# Stored data for newform 294.3.g.a, downloaded from the LMFDB on 25 April 2024. {"label": "294.3.g.a", "space_label": "294.3.g", "level": 294, "weight": 3, "hecke_orbit": 1, "hecke_orbit_code": 412367192358, "dim": 4, "is_polredabs": true, "nf_label": "4.0.576.2", "trace_hash": 1813352429826718025, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[5, [144, -144, 36, 12, 1]]], "qexp_display": "q+\\beta _{1}q^{2}+(-2-\\beta _{2})q^{3}+2\\beta _{2}q^{4}+\\cdots", "char_order": 6, "char_parity": -1, "char_degree": 2, "char_conductor": 7, "char_orbit_label": "g", "char_is_real": false, "Nk2": 2646, "analytic_conductor": 8.010919772192729, "hecke_ring_index": 1, "level_radical": 42, "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": "0.170", "prec": 17}, "analytic_rank_proved": true, "char_values": [294, 6, [197, 199], [6, 5]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 2, "level_primes": [2, 3, 7], "conrey_indexes": [19, 31], "field_disc": 576, "field_disc_factorization": [[2, 6], [3, 2]], "field_poly": [4, 0, 2, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.831", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "48.929", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "926.200", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "2.2.3.c6", "trace_display": [0, -6, -12, 0], "traces": [0, 4, 0, -6, -4, -12, 0, 0, 0, 6, 24, -12, 12, 0, 0, 24, -8, 48, 0, 42, 0, 0, 0, 24, 0, 22, -96, 0, 0, 0, -24, -102, 0, 36, 0, 0, -24, 22, -24, 6, -48, 0, 0, 28, -24, -36, -72, 132, 0, 0, -192, -48, -12, 120, 0, 0, 0, -84, -96, 24, -24, 72, 0, 0, 32, 180, 0, 110, -96, 0, 0, 312, 0, 66, -48, -66, 0, 0, 192, -10, 48, -18, -48, 0, 0, -288, -24, 0, 0, 72, 0, 0, -96, 102, 24, -132, 0, 0, 0, -72, 44, -36, -24, -42, 0, 0, 144, -288, 36, -290, -144, 0, 0, 168, 24, 288, 0, -18, 0, 0, 96, 170, -96, 156, 204, 0, 0, 500, 0, -42, 168, 108, 0, 0, -336, 36, 48, -168, 216, 0, 0, -264, 168, -36, 24, -576, 0, 0, -88, -264, 288, 340, 48, 0, 0, 120, 12, -648, 264, -360, 0, 0, 0, -100, -312, -72, 456, 0, 0, -872, 240, 126, -28, 648, 0, 0, 96, -24, 0, -84, 72, 0, 0, -144, -144, 156, -72, -288, 0, 0, 432, -252, -48, -218, 48, 0, 0, -288, 0, 216, 192, -330, 0, 0, 192, -216, -456, -72, 24, 0, 0, -296, 240, -468, -72, -228, 0, 0, 192, -66, 144, 144, 144, 0, 0, 132, 168, 180, 84, -222, 0, 0, 384, 492, -288, -216, -48, 0, 0, 1128, -48, 576, 0, 54, 0, 0, 96, -150, 144, -60, 240, 0, 0, -288, -120, 432, -32, -36, 0, 0, -720, 0, 144, -192, 0, 0, 0, -144, 220, 780, 72, 360, 0, 0, 96, 132, 144, 410, -120, 0, 0, -384, -24, -114, -312, 396, 0, 0, 0, -146, 576, 72, -132, 0, 0, 576, -96, 108, -144, -1800, 0, 