, -48310, -16054, -30996, 0, -46002, 43230, 21481, 4776, 17577, -45008, 0, -22104, 16182, 34642, 12069, -8080, -50940, 0, -79462, -3216, 50385, 18358, 25266, -336, 0, -105240, -5427, -35876, 11826, 5652, -166560, 0, 34344, 43748, -34815, -15660, 19248, 40944, 0, -28192, -89490, 5598, -13277, 24852, -12672, 0, 151596, -2064, 9409, 14424, -6390, -6312, 0, -9936, -35373, -18560, -22995, -30476, 7548, 0, 63570, -1914, -22077, -2464, -92460, -540, 0, 30608, 6654, 25540, 60160, 2952, -53828, 0, 34992, -38040, 21839, 7644, -15384, 224, 0, -54688, 36862, -6312, -4657, -1470, -40518, 0, 47012, 4374, 50580, -23976, 29931, 99608, 0, 1920, -78308, -11818, -1971, 724, 305590, 0, -87508, -2040, 18276, 37310, -52053, -3888, 0, 9280, -16665, 3584, -26328, 13128, -108348, 0, -10746, -9282, -8988, 10224, 106850, -104192, 0, 23192, 48268, -9090, 14996, -16640, -17502, 0, -77320, 2652, -36731, 8382, 189, -61200], "weight_parity": 1, "has_non_self_twist": 1, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": false, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 7, 3, 1, 3, 0]], "char_orbit_index": 5, "prim_orbit_index": 3, "minimal_twist": "42.4.e.c", "char_is_minimal": false, "conrey_index": 67, "id": 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], [1, 0, 0, 0], [0, 0, -2, 0], [3, 0, -3, 0], [-4, 0, 4, 0], [0, 1, 2, 0], [-6, 0, 0, 0], [0, 0, 0, 0], [8, 0, 0, 0], [0, 0, -9, 0], [6, -2, -4, -2], [-33, -1, 34, -1], [0, 0, 12, 0], [-20, 0, 0, -1], [0, 0, 0, 0], [9, 0, 0, -3], [0, 0, -16, 0], [-48, 4, 44, 4], [-18, 0, 18, 0], [0, -3, 23, 0], [-12, 0, 0, 4], [0, 0, 0, 0], [66, 0, 0, 2], [0, 4, -76, 0], [24, 0, -24, 0], [-220, 5, 215, 5], [0, -2, 42, 0], [-27, 0, 0, 0], [0, 0, 0, 0], [33, 0, 0, 11], [0, -6, -12, 0], [-259, -2, 261, -2], [-32, 0, 32, 0], [0, -3, 102, 0], [96, 0, 0, -8], [0, 0, 0, 0], [36, 0, 0, 0], [0, -9, 1, 0], [40, 6, -46, 6], [-60, -3, 63, -3], [0, 8, 16, 0], [216, 0, 0, -6], [0, 0, 0, 0], [-46, 0, 0, -15], [0, 4, -136, 0], [27, -9, -18, -9], [-144, -8, 152, -8], [0, 12, 282, 0], [-48, 0, 0, 0], [0, 0, 0, 0], [440, 0, 0, -10], [0, 12, 132, 0], [80, 4, -84, 4], [123, -3, -120, -3], [0, 0, 54, 0], [237, 0, 0, 31], [0, 0, 0, 0], [60, 0, 0, 9], [0, 22, -88, 0], [9, -25, 16, -25], [-36, 12, 24, 12], [0, -4, 114, 0], [518, 0, 0, 4], [0, 0, 0, 0], [64, 0, 0, 0], [0, -18, 294, 0], [198, 6, -204, 6], [-338, -11, 349, -11], [0, -16, -176, 0], [-216, 0, 0, -12], [0, 0, 0, 0], [246, 0, 0, -20], [0, 0, -72, 0], [-478, 35, 443, 35], [-16, 18, -2, 18], [0, 15, 645, 0], [-80, 0, 0, -12], [0, 0, 0, 0], [120, 0, 0, 6], [0, -8, 267, 0], [48, -16, -32, -16], [-81, 0, 81, 0], [0, -12, -420, 0], [123, 0, 0, -25], [0, 0, 0, 0], [-1488, 0, 0, 56], [0, -30, 122, 0], [99, 33, -132, 33], [-264, -8, 272, -8], [0, -42, 408, 0], [-54, 0, 0, 18], [0, 0, 0, 0], [288, 0, 0, 16], [0, -6, 783, 0], [588, -24, -564, -24], [948, 14, -962, 14], [0, 0, 96, 0], [-959, 0, 0, -35], [0, 0, 0, 0], [297, 0, 0, 9], [0, -20, -860, 0]]}