# Stored data for newform 30.3.f.a, downloaded from the LMFDB on 24 April 2024. {"label": "30.3.f.a", "space_label": "30.3.f", "level": 30, "weight": 3, "hecke_orbit": 1, "hecke_orbit_code": 343647715358, "dim": 4, "is_polredabs": true, "nf_label": "4.0.2304.2", "trace_hash": 952213134059371011, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [], "qexp_display": "q+(1-\\beta _{2})q^{2}+\\beta _{1}q^{3}-2\\beta _{2}q^{4}+(-2\\beta _{1}+\\cdots)q^{5}+\\cdots", "char_order": 4, "char_parity": -1, "char_degree": 2, "char_conductor": 5, "char_orbit_label": "f", "char_is_real": false, "Nk2": 270, "analytic_conductor": 0.8174407930808907, "hecke_ring_index": 1, "level_radical": 30, "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": "0.250", "prec": 17}, "analytic_rank_proved": true, "char_values": [30, 4, [11, 7], [4, 1]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 2, "level_primes": [2, 3, 5], "conrey_indexes": [7, 13], "field_disc": 2304, "field_disc_factorization": [[2, 8], [3, 2]], "field_poly": [9, 0, 0, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.001", "prec": 17}, {"__RealLiteral__": 0, "data": "3.804", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "54.370", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1232.352", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "2.2.3.c4", "trace_display": [4, 0, 0, -16], "traces": [0, 4, 4, 0, 0, 0, 0, -16, -8, 0, 4, -16, 0, 12, 0, -24, -16, 44, 12, 0, 8, 48, -16, -16, 0, 92, 24, 0, 32, 0, -48, -80, -16, -48, 0, -112, 24, -108, -64, 0, 8, 32, 48, 48, 0, -12, -32, 96, 0, 0, 92, 48, 24, 100, 0, 192, 64, 48, 64, 0, -48, -96, -80, -48, 0, -204, -96, -16, -88, 0, -32, 64, 24, -188, 0, 48, -128, -128, 96, 0, 0, -36, 32, 192, 0, -52, 96, -48, 32, 0, -12, 288, -32, -96, 0, 64, 0, 132, -124, 0, 0, -200, 48, -32, 0, 192, 200, 80, 0, 0, 176, 0, 64, 172, 0, -272, 128, -36, -80, 0, 0, -36, -96, 48, 0, 0, -96, -64, 32, 0, -384, -496, -96, 64, 0, 72, -176, 84, 144, 0, 160, -144, 64, -432, 0, -64, -376, -384, 216, 0, 0, 400, -128, 132, 0, 384, 192, 492, 48, 0, -16, 704, -36, -352, 0, 144, 384, 256, -96, 0, 88, 192, 96, 356, 0, -560, 64, 0, -352, 0, 0, 392, 288, 192, 0, -108, -192, -368, -192, 0, 256, -1184, 0, 156, 0, -96, -248, -732, -48, 0, -184, -432, -200, -64, 0, -192, -64, 48, -48, 0, 240, -256, 200, -48, 0, 432, 0, -64, 520, 0, -32, 648, 0, 384, 0, 0, 344, 400, -96, 0, -576, 192, 128, -468, 0, 384, -160, 624, 160, 0, 96, -512, -36, 0, 0, 124, 96, 576, 160, 0, 284, 1296, -96, -512, 0, -528, 64, -788, -240, 0, -360, -192, -496, 64, 0, 764, 128, 144, 32, 0, 0, -528, -176, -240, 0, -368, 288, 12, 256, 0, 384, -480, -144, 752, 0, -336, -864, 64, -48, 0, -256, 480, -376, -420, 0, 80, 432, 144, -456, 0, -96, -1344, 