# Stored data for newform 15.3.f.a, downloaded from the LMFDB on 23 April 2024. {"label": "15.3.f.a", "space_label": "15.3.f", "level": 15, "weight": 3, "hecke_orbit": 1, "hecke_orbit_code": 343647715343, "dim": 4, "is_polredabs": true, "nf_label": "4.0.2304.2", "trace_hash": 445990341755593137, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [], "qexp_display": "q+(-1+\\beta _{1}-\\beta _{2})q^{2}+\\beta _{3}q^{3}+(-2\\beta _{1}+\\cdots)q^{4}+\\cdots", "char_order": 4, "char_parity": -1, "char_degree": 2, "char_conductor": 5, "char_orbit_label": "f", "char_is_real": false, "Nk2": 135, "analytic_conductor": 0.40872039654044534, "hecke_ring_index": 1, "level_radical": 15, "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": "0.247", "prec": 17}, "analytic_rank_proved": true, "char_values": [15, 4, [11, 7], [4, 1]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 2, "level_primes": [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": "0.007", "prec": 17}, {"__RealLiteral__": 0, "data": "3.859", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "54.188", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1186.466", "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, -4, 4], "traces": [0, 4, -4, 0, 0, -4, -12, 4, 12, 0, 4, 16, 24, -32, 0, 24, -20, -40, -12, 0, -36, -24, 20, 56, 0, 16, 88, 0, 44, 0, -24, -16, -76, -36, 0, -40, 12, 64, -96, 0, 48, -56, 12, -8, 0, 36, -136, 128, 48, 0, 164, 72, -80, 56, 0, -124, 0, -72, -12, 0, -84, 200, 88, 12, 0, -112, 24, -200, -104, 0, -60, -272, -36, 76, 0, 24, 312, 88, 120, 0, 164, -36, 128, -16, 0, 232, -224, -84, 12, 0, -96, -16, 104, -72, 0, 144, -84, -20, -188, 0, -396, 136, 48, -308, 0, 60, -256, 128, 72, 0, -56, 216, -116, 224, 0, 160, 264, 96, 516, 0, 72, -204, -416, -72, 0, -364, 48, 100, 132, 0, 272, 160, 60, -120, 0, -36, -168, -304, -192, 0, 40, -120, 272, -56, 0, -132, 424, -48, -496, 0, 96, 8, -144, -120, 0, -200, -408, 136, 120, 0, 220, 64, 36, 640, 0, 24, 200, 104, -60, 0, -72, -72, 472, 224, 0, 340, -368, 372, -456, 0, 204, -616, -152, 216, 0, -40, 192, -376, 112, 0, -624, 16, 120, -356, 0, -168, 332, -328, 60, 0, 108, -48, -820, -240, 0, -160, 496, -168, 64, 0, 0, 824, 344, 0, 0, 464, -36, 128, 144, 0, 324, 496, -408, 268, 0, 36, -40, 464, 216, 0, -440, -168, 132, -88, 0, -632, -1632, 120, 88, 0, -24, -64, 492, 0, 0, 468, 312, 336, -120, 0, 544, -1472, -132, 152, 0, -432, 148, -112, -216, 0, -88, 216, 164, -1240, 0, 400, 240, -432, 296, 0, -144, 56, 488, 168, 0, 496, 696, -368, 456, 0, -180, 1432, -264, -152, 0, 216, -368, 88, -228, 0, 72, 192, -1076, -280, 0, -804, 600, 108, 492, 0, -144, -496, 712, 684, 0, 448, 24, 88, 248, 0, -160, -464, 168, 100, 