0, -672, 36, -168, -336, 72, 0, 0, 84, -264, -348, -192, 930, 0, 0, 40, 120, -216, 0, -96, 0, 0, 768, -36, -2238, 96, 870, 0, 0, 288, 370, 120, -66, -744, 0, 0, 1156, -192, -252, 288, 612, 0, 0, 96, -288, -216, 288, 0, 0, 0, 36, 0, 300, 168, 72, 0, 0, -720, -312, -144, -380, -528, 0, 0, -2184, 96, 1266, 96, -468, 0, 0, -408, 650, 144, 408, -48, 0, 0, -836, -264, -750, -168, 624, 0, 0, 672, 42, -144, 1212, -504, 0, 0, -216, -552, -1524, 72, 654, 0, 0, -176, 840, 504, 678, 72, 0, 0, -264, -48, 1374, -528, 504, 0, 0, -432, -792, 384, -402, 144, 0, 0, -340, 144, 396, -144, 1104, 0, 0, 1152, 36, 312, -108, -72, 0, 0, 1152, -580, 72, -480, -360, 0, 0, -1488, 288, 132, -144, 0, 0, 0, 1464, -288, -936, -168, -1020, 0, 0, -96, 454, -144, 144, -576, 0, 0, 932, 0, -180, 24, 468, 0, 0, 960, 648, -336, -84, -792, 0, 0, 720, 240, -1128, -96, -1218, 0, 0, -680, -240, 0, -14, 192, 0, 0, -336, 312, 576, -648, 216, 0, 0, -912, 658, -816, -84, -888, 0, 0, 2448, -432, 1308, -500, -348, 0, 0, 0, -126, -72, -828, 84, 0, 0, -1296, 336, 1968, 288, 1410, 0, 0, 1056, -672, -144, -526, 1008, 0, 0, -1080, 0, 2160, 336, 252, 0, 0, -144, -238, 96, 354, -96, 0, 0, 104, -336, 216, 576, 576, 0, 0, 384, -156, 804, 1356, 216, 0, 0, 576, 648, -468, 264, 504, 0, 0, -672, -756, -648, -250, 72, 0, 0, -2928, 48, -1794, 384, 654, 0, 0, -96, 720, 960, -540, -1344, 0, 0, -1140, -240, 432, 88, -2652, 0, 0, 1056, -216, -1368, -1272, -576, 0, 0, 660, 680, -1020, 576, -330, 0, 0, 960, 324, -288, 1124, 2808, 0, 0, 1176, 456, -1122, -120, 216, 0, 0, -48, -746, 672, 252, 1296, 0, 0, -2392, 528, 444, 96, -2220, 0, 0, 1152, 468, 192, 0, 216, 0, 0, 456, -360, -3780, 0, -144, 0, 0, 400, -1116, -288, 72, 624, 0, 0, -384, -144, -426, 216, -432, 0, 0, -288, -1728, 168, -792, 2328, 0, 0, 916, 432, -198, 872, -2232, 0, 0, -960, -180, 432, -888, -252, 0, 0, 444, -56, 2088, -144, 114, 0, 0, -1008, 1044, -576, -1152, 1392, 0, 0, -1392, 288, 174, -96, 648, 0, 0, 96, -1460, 864, 30, 0, 0, 0, -2160, -168, -1692, 384, 228, 0, 0, -672, -576, -708, 2304, 0, 0, 0, -108, 1224, 480, 144, -2154, 0, 0, 576, 660, -144, -538, -312, 0, 0, -456, -144, 2448, 1008, 180, 0, 0, -480, 970, -528, -120, 288, 0, 0, 2104, 1176, 432, -432, 624, 0, 0, 1008, -432, 1560, -1368, 96, 0, 0, 72, -436, 1740, 72, 606, 0, 0, 240, 996, 1080, -936, -1440, 0, 0, 2592, -144, 2304, 288, 576, 0, 0, 0, -696, -1296, 288, -432, 0, 0, 2016, 384, 216, -408, -396, 0, 0, 3408, -780, -1152, 204, -216, 0, 0, -720, -288, 24, -192, 438, 0, 0, 864, 420, -144, 1004, 912, 0, 0, -3192, -144, -2586, -672, -1230, 0, 0, 240, 1656, -504, -306, -1968, 0, 0, 1244, 336, 576, 296, 1464, 0, 0, -960, 114, -2568, -1128, 