400, 384, 0, -768, 264, -864, 256, 0, 304, 1024, 192, 252, 0, -240, 96, 60, -432, 0, -32, -48, 704, -896, 0, 660, -704, 0, -64, 0, 192, 448, 384, -324, 0, 848, -192, -156, 164, 0, 280, 1088, 192, 1248, 0, -144, 712, 752, 96, 0, -384, -288, 64, 948, 0, 192, -704, 336, -16, 0, 24, 36, 392, 384, 0, -4, 384, -1168, 64, 0, -216, -2528, -192, -332, 0, -504, -384, -576, 144, 0, 384, 336, -1184, -1776, 0, -512, 312, -144, -264, 0, -240, 224, -248, -48, 0, -48, -96, 820, 48, 0, -368, 1032, -432, -1008, 0, 0, -128, 432, -96, 0, -160, 48, -64, 320, 0, -864, -96, 48, 640, 0, 96, 1184, -256, 288, 0, 820, -96, 1152, -160, 0, 960, -256, 0, 548, 0, 336, 1040, 320, 96, 0, -416, 372, 648, 912, 0, 352, 768, -768, -128, 0, 276, -512, 344, 384, 0, 960, -192, -36, -480, 0, -608, -1096, 192, -1552, 0, 576, -936, 128, 72, 0, 192, 0, -160, 768, 0, -384, 320, -300, 384, 0, 192, -648, -512, -768, 0, -828, 0, -288, 192, 0, -1412, -1328, 96, 896, 0, 48, 320, -448, 336, 0, 568, -1104, 1296, -480, 0, -1536, -1024, -576, 128, 0, -480, 1888, 64, 144, 0, -448, -480, 192, -864, 0, 48, 1080, -192, 384, 0, 1104, 128, -1264, 192, 0, 1728, 240, 128, 480, 0, 176, 64, 672, -776, 0, -144, 184, -528, -192, 0, -520, -480, 432, -168, 0, 16, 1408, 288, -2688, 0, 1296, 512, -540, -240, 0, 448, -1248, -480, 2256, 0, -844, 1504, 144, -128, 0, 96, 1184, -864, -144, 0, 208, -96, 1852, -4, 0, -384, -192, 480, 1328, 0, 540, -840, 1680, 768, 0, 80, 624, 432, -556, 0, -160, -912, -816, 1056, 0, -192, 320, -1344, -48, 0, -1536, 768, 624, 256, 0, -864, -576, 264, -1428, 0, -240, 512, -84, 240, 0, -160, -432, 1024, 832, 0, 1732, 504, -960, -984, 0, -576, 208, 96, -1248, 0, -736, -864, -2700, -640, 0, -32, -2336, -48, -1632, 0, 240, -1792, -992, 72, 0, 552, -192, -704, 996, 0, 192, -128, 564, 1344, 0, 96, -1888, 448, 1200, 0, 704, -648, -320, -512, 0, -32, -1152, -192, 868, 0, 144, 328, 68, 336, 0, 384, 1392, 1088, 576, 0, -12, 2496, 1440, -192, 0, 48, 1152, 712, -384, 0, -256, 192, 544, -1120, 0, 352, 1472, -288, 1728, 0, -1152, 1896, 2336, 0, 0, 256, -144, -704, -832, 0, 1776, -32, -288, 416, 0, 48, 1216, 36, -1440, 0, 384, 768, -288, -576, 0, -384, 96, 384, 1876, 0, -1128, 128, 1792, 96, 0, -216, 1824, -2528, -1712, 0, 456, -664, -576, 736, 0, -1008, -3696, -384, 336, 0, -1536, 288, -1908, -1024, 0, 256, 200, 336, -2080, 0, -420, -3552, 240, 0, 0, -256, 720, 312, -1188, 0, -1840, -528, -1296, 264, 0, -288, 128, 224, -144, 0, 492, -96, -2336, 1464, 0, 2448, -32, -96, 1248, 0, 432, 96, 156, -384, 0, -368, 1056, 1032, 368, 0, 3072, -2016, 1152, 400, 0, -36, -1984, -128, 1728, 0, -128, -192, -192, 696, 0, 64, 1280, 48, -256, 0, -1296, 640, -768, -96, 0, -1344, -480, -96, 172, 0, 2464, 1280, 288, -720, 0, -288, 1956, 