0, -120, -480, -1072, -312, 0, -1068, -360, 248, 192, 0, -272, -1568, -72, -240, 0, 156, 488, -352, 192, 0, 752, 216, 1012, -268, 0, 608, 368, 288, 240, 0, 240, 440, 320, -348, 0, -240, 72, -52, 488, 0, 272, 1752, 312, -900, 0, 108, 436, -32, -288, 0, -1000, -1032, -188, -184, 0, 1440, -176, -168, -488, 0, -396, 648, -408, 36, 0, 336, -1368, 200, 320, 0, -520, -920, 24, -364, 0, 768, -976, -468, -324, 0, -120, -384, 328, 1032, 0, -656, -200, 648, 272, 0, 36, -120, -392, 96, 0, -200, 888, -68, 600, 0, -368, 1384, 672, 264, 0, 60, -88, -1112, 384, 0, -1048, 816, -232, 592, 0, -424, 1984, -144, -380, 0, 552, 72, -480, 348, 0, -312, -420, -160, -352, 0, 504, 448, 84, -76, 0, -156, 208, -592, -720, 0, 520, -504, 124, -984, 0, 280, -392, -96, 412, 0, -240, -1624, 1808, -240, 0, 672, 168, 804, -752, 0, 1224, -1024, -168, -1296, 0, -600, -1456, 640, -312, 0, 272, 108, -1100, 816, 0, -1408, -1040, -408, 1224, 0, 36, -496, -272, 216, 0, 684, 696, 1652, -832, 0, 1916, 608, -384, 2636, 0, -168, 1304, 92, -216, 0, -376, 144, 872, -472, 0, -816, -536, 36, -1448, 0, -240, 2792, -272, 372, 0, -680, 432, -120, 592, 0, -872, -1248, -900, 204, 0, 216, 1784, 520, 648, 0, -576, -288, -2216, -1472, 0, -316, -576, -240, 240, 0, 360, -2472, 680, 264, 0, 680, 1008, -1504, 944, 0, -368, 688, -36, -816, 0, -936, -2344, 904, -216, 0, 440, 948, -1580, -1364, 0, -1308, 304, -132, -208, 0, -312, 2192, 1808, 888, 0, 3384, 144, 544, 1952, 0, 360, -744, 144, 1472, 0, 612, 1496, 208, -600, 0, -660, -1776, 1300, -960, 0, 632, -1808, 312, -1256, 0, -480, 360, 296, 804, 0, 1080, -72, -1840, -840, 0, -644, -1448, -72, -472, 0, 60, 128, 120, 288, 0, -1768, 816, 1216, -192, 0, 1968, 424, -24, -608, 0, 696, 624, 80, -108, 0, -1088, -48, 1216, -160, 0, -1132, -296, -228, -392, 0, -624, -472, -2288, -336, 0, -240, -1032, 840, -1496, 0, -1992, -496, 372, 796, 0, 504, 1420, 992, -264, 0, 456, -1344, -224, 2000, 0, 2104, 1440, -48, 1000, 0, -1200, 1016, -1552, 264, 0, -24, -288, 128, 2688, 0, 260, 280, -360, 1680, 0, 1272, -2392, -1232, -1236, 0, -272, 0, -504, -368, 0, 848, 3600, 48, -984, 0, -36, -856, 428, -576, 0, 1128, 1188, -524, 120, 0, 620, 1600, 1416, -1328, 0, -228, -2296, -656, 384, 0, -2960, 1296, 368, 752, 0, -1308, 3016, 48, -1640, 0, 1416, -1264, -1120, -180, 0, -2168, 72, -2384, -840, 0, 72, -2408, 1068, -360, 0, 192, -1528, -1896, -768, 0, 120, -600, 2908, -880, 0, 800, 72, -168, 2676, 0, -312, -1088, 208, -252, 0, -376, 168, 3448, 40, 0, 720, 1264, -36, -2032, 0, 600, -1464, 608, 360, 0, 1100, -72, 2504, 2032, 0, -1000, -1792, 1188, 1092, 0, -36, 2408, 960, -576, 0, 1856, -1320, -1392, 1776, 0, 1440, 952, 24, 1564, 0, -156, -1320, -1360, 312, 0, 448, -1896, -2768, -1112, 0, 