# Stored data for newform 33.6.d.a, downloaded from the LMFDB on 23 April 2024.
{"label": "33.6.d.a", "space_label": "33.6.d", "level": 33, "weight": 6, "hecke_orbit": 1, "hecke_orbit_code": 206259093537, "dim": 2, "is_polredabs": true, "nf_label": "2.0.11.1", "trace_hash": 1776200820028636668, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[2, [0, 1]]], "qexp_display": "q+(2^{4}-\\beta )q^{3}-2^{5}q^{4}+(29-58\\beta )q^{5}+\\cdots", "char_order": 2, "char_parity": 1, "char_degree": 1, "char_conductor": 33, "char_orbit_label": "d", "char_is_real": true, "Nk2": 1188, "analytic_conductor": 5.292666053828361, "hecke_ring_index": 1, "level_radical": 33, "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": 1, "is_self_dual": false, "is_self_twist": true, "is_cm": true, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.760", "prec": 17}, "analytic_rank_proved": true, "char_values": [33, 2, [23, 13], [1, 1]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 4, "level_primes": [3, 11], "conrey_indexes": [32], "field_disc": -11, "field_disc_factorization": [[-1, 1], [11, 1]], "field_poly": [3, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.002", "prec": 17}, {"__RealLiteral__": 0, "data": "1.888", "prec": 17}, {"__RealLiteral__": 0, "data": "0.131", "prec": 17}, {"__RealLiteral__": 0, "data": "21.979", "prec": 20}, {"__RealLiteral__": 0, "data": "2.893", "prec": 17}, {"__RealLiteral__": 0, "data": "286.333", "prec": 24}], "related_objects": [], "self_twist_discs": [-11], "cm_discs": [-11], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "5.2.1.d2", "trace_display": [0, 31, 0, 0], "traces": [0, 2, 0, 31, -64, 0, 0, 0, 0, 475, 0, 0, -992, 0, 0, -319, 2048, 0, 0, 0, 0, 0, 0, 0, 0, -12252, 0, 7192, 0, 0, 0, 15550, 0, -1331, 0, 0, -15200, -2534, 0, 0, 0, 0, 0, 0, 0, -9889, 0, 0, 31744, 33614, 0, 0, 0, 0, 0, -77198, 0, 0, 0, 0, 10208, 0, 0, 0, -65536, 0, 0, 145834, 0, 16511, 0, 0, 0, 0, 0, -189906, 0, 0, 0, 0, 0, 107527, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 241025, 0, 0, 0, -326366, 0, -41261, 392064, 0, 0, -360488, 0, 0, 0, 0, -230144, 0, 0, -39277, 0, 0, 0, 957638, 0, 0, 0, 0, 0, -322102, 0, 0, -497600, 0, 0, 0, 0, 0, 0, 0, 42592, 0, 0, -229042, 0, 0, 0, 0, 0, -58102, 0, 0, 486400, 0, 0, 521017, 81088, 0, 0, 0, 0, 0, 0, 0, 0, -560234, 0, -71236, 0, 0, 0, 328288, 0, -1196569, 0, 0, 0, 742586, 0, 0, 0, 0, 0, 0, 0, 157091, 0, 0, 316448, 559750, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1015808, 0, 0, 0, -1075648, 0, 0, -1599800, 0, 2260427, 0, 0, 0, 0, 0, 511841, 0, 0, 0, 0, 0, -176275, 0, 0, 0, 0, 0, 0, 2470336, 0, 0, -495062, 0, -2909850, 0, 0, 0, 2342050, 0, 0, 0, 0, 0, -3369916, 0, 0, 0, 0, -326656, 0, 0, 1585681, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3995662, 0, 0, 2097152, 0, 0, 0, 0, 0, 0, 0, 0, -4131688, 0, 392975, -4666688, 0, 0, 0, 0, 0, 0, 0, -528352, 0, 0, 3693125, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2839714, 0, -5058673, 0, 0, 0, 9111278, 0, -955658, 0, 0, 6076992, 0, 0, 0, 0, 0, 0, 0, 0, -5587564, 0, 0, 0, -2097638, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3440864, 0, 0, 0, 0, 0, 0, 1473850, 0, -601825, 0, 0, 0, 0, 0, 635261, 0, 0, 0, 0, 0, 14843389, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10223950, 0, 0, 0, 0, 0, 4952198, 0, -4992581, 0, 0, 0, -2626334, 0, 0, 0, 0, -7712800, 0, 0, 957319, 0, 0, 0, 3777250, 0, 0, 0, 0, 0, 0, 0, 0, 10443712, 0, 0, 0, 0, 0, 0, 0, 1320352, 3120484, 0, 0, -12546048, 0, 0, 0, 0, -4697275, 0, 0, 0, 0, 0, 1166627, 11535616, 0, 0, 0, 0, 0, 0, 0, 0, -13714100, 0, -1801162, 0, 0, 0, 0, 0, 0, 0, 0, 7364608, -10210262, 0, 0, 0, 0, 0, 0, 0, 7983325, 0, 0, 1256864, 22792550, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -30644416, 0, 0, 14219638, 0, -2480225, 0, 0, 0, 0, 0, -8683627, 0, 0, 0, 0, 0, -2208316, 0, 0, 