# Stored data for newform 441.4.e.y, downloaded from the LMFDB on 19 April 2024. {"label": "441.4.e.y", "space_label": "441.4.e", "level": 441, "weight": 4, "hecke_orbit": 25, "hecke_orbit_code": 108086666001908153, "dim": 8, "is_polredabs": true, "nf_label": "8.0.5922408960000.19", "trace_hash": 1632508367895834507, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[2, [256, 16, 17, -1, 1]], [5, [614656, 0, 145824, 0, 33812, 0, 186, 0, 1]], [13, [2458624, 0, -3234, 0, 1]]], "qexp_display": "q+(1-\\beta _{2}+\\beta _{6})q^{2}+(-8-8\\beta _{1}+\\beta _{6}+\\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": 7056, "analytic_conductor": 26.019842312531612, "hecke_ring_index": 49, "level_radical": 21, "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": "0.506", "prec": 17}, "analytic_rank_proved": true, "char_values": [441, 3, [344, 199], [3, 1]], "hecke_ring_generator_nbound": 25, "inner_twist_count": 4, "level_primes": [3, 7], "conrey_indexes": [226, 361], "field_disc": 5922408960000, "field_disc_factorization": [[2, 12], [3, 4], [5, 4], [13, 4]], "field_poly": [86044, 16800, -15314, -2912, 1307, 176, -54, -4, 1], "hecke_ring_index_factorization": [[7, 2]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.019", "prec": 17}, {"__RealLiteral__": 0, "data": "7.431", "prec": 17}, {"__RealLiteral__": 0, "data": "0.888", "prec": 17}, {"__RealLiteral__": 0, "data": "396.927", "prec": 24}, {"__RealLiteral__": 0, "data": "391.215", "prec": 24}, {"__RealLiteral__": 0, "data": "36745.499", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "3.2.3.c3", "trace_display": [2, 0, 0, 0], "traces": [0, 8, 2, 0, -34, 0, 0, 0, -132, 0, 0, 100, 0, 0, 0, 0, 174, 0, 0, 0, 0, 0, -680, 352, 0, 128, 0, 0, 0, -520, 0, 0, -30, 0, 0, 0, 0, -212, 0, 0, 0, 0, 0, 1080, 460, 0, -696, 0, 0, 0, -2732, 0, 0, 16, 0, 0, 0, 0, 780, 0, 0, 0, 0, 0, -3356, -756, 0, 1944, 0, 0, 0, -4496, 0, 0, -284, 0, 0, 0, 0, 1048, 0, 0, 0, 0, 0, -6568, 4820, 0, -1260, 0, 0, 0, -7024, 0, 0, 2192, 0, 0, 0, 0, -342, 0, 0, 0, 0, 0, 4696, 3768, 0, 516, 0, 0, 0, 4632, 0, 0, 1300, 0, 0, 0, 0, 484, 0, 0, 0, 0, 0, 3152, -7294, 0, 4928, 0, 0, 0, 11824, 0, 0, 1752, 0, 0, 0, 0, 696, 0, 0, 0, 0, 0, 2824, -2616, 0, -6120, 0, 0, 0, -1888, 0, 0, -12744, 0, 0, 0, 0, -2172, 0, 0, 0, 0, 0, -4640, -13992, 0, -9140, 0, 0, 0, 15720, 0, 0, 4552, 0, 0, 0, 0, -6328, 0, 0, 0, 0, 0, 25072, 7128, 0, 6228, 0, 0, 0, -5728, 0, 0, -682, 0, 0, 0, 0, -868, 0, 0, 0, 0, 0, -8048, 2476, 0, -584, 0, 0, 0, 48616, 0, 0, 5852, 0, 0, 0, 0, -14312, 0, 0, 0, 0, 0, 6760, -4912, 0, 10240, 0, 0, 0, -9088, 0, 0, -19742, 0, 0, 0, 0, 13496, 0, 0, 0, 0, 0, 11360, 9888, 0, -3602, 0, 0, 0, 21952, 0, 0, 10152, 0, 0, 0, 0, 21464, 0, 0, 0, 0, 0, -848, -11780, 0, 12472, 0, 0, 0, -44480, 0, 0, 17288, 0, 0, 0, 0, -9476, 0, 0, 0, 0, 0, 8608, 3108, 0, -31972, 0, 0, 0, -32640, 0, 0, 5692, 0, 0, 0, 0, -14512, 0, 0, 0, 0, 0, -42256, -13424, 0, -11960, 0, 0, 0, 35688, 0, 0, -19324, 0, 0, 0, 0, 15412, 0, 0, 0, 0, 0, 10152, -7530, 0, 40264, 0, 0, 0, -26920, 0, 0, -404, 0, 0, 0, 0, -17580, 0, 0, 0, 0, 0, -49008, 