# Stored data for newform 300.3.c.g, downloaded from the LMFDB on 18 April 2024. {"label": "300.3.c.g", "space_label": "300.3.c", "level": 300, "weight": 3, "hecke_orbit": 7, "hecke_orbit_code": 27021735253508396, "dim": 8, "is_polredabs": true, "nf_label": "8.0.4069419264.1", "trace_hash": 291443373417322818, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[7, [961, 0, 9532, 0, 6470, 0, 188, 0, 1]], [13, [-1559, 3916, -418, -4, 1]]], "qexp_display": "q-\\beta _{4}q^{2}+\\beta _{5}q^{3}+(-1+\\beta _{7})q^{4}+(-1+\\cdots)q^{6}+\\cdots", "char_order": 2, "char_parity": -1, "char_degree": 1, "char_conductor": 4, "char_orbit_label": "c", "char_is_real": true, "Nk2": 2700, "analytic_conductor": 8.174407930808908, "hecke_ring_index": 256, "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": "0.506", "prec": 17}, "analytic_rank_proved": true, "char_values": [300, 2, [151, 101, 277], [1, 2, 2]], "hecke_ring_generator_nbound": 7, "inner_twist_count": 2, "level_primes": [2, 3, 5], "conrey_indexes": [151], "field_disc": 4069419264, "field_disc_factorization": [[2, 8], [3, 4], [443, 2]], "field_poly": [1, -12, 55, -84, 50, 0, -7, 0, 1], "hecke_ring_index_factorization": [[2, 8]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.106", "prec": 17}, {"__RealLiteral__": 0, "data": "7.548", "prec": 17}, {"__RealLiteral__": 0, "data": "8.156", "prec": 17}, {"__RealLiteral__": 0, "data": "296.469", "prec": 24}, {"__RealLiteral__": 0, "data": "706.428", "prec": 24}, {"__RealLiteral__": 0, "data": "16225.463", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 8, "sato_tate_group": "2.2.3.c2", "trace_display": [2, 0, 0, 0], "traces": [0, 8, 2, 0, -8, 0, -6, 0, 20, -24, 0, 0, 0, 8, 22, 0, 40, 0, -6, 0, 0, 24, 4, 0, -36, 0, -66, 0, 104, -32, 0, 0, 112, 0, 124, 0, 24, -176, -170, 0, 0, -16, 54, 0, 40, 0, -76, 0, 24, 16, 0, 0, 56, -304, 18, 0, -172, 72, -12, 0, 0, 136, -238, 0, 16, 0, -108, 0, 88, -96, 0, 0, -60, 240, -108, 0, 120, -384, 150, 0, 0, 72, 320, 0, -144, 0, 214, 0, -200, 128, 0, 0, 312, 72, 12, 0, 96, 216, 60, 0, 0, 112, 348, 0, 508, 0, 120, 0, 0, -520, 0, 0, -392, 96, 102, 0, -488, -24, 444, 0, 0, -440, -514, 0, -280, 0, -66, 0, -208, 264, 0, 0, -552, -8, -562, 0, 152, 752, 324, 0, 0, 336, 544, 0, -120, 0, 556, 0, -512, 336, 0, 0, 516, 0, -116, 0, 336, -264, -248, 0, 0, -352, 18, 0, 664, 0, -252, 0, -372, 352, 0, 0, -408, -288, 468, 0, -896, 48, -224, 0, 