280, -48, 216, -2556, 0, -120, 892, -1064, 72, 0, 36, -408, 372, 296, 0, -792, 2224, -1632, 1240, 0, -576, 408, 248, -312, 0, -1744, 192, -472, -2968, 0, -1328, -1688, -1440, -32, 0, 108, 3296, 576, -60, 0, -760, 336, 1144, -1320, 0, 1484, 1192, 564, -1808, 0, -1056, 3968, -712, 840, 0, -2784, -144, -1700, 48, 0, 900, -1440, 528, 1152, 0, -816, -256, -424, 288, 0, 2560, 1416, -752, 2224, 0, 320, -1952, 72, 440, 0, 1632, 1128, 808, 144, 0, 1320, 1440, -2668, 2176, 0, -2960, -3104, 924, 780, 0, 600, -1416, 3512, 2304, 0, 2512, 648, 532, 848, 0, -2608, -2696, -576, -928, 0, -180, 400, 656, -120, 0, -1104, -1560, -360, -1552, 0, -664, 1152, -984, -960, 0, 468, -2916, 3568, 384, 0, 2552, 432, 1540, -900, 0, 588, -1856, -216, 1560, 0, -1608, 728, 2600, -2208, 0, 2332, 648, 284, -2704, 0, 1456, 528, -888, -2928, 0, 264, -3352, 808, 1800, 0, -2808, -360, -2864, -3456, 0, -732], "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": "15.3.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, 1, -1, 0], [0, 0, 0, 1], [0, -2, 1, -2], [-1, -2, 3, 1], [-3, 1, 0, -1], [1, 2, 1, 0], [3, 0, -3, 1], [0, 0, -3, 0], [1, 2, -8, 4], [4, 3, 0, -3], [6, -1, 6, 0], [-8, 0, 8, -2], [0, -1, 4, -1], [6, -3, -3, -1], [-5, -4, 0, 4], [-10, -6, -10, 0], [-3, 0, 3, -3], [0, 6, -6, 6], [-9, 7, 17, -6], [-6, -1, 0, 1], [5, -2, 5, 0], [14, 0, -14, 2], [0, 3, -3, 3], [4, -2, 3, -14], [22, -10, 0, 10], [0, 3, 0, 0], [11, 0, -11, -2], [0, 7, 18, 7], [-6, 8, -12, 1], [-4, 6, 0, -6], [-19, 7, -19, 0], [-9, 0, 9, 4], [0, -4, 2, -4], [-10, -5, -10, 5], [3, -6, 0, 6], [16, -18, 16, 0], [-24, 0, 24, -18], [0, -8, 6, -8], [12, -6, 9, 8], [-14, 6, 0, -6], [3, -4, 3, 0], [-2, 0, 2, 20], [0, -5, -32, -5], [9, 3, 3, 6], [-34, 16, 0, -16], [32, 10, 32, 0], [12, 0, -12, -5], [0, 4, -35, 4], [41, -8, -13, 19], [18, 10, 0, -10], [-20, 34, -20, 0], [14, 0, -14, 12], [0, -3, 9, -3], [-31, -2, 3, 16], [0, 5, 0, -5], [-18, 6, -18, 0], [-3, 0, 3, 4], [0, -31, 36, -31], [-21, -17, 18, -9], [50, -18, 0, 18], [22, -16, 22, 0], [3, 0, -3, -6], [0, -10, 79, -10], [-28, 14, -26, -22], [6, -5, 0, 5], [-50, 4, -50, 0], [-26, 0, 26, 34], [0, 14, -6, 14], [-15, 0, 5, -10], [-68, 0, 0, 0], [-9, 3, -9, 0], [19, 0, -19, -48], [0, 34, -86, 34], [6, -3, 42, 4], [78, -18, 0, 18], [22, 14, 22, 0], [30, 0, -30, 22], [0, -10, 0, -10], [41, 2, -3, -21], [-9, 0, 0, 0], [32, -26, 32, 0], [-4, 0, 4, -14], [0, 11, 6, 11], [58, 36, 16, -8], [-56, 18, 0, -18], [-21, -18, -21, 0], [3, 0, -3, -14], [0, 36, -6, 36], [-24, 12, -3, -6], [-4, -14, 0, 14], [26, -58, 26, 0], [-18, 0, 18, -4], [0, 22, -34, 22], [36, -18, -48, 24], [-21, 19, 0, -19], [-5, -16, -5, 0], [-47, 0, 47, -43], [0, -9, -12, -9], [-99, 12, -68, -16]]}