27624, 0, -2056, 0, 0, 0, -23336, 0, 0, -10632, 0, 0, 0, 0, -27848, 0, 0, 0, 0, 0, -62648, 30072, 0, -16824, 0, 0, 0, -65792, 0, 0, 2900, 0, 0, 0, 0, 69548, 0, 0, 0, 0, 0, 36876, 27596, 0, 33152, 0, 0, 0, -15280, 0, 0, 12264, 0, 0, 0, 0, -2912, 0, 0, 0, 0, 0, -19248, 3448, 0, -2604, 0, 0, 0, -61456, 0, 0, 53216, 0, 0, 0, 0, 28436, 0, 0, 0, 0, 0, 91392, 18888, 0, -37948, 0, 0, 0, -28464, 0, 0, -4216, 0, 0, 0, 0, 23028, 0, 0, 0, 0, 0, 24544, -19500, 0, 45616, 0, 0, 0, 74720, 0, 0, -13800, 0, 0, 0, 0, -71432, 0, 0, 0, 0, 0, -47228, -21756, 0, -13456, 0, 0, 0, -464, 0, 0, -4928, 0, 0, 0, 0, -16648, 0, 0, 0, 0, 0, 4184, -18480, 0, -22496, 0, 0, 0, 15804, 0, 0, -50000, 0, 0, 0, 0, 17024, 0, 0, 0, 0, 0, -43408, -3128, 0, 13532, 0, 0, 0, 54488, 0, 0, -37016, 0, 0, 0, 0, -1752, 0, 0, 0, 0, 0, -107896, 13592, 0, -42340, 0, 0, 0, 69672, 0, 0, -56320, 0, 0, 0, 0, -32960, 0, 0, 0, 0, 0, 70544, -75836, 0, 4268, 0, 0, 0, -352, 0, 0, 110818, 0, 0, 0, 0, 13640, 0, 0, 0, 0, 0, 125648, 5272, 0, 12732, 0, 0, 0, -22088, 0, 0, 45712, 0, 0, 0, 0, -65280, 0, 0, 0, 0, 0, 12192, -560, 0, -27652, 0, 0, 0, 158408, 0, 0, 22064, 0, 0, 0, 0, 10944, 0, 0, 0, 0, 0, 92976, -29512, 0, 15292, 0, 0, 0, 84240, 0, 0, -51644, 0, 0, 0, 0, 114092, 0, 0, 0, 0, 0, -3896, -5444, 0, 27936, 0, 0, 0, -101096, 0, 0, -24476, 0, 0, 0, 0, -15600, 0, 0, 0, 0, 0, 76176, -45692, 0, 26090, 0, 0, 0, 133072, 0, 0, -11576, 0, 0, 0, 0, -17460, 0, 0, 0, 0, 0, -4824, 86128, 0, 3416, 0, 0, 0, 123016, 0, 0, -1780, 0, 0, 0, 0, 15020, 0, 0, 0, 0, 0, 16800, 11912, 0, 74848, 0, 0, 0, -44956, 0, 0, -28340, 0, 0, 0, 0, -60824, 0, 0, 0, 0, 0, -54160, -18960, 0, -36556, 0, 0, 0, -104848, 0, 0, 47204, 0, 0, 0, 0, -51200, 0, 0, 0, 0, 0, -141944, 16188, 0, -47608, 0, 0, 0, -147696, 0, 0, 31528, 0, 0, 0, 0, 16928, 0, 0, 0, 0, 0, -143480, 51828, 0, -67120, 0, 0, 0, 91352, 0, 0, -46636, 0, 0, 0, 0, -44324, 0, 0, 0, 0, 0, 187920, -66250, 0, -88028, 0, 0, 0, -141568, 0, 0, -57020, 0, 0, 0, 0, 26600, 0, 0, 0, 0, 0, 38416, -130744, 0, 105152, 0, 0, 0, 178512, 0, 0, 12376, 0, 0, 0, 0, 33376, 0, 0, 0, 0, 0, -135832, 57068, 0, 28744, 0, 0, 0, -40728, 0, 0, 15536, 0, 0, 0, 0, -60872, 0, 0, 0, 0, 0, 112496, 6792, 0, -63764, 0, 0, 0, -94240, 0, 0, -32564, 0, 0, 0, 0, 4380, 0, 0, 0, 0, 0, -104144, 92512, 0, 119256, 0, 0, 0, -415728, 0, 0, -21160, 0, 0, 0, 0, 160324, 0, 0, 0, 0, 0, -45488, -62748, 0, -84296, 0, 0, 0, 59568, 0, 0, 140976, 0, 0, 0, 0, 135280, 0, 0, 0, 0, 0, -30728, 206336, 0, -40820, 0, 0, 0, 169824, 0, 0, -8000, 0, 0, 0, 0, 119280, 0, 0, 0, 0, 0, 108400, 45684, 0, 54124, 0, 0, 0, -198592, 0, 0, 107784, 0, 0, 0, 0, -81044, 0, 0, 0, 0, 0, 15584, -27486, 0, 42728, 0, 0, 0, -240176, 0, 0, -35880, 0, 0, 0, 0, -202136, 0, 0, 0, 0, 0, -225792, 83920, 0, 25520, 0, 0, 0, -35936, 0, 0, 112584, 0, 0], "weight_parity": 1, "has_non_self_twist": 1, "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], [1, 1, 7, 3, 1, 3, 0], [1, 1, 7, 4, -1, 6, 0], [1, 1, 7, 2, -1, 2, 0]], "char_orbit_index": 5, "prim_orbit_index": 3, "minimal_twist": "49.4.a.e", "char_is_minimal": false, "conrey_index": 