0, -200, -1382, 0, -264, 0, -462, 0, 832, -72, 0, 0, -720, -472, -762, 0, 640, -176, -12, 0, 0, -312, 248, 0, -408, 0, 976, 0, -456, 256, 0, 0, 1352, 144, 648, 0, 108, 600, -678, 0, 0, 256, 900, 0, 480, 0, 88, 0, -96, -40, 0, 0, -664, 1488, 198, 0, 96, 192, -156, 0, 0, -1048, -1606, 0, -888, 0, -720, 0, 956, 336, 0, 0, -312, 1088, -1160, 0, 736, 512, 102, 0, 0, 96, 616, 0, -792, 0, 298, 0, 824, -768, 0, 0, 1760, -1224, 1028, 0, 552, 8, -792, 0, 0, 1568, 876, 0, -88, 0, -1732, 0, -336, 1016, 0, 0, -896, -976, 876, 0, -856, 0, 244, 0, 0, 1144, -1530, 0, 88, 0, -372, 0, 1336, -192, 0, 0, -972, -24, -654, 0, 704, 96, 360, 0, 0, -624, 668, 0, -72, 0, 1850, 0, -448, -1936, 0, 0, 1856, 528, 1224, 0, 744, -2280, -432, 0, 0, -2048, 510, 0, 804, 0, -476, 0, -504, -16, 0, 0, -1056, 416, 252, 0, -1344, 192, -132, 0, 0, 624, -406, 0, -312, 0, -1002, 0, 416, 48, 0, 0, -1152, -680, -1448, 0, -152, -288, -162, 0, 0, 192, 892, 0, -720, 0, 58, 0, -1464, 2544, 0, 0, 2072, -624, 740, 0, -120, 856, -154, 0, 0, 1392, 894, 0, 2520, 0, 620, 0, -600, -1144, 0, 0, 16, -816, 228, 0, -1232, -1632, 1292, 0, 0, -560, -2210, 0, 880, 0, 240, 0, -184, -960, 0, 0, -72, -2808, -130, 0, -232, -928, 444, 0, 0, -48, 1316, 0, -432, 0, 1030, 0, 848, -2304, 0, 0, 1600, 792, -1568, 0, 444, -16, 642, 0, 0, -368, 1164, 0, 1728, 0, -1520, 0, -168, -72, 0, 0, -1176, 3328, 936, 0, -1976, 912, 2104, 0, 0, 912, -46, 0, -2184, 0, -54, 0, -420, 888, 0, 0, -648, 2624, -966, 0, -760, -400, 900, 0, 0, 1104, 1064, 0, 516, 0, 2152, 0, -1072, 2416, 0, 0, -160, -216, -1800, 0, 1104, 1408, -676, 0, 0, 2464, 36, 0, 936, 0, 944, 0, 0, 264, 0, 0, -424, -4240, 96, 0, 308, -240, -292, 0, 0, 408, -408, 0, -1344, 0, -54, 0, 64, -408, 0, 0, -216, -640, -682, 0, 272, -944, 714, 0, 0, -1152, -596, 0, 336, 0, -558, 0, -928, -2848, 0, 0, -968, 3648, 2800, 0, -48, -1080, -1114, 0, 0, -5456, 174, 0, -1576, 0, -1388, 0, 432, -1816, 0, 0, 1392, 1072, 324, 0, 1120, 312, -756, 0, 0, 248, -854, 0, 2216, 0, 264, 0, -576, 1056, 0, 0, -264, 560, 442, 0, 1880, -816, -816, 0, 0, 288, 1532, 0, -1080, 0, 322, 0, 1944, 3968, 0, 0, 656, -1944, -512, 0, 264, 5520, -632, 0, 0, 704, 24, 0, -344, 0, -892, 0, 180, 768, 0, 0, -1608, -2992, -510, 0, 400, -720, 180, 0, 0, 2256, -1544, 0, -1384, 0, 324, 0, -1128, -936, 0, 0, 912, -3120, 1718, 0, -3296, 640, -72, 0, 0, -1584, -3132, 0, -360, 0, -3606, 0, 2104, 2064, 0, 0, -1832, 1152, -1172, 0, -168, -1152, -1588, 