936, 0, 0, -792, -144, 4368, -576, 432, 0, 0, -2544, -1380, 0, -1728, -2160, 0, 0, 120, -576, -3702, -192, -216, 0, 0, 264, -652, 1440, 120, -288, 0, 0, 748, 288, -864, -72, -2100, 0, 0, 576, -108, 1584, 876, 432, 0, 0, 3600, -984, 1728, -132, 2448, 0, 0, -672, 348, 1008, 226, -360, 0, 0, -1920, 168, 360, -288, 1008, 0, 0, -144, 1474, 288, -114, 3552, 0, 0, -1820, -1800, -126, -384, 2796, 0, 0, -1968, 348, -648, 864, 576, 0, 0, -1860, -432, -3936, 0, -2736, 0, 0, 288, -324, -60, 3774, -2280, 0, 0, 2112, 216, 2520, -1128, 0, 0, 0, 192, 244, -1200, 864, -1152, 0, 0, -1372, 0, -1152, -384, -1968, 0, 0, -3216, 2238, -288, 1140, -288, 0, 0, -1740, 912, -4296, -96, -2448, 0, 0, 600, -264, -432, 562, -288, 0, 0, 480, -120, -798, 120, 198, 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, 7, 4, -1, 6, 0]], "char_orbit_index": 7, "prim_orbit_index": 4, "minimal_twist": "42.3.g.a", "char_is_minimal": false, "conrey_index": 19, "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], [0, 1, 0, 0], [-2, 0, -1, 0], [0, 0, 2, 0], [-2, -2, 2, -4], [0, -2, 0, -1], [0, 0, 0, 0], [0, 0, 0, 2], [3, 0, 3, 0], [8, -2, 4, 2], [0, 0, 6, 0], [2, 0, -2, 0], [1, 16, 2, 8], [0, 0, 0, 0], [6, 0, 0, 6], [-4, 0, -4, 0], [16, -2, 8, 2], [0, 3, 0, 3], [7, 2, -7, 4], [-4, 8, -8, 4], [0, 0, 0, 0], [0, 0, 0, 6], [12, 18, 12, 0], [0, 2, 0, -2], [0, 24, -11, 24], [-16, 1, 16, 2], [-3, 0, -6, 0], [0, 0, 0, 0], [0, 0, 0, 24], [-12, 6, -12, 0], [-34, -6, -17, 6], [0, -4, 0, -4], [6, 0, -6, 0], [-4, 16, -8, 8], [0, 0, 0, 0], [-6, 0, 0, 0], [11, 12, 11, 0], [-8, 7, -4, -7], [0, -24, -3, -24], [-8, -4, 8, -8], [26, 8, 52, 4], [0, 0, 0, 0], [7, 0, 0, 6], [-12, 0, -12, 0], [-12, 6, -6, -6], [0, 12, 36, 12], [22, -2, -22, -4], [4, 0, 8, 0], [0, 0, 0, 0], [-48, 0, 0, -11], [-24, 6, -24, 0], [-4, -16, -2, 16], [0, -18, -60, -18], [0, -3, 0, -6], [-12, 24, -24, 12], [0, 0, 0, 0], [-21, 0, 0, -6], [-48, 0, -48, 0], [8, 14, 4, -14], [0, -12, 12, -12], [12, 8, -12, 16], [-12, -34, -24, -17], [0, 0, 0, 0], [8, 0, 0, 0], [90, -42, 90, 0], [0, 6, 0, -6], [0, 42, -55, 42], [-16, -4, 16, -8], [-12, -36, -24, -18], [0, 0, 0, 0], [78, 0, 0, -42], [0, -6, 0, 0], [22, -40, 11, 40], [0, 11, 24, 11], [-11, -24, 11, -48], [14, -8, 28, -4], [0, 0, 0, 0], [48, 0, 0, -3], [-5, -66, -5, 0], [16, -8, 8, 8], [0, 0, 9, 0], [-8, 26, 8, 52], [-10, -76, -20, -38], [0, 0, 0, 0], [-72, 0, 0, -60], [-12, 7, -12, 0], [0, 24, 0, -24], [0, -12, 0, -12], [12, 0, -12, 0], [12, -12, 24, -6], [0, 0, 0, 0], [-24, 0, 0, 36], [51, 18, 51, 0], [8, 22, 4, -22], [0, -54, 66, -54], [0, 4, 0, 8], [12, -8, 24, -4], [0, 0, 0, 0], [-18, 0, 0, 0], [22, -48, 22, 0]]}