226, "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, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0], [1, 0, -1, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-8, -8, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 1, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-17, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 2, 4, 0, 0, 0], [28, 28, 0, 0, 0, 0, 6, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 6, 0, -6, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-9, -48, 9, 0, 0, 0, -9, 0], [0, 0, 0, -1, 9, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -4, -11, 0, -4], [0, 0, 0, 2, 0, -2, 0, -12], [0, 0, 0, 0, 0, 0, 0, 0], [-74, 0, -22, 0, 0, 0, 0, 0], [8, -84, -8, 0, 0, 0, 8, 0], [0, 0, 0, 0, 0, 0, 0, 0], [43, 43, 0, 0, 0, 0, 22, 0], [0, 0, 0, 0, -16, 16, 0, -16], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-58, 0, -14, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 38, -4, 0, 0, 0], [16, 16, 0, 0, 0, 0, 47, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 21, 0, -21, 0, -34], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [6, 56, -6, 0, 0, 0, 6, 0], [0, 0, 0, 25, -38, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -20, -2, 0, -20], [0, 0, 0, 31, 0, -31, 0, 3], [0, 0, 0, 0, 0, 0, 0, 0], [170, 0, -70, 0, 0, 0, 0, 0], [-26, -128, 26, 0, 0, 0, -26, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-128, -128, 0, 0, 0, 0, 92, 0], [0, 0, 0, 0, -32, 26, 0, -32], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-331, 0, -21, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -32, -24, 0, 0, 0], [-14, -14, 0, 0, 0, 0, -36, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 12, 0, -12, 0, 4], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-58, -224, 58, 0, 0, 0, -58, 0], [0, 0, 0, 49, -20, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -27, 68, 0, -27], [0, 0, 0, -122, 0, 122, 0, -60], [0, 0, 0, 0, 0, 0, 0, 0], [-471, 0, 103, 0, 0, 0, 0, 0], [-70, 154, 70, 0, 0, 0, -70, 0], [0, 0, 0, 0, 0, 0, 0, 0], [448, 448, 0, 0, 0, 0, -76, 0], [0, 0, 0, 0, -106, -13, 0, -106], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-548, 0, -28, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 37, 25, 0, 0, 0], [-96, -96, 0, 0, 0, 0, -50, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -63, 0, 63, 0, 70], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [188, -168, -188, 0, 0, 0, 188, 0], [0, 0, 0, -18, 12, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -50, 99, 0, -50], [0, 0, 0, -1, 0, 1, 0, -8], [0, 0, 0, 0, 0, 0, 0, 0], [-916, 0, 190, 0, 0, 0, 0, 0], [170, -1120, -170, 0, 0, 0, 170, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-352, -352, 0, 0, 0, 0, -74, 0], [0, 0, 0, 0, 75, 157, 0, 75], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-956, 0, 156, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -142, -76, 0, 0, 0], [460, 460, 0, 0, 0, 0, -176, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -189, 0, 189, 0, -91], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-155, 8, 155, 0, 0, 0, -155, 0]]}