0, 0, -2944, -450, 0, 32, 0, 1412, 0, 624, 1528, 0, 0, -1152, 4576, -1068, 0, 944, 1392, -3440, 0, 0, -3456, 620, 0, -1560, 0, 690, 0, 2268, -216, 0, 0, 1440, 5168, 3034, 0, 3552, 4096, -960, 0, 0, 1224, -3464, 0, 228, 0, 386, 0, -1920, 112, 0, 0, -432, -3456, 1132, 0, 432, -1752, -630, 0, 0, 3296, -936, 0, -808, 0, 840, 0, 864, 2424, 0, 0, 4008, -5296, -642, 0, 828, 48, 640, 0, 0, 1728, 4216, 0, 1104, 0, 696, 0, -672, -3312, 0, 0, 600, 104, -382, 0, -40, -1152, -558, 0, 0, -384, -1368, 0, 1728, 0, -2, 0, 5232, -6256, 0, 0, -1656, 3168, -2456, 0, -480, 616, 1370, 0, 0, -2672, -2220, 0, -4160, 0, -732, 0, -936, -1328, 0, 0, -720, 5888, -984, 0, 2904, -216, 2728, 0, 0, 184, 2308, 0, 984, 0, -36, 0, -1392, 1944, 0, 0, 936, 2232, 602, 0, -2800, 1536, -564, 0, 0, 2064, -308, 0, -288, 0, -3198, 0, -856, 3840, 0, 0, -2060, -648, -228, 0, -2640, -2152, 2818, 0, 0, -864, -180, 0, -3384, 0, 2896, 0, -456, 4544, 0, 0, 136, -3312, -348, 0, 1936, -1824, -3528, 0, 0, 2752, 4384, 0, 3440, 0, 1254, 0, -3368, -336, 0, 0, 2376, -6016, -1468, 0, 1592, -2960, -1044, 0, 0, -3720, 1304, 0, 1032, 0, -808, 0, -3136, -2752, 0, 0, -4952, 1776, 1820, 0, -1524, 1224, 2642, 0, 0, 2192, -2598, 0, -48, 0, 4364, 0, 1248, -5840, 0, 0, 3736, 4288, -360, 0, -1272, 3264, 1516, 0, 0, -3632, 2668, 0, 3160, 0, 924, 0, -1500, 4224, 0, 0, 0, 160, 3074, 0, -5096, 5072, 234, 0, 0, 1560, -2080, 0, 2592, 0, -4616, 0, 2552, 992, 0, 0, -6624, -4992, -1136, 0, -2640, -2224, 3486, 0, 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": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 4, 2, -1, 2, 0]], "char_orbit_index": 3, "prim_orbit_index": 2, "minimal_twist": "300.3.c.e", "char_is_minimal": true, "conrey_index": 151, "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], [0, 0, 0, 0, -1, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0], [-1, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, -1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, -1, -1, -1], [3, 0, 0, 1, 1, 2, -1, 0], [-3, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-1, -1, -2, -2, 1, -1, -1, 0], [0, -1, 0, 0, 1, -1, 0, 0], [2, -1, 0, 4, 1, 1, 0, -1], [2, 1, -1, -4, 1, -3, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0], [3, 1, -4, -2, -3, -3, -2, -1], [-2, 2, -5, 1, -6, -2, -2, -1], [0, 0, 0, 0, 3, 0, 0, 0], [-1, -1, 2, 2, -7, -4, 1, -2], [0, 0, 0, 0, 0, 0, 0, 0], [2, 1, -1, -3, -1, -1, 0, 