1184, -1776, 0, -164, 576, 1680, -400, 0, -384, 864, -96, 940, 0, -576, -320, 1332, -672, 0, 1056, 0, -256, 800, 0, 700, 1096, 1056, 128, 0, -96, -3552, 1040, 396, 0, -3152, 192, 2412, 688, 0, -768, -2464, 372, 2368, 0, -480, 1824, -2304, 0, 0, 928, 144, 768, -960, 0, 16, -256, -48, -1976, 0, 552, 472, -512, 1536, 0, 768, 768, -3632, -800, 0, 1248, 4768, -192, -2112, 0, 384, -960, 1792, 144, 0, -64, -144, -1096, -192, 0, -2484, -3104, 96, -256, 0, 960, 1088, -936, -1488, 0, 2128, 144, -4196, 1600, 0, -384, -2040, 0, 448, 0, -144, 1536, -3296, -1248, 0, -1856, -3408, 320, 1068, 0, 576, 768, 960, 1696, 0, 192, -708, -648, 240, 0, 1380, -1536, 3424, 72, 0, 264, 592, 0, -1216, 0, 288, 384, -300, 240, 0, -3072, -1560, -1328, -4592, 0, -1980, 1792, 1728, -1152, 0, 624, 2032, 320, 480, 0, -48, 672, 3724, 3136, 0, 568], "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, 5, 3, -1, 4, 0]], "char_orbit_index": 6, "prim_orbit_index": 3, "minimal_twist": "30.3.f.a", "char_is_minimal": true, "conrey_index": 7, "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], [1, 0, -1, 0], [0, 1, 0, 0], [0, 0, -2, 0], [0, -2, 1, 2], [0, 1, 0, -1], [-4, 0, 4, -4], [-2, 0, -2, 0], [0, 0, 3, 0], [1, 0, 1, 4], [-4, -4, 0, 4], [0, 0, 0, -2], [3, 8, 3, 0], [0, -4, 8, -4], [-6, 0, -6, 1], [-4, 0, 0, 0], [11, 0, -11, -4], [3, 0, 3, 0], [0, -4, -16, -4], [2, 4, 0, 4], [12, -4, 0, 4], [-4, 0, 4, 8], [-4, 12, -4, 0], [0, -2, 0, -2], [23, -4, 0, -4], [6, 8, 0, -8], [0, 0, 0, 3], [8, -8, 8, 0], [0, 4, 16, 4], [-12, 1, 0, 1], [-20, -8, 0, 8], [-4, 0, 4, 0], [-12, -4, -12, 0], [0, -4, -22, -4], [-28, 4, 20, -16], [6, 0, 0, 0], [-27, 0, 27, 0], [-16, -8, -16, 0], [0, 3, 24, 3], [2, 8, -2, 0], [8, 4, 0, -4], [12, 0, -12, 8], [12, -20, 12, 0], [0, 8, 8, 8], [-3, -6, 0, -6], [-8, 12, 0, -12], [24, 0, -24, 12], [0, -4, 0, 0], [0, 32, -31, 32], [23, -8, -23, 0], [12, 11, 0, -11], [6, 0, -6, -16], [25, -36, 25, 0], [0, 3, 0, 3], [48, 4, -4, -12], [16, -8, 0, 8], [12, 0, -12, -16], [16, 8, 16, 0], [0, 0, -20, 0], [-12, 2, 12, 0], [-24, 16, 0, -16], [-20, 0, 20, 16], [-12, 12, -12, 0], [0, 0, 8, 0], [-51, -12, -45, 8], [-24, -4, 0, 4], [-4, 0, 4, 36], [-22, -8, -22, 0], [0, -4, 36, -4], [-8, -12, 48, -20], [16, -4, 0, 4], [6, 0, -6, 0], [-47, 8, -47, 0], [0, 0, 54, 0], [12, 23, -12, 0], [-32, -8, 0, 8], [-32, 0, 32, -16], [24, 6, 24, 0], [0, -52, 12, -52], [0, 8, -4, -8], [-9, 0, 0, 0], [8, 0, -8, -8], [48, 28, 48, 0], [0, 8, -24, 8], [-13, 4, 35, 44], [24, -20, 0, 20], [-12, 0, 12, 16], [8, 16, 8, 0], [0, -12, -88, -12], [-3, -12, 3, 0], [72, -20, 0, 20], [-8, 0, 8, -24], [-24, -20, -24, 0], [0, 12, -48, 12], [16, 36, 48, 28], [0, -4, 0, 4], [33, 0, -33, -40], [-31, 64, -31, 0], [0, -12, -12, -12], [0, -8, -46, 8]]}