0, 0, 0, 0, 10307264, 0, 0, -8800466, 0, 5088464, 0, 0, 0, 0, 0, -18334525, 15923200, 0, 0, 14959600, 0, 0, 0, 0, 0, 0, 0, 11510083, 0, 0, 0, 0, 0, 0, 0, 0, 0, -14060684, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1362944, -36693336, 0, 4869821, 0, 0, 0, 0, 0, 566225, 0, 0, 7329344, 0, 0, 8676125, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 404173, 0, 0, 0, 0, 0, 0, 0, 0, 1859264, 36845138, 0, 0, 0, 0, 0, 0, 0, -3220063, 0, 0, -15564800, 16107934, 0, 0, 0, 0, 0, -17239112, 0, 0, 0, 0, -16672544, 0, 0, 0, -2594816, 0, 0, 0, 0, -24796900, 0, 0, 0, 0, 0, 34635575, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3825422, 0, 11854898, 0, 0, 0, 17237002, 0, 0, 17927488, 0, 0, -25740554, 0, 0, 0, 0, 2279552, 0, 0, -5464525, 0, 0, 0, -41935538, 0, 0, 0, 0, 0, 38016022, 0, 0, -10505216, 0, 0, 0, 0, 0, 0, 0, 38290208, -43020146, 0, 0, 0, 0, 0, 0, 0, -7673461, 0, 0, 0, 0, 0, -44058192, -23762752, 0, 0, 0, 0, 0, 0, 0, 0, 67664366, 0, 36301775, 0, 0, 0, 50062654, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -52233698, 0, 0, -5026912, -51831278, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10126336, 0, 0, 0, -17912000, 0, 0, 34175566, 0, 23027050, 0, 0, 0, 0, 0, -5361433, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 51218746, 0, -2502775, 0, 0, 0, -39152084, 0, 61932761, 0, 0, 0, 0, 0, 0, 0, 0, 32505856, 0, 0, 6932552, 0, 0, 0, -95259300, 0, 0, 0, 0, 0, -42658550, 0, 0, 34420736, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -64041164, 51193600, 0, 0, 0, 0, 12182225, 0, 0, -72333664, 0, 0, 6866684, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 71409562, 0, 8153706, 0, 0, -16378912, 38137378, 0, 0, 0, 0, 0, 0, 0, 55917800, 0, 0, 0, -41022298, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5640800, 0, 0, 0, 0, 0, 0, -30096722, 0, 0, 0, 0, 0, 0, 0, -44015567, 0, 0, 0, 0, 0, -77511925, 0, 0, 0, 0, 0, 0, -79050752, 0, 0, -12599888, 0, 141224809, 0, 0, 0, 0, 0, -19598975, 15841984, 0, 0, 32841050, 0, 0, 0, 0, 93115200, 0, 0, 0, 0, 0, 0, 61233616, 0, 0, 0, 0, 0, 0, 0, 0, -74945600, 0, 0, 0, 0, 0, 0, 0, 0, 15523284, 0, -85615900, 0, 0, 0, 0, 0, -1858450, 0, 0, 0, 0, 0, -32513389, 107837312, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4723873, 0, 0, 0, -186763654, 0, 0, 0, 0, 10452992, 63642948, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -50741792, 0, 0, 0, 0, 0, 0, 95099950, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 123536200, 0, 22844675, 0, 0, 0, 0, 0, -9112264, 0], "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, 11, 2, -1, 2, -11], [1, 1, 3, 2, -1, 2, 0], [1, 1, 33, 4, 1, 2, 0]], "char_orbit_index": 4, "prim_orbit_index": 4, "minimal_twist": "33.6.d.a", "char_is_minimal": true, "conrey_index": 32, "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], [1, 0], [0, 0], [16, -1], [-32, 0], [29, -58], [0, 0], [0, 0], [0, 0], [253, -31], [0, 0], [121, -242], [-512, 32], [0, 0], [0, 0], [290, -899], [1024, 0], [0, 0], [0, 0], [0, 0], [-928, 1856], [0, 0], [0, 0], [-1501, 3002], [0, 0], [-6126, 0], [0, 0], [3955, -718], [0, 0], [0, 0], [0, 0], [7775, 0], [0, 0], [1210, -3751], [0, 0], [0, 0], [-8096, 992], [-1267, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [-3872, 7744], [1943, -13775], [0, 0], [5282, -10564], [16384, -1024], [16807, 0], [0, 0], [0, 0], [0, 0], [6476, -12952], [0, 0], [-38599, 0], [0, 0], [0, 0], [0, 0], [-14281, 28562], [-9280, 28768], [0, 0], [0, 0], [0, 0], [-32768, 0], [0, 0], [0, 0], [72917, 0], [0, 0], [-15010, 46531], [0, 0], [16025, -32050], [0, 0], [0, 0], [0, 0], [-98016, 6126], [0, 0], [0, 0], [0, 0], [0, 0], [29696, -59392], [61126, -14725], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [-35725, 71450], [0, 0], [0, 0], [48032, -96064], [124400, -7775], [0, 0], [0, 0], [0, 0], [-163183, 0], [0, 0], [8107, -57475], [196032, 0]]}