0], [-1, -1, -2, -8, 5, 3, 0, 3], [1, 1, 4, 4, -5, 5, -1, -4], [-5, 0, 0, -3, 1, 2, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-10, 0, -2, 0, -5, -8, -4, -4], [0, 0, 0, 0, 0, -3, 0, 0], [14, -1, 4, 0, 1, 7, 4, 2], [-6, 2, -7, -1, -2, -2, 0, -5], [0, 0, 0, 0, 0, 0, 0, 0], [-4, -4, -4, -4, -4, -7, 3, 3], [12, -2, 0, -6, 0, -6, 2, 6], [0, 0, -1, -3, 4, 0, 2, -3], [15, -3, 0, 0, 1, -15, 0, 5], [0, 0, 0, 0, 0, 0, 0, 0], [3, 0, 0, 0, 0, 0, 0, -3], [-24, 2, -10, 2, -2, -2, 0, -8], [-20, 1, 5, 0, -1, -3, 0, 5], [1, 1, 0, 0, 3, 2, -4, -3], [0, 0, 0, 0, 0, 0, 0, 0], [-4, 2, 5, -9, -6, -2, -2, 9], [7, -1, 2, 0, 0, 3, 4, 3], [3, 3, 2, 2, 5, -8, 3, 4], [4, -2, -4, -8, 10, 22, 4, 4], [0, 0, 0, 0, 0, 0, 0, 0], [-11, 5, -6, 0, -5, -15, 0, 1], [2, 2, 8, 8, -10, -12, -4, -10], [3, 1, -4, -6, 9, 5, 2, 3], [2, 0, -6, 14, -8, 0, -4, -2], [0, 0, 0, 0, 0, 0, 0, 0], [1, 1, -6, -6, 15, 1, -1, 6], [7, 2, 0, -16, 14, -14, 0, 9], [-38, 0, 1, 7, -8, 0, -4, 5], [3, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-23, 0, 0, 11, -17, 14, 1, -4], [7, 2, -7, 3, -6, -2, -2, -3], [-1, -7, 4, 0, 5, -19, 8, 1], [4, 4, 0, 0, 12, 2, -4, 0], [0, 0, 0, 0, 0, 0, 0, 0], [24, -7, 14, -2, 23, 7, 8, -1], [-28, -7, 9, -4, 9, 21, 0, 9], [0, 0, 0, 0, 0, 3, 3, 3], [2, -2, 8, 0, -6, 30, 0, 6], [0, 0, 0, 0, 0, 0, 0, 0], [-13, -3, 4, 0, 1, 1, 8, -3], [1, 1, 14, 14, -25, 14, 1, -12], [10, 0, 12, -4, -12, 16, -8, 2], [-16, 4, -5, -3, -12, -4, -4, 3], [0, 0, 0, 0, 0, 0, 0, 0], [5, 5, 0, 0, 15, -1, -3, 2], [-9, 0, 0, -3, -3, -6, 3, 0], [20, 10, -18, -14, -18, -10, -4, -4], [-10, -10, 4, 0, 20, -34, 8, -2], [0, 0, 0, 0, 0, 0, 0, 0], [24, 5, 4, 8, 19, 13, -4, 0], [-46, -2, -3, 19, -6, 2, -4, -1], [15, 4, -9, -12, 2, -12, 0, 0], [2, 2, 12, 12, -18, -6, 0, -10], [0, 0, 0, 0, 0, 0, 0, 0], [9, 0, 0, 0, 0, 0, 0, 0], [45, 7, 0, 0, 13, 35, 0, 15], [-4, -4, 4, 4, -20, -18, -12, -20], [-17, -2, 4, 12, -10, 14, 0, -3], [0, 0, 0, 0, 0, 0, 0, 0], [34, -1, 17, 24, -11, 3, 0, -13], [5, 5, 0, 0, 15, 1, 1, 6], [-30, -8, -16, 2, 2, 28, 6, -4], [16, 0, -4, -4, 8, 0, 4, -8], [0, 0, 0, 0, 0, 0, 0, 0], [-3, -3, 14, 14, -37, 48, 15, -2], [48, -6, 20, 16, 6, -14, 4, 0], [12, -3, -5, 9, 11, 3, 4, -12], [2, 12, 6, -8, -8, -36, 0, 4], [0, 0, 0, 0, 0, 0, 0, 0], [12, -6, 0, 6, 0, 14, 6, -6], [35, -8, 4, 12, 24, 8, 8, -12], [2, -2, -8, 0, -12, -42, -16, -2], [3, 3, 6, 6, -3, 3, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0]]}