# Stored data for newform 294.3.g.b, downloaded from the LMFDB on 23 April 2024.
{"label": "294.3.g.b", "space_label": "294.3.g", "level": 294, "weight": 3, "hecke_orbit": 2, "hecke_orbit_code": 4504011994562854, "dim": 4, "is_polredabs": true, "nf_label": "4.0.576.2", "trace_hash": 435426126531380342, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[5, [36, -72, 54, -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": "0.169", "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": "0.017", "prec": 17}, {"__RealLiteral__": 0, "data": "4.005", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "60.082", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1391.373", "prec": 27}], "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, 12, 12, 12, 0, 0, -24, -8, -12, 0, 12, 0, 0, -24, -12, 0, -14, 24, 0, 0, 120, -12, -72, 0, -36, 0, 0, -24, 40, 96, -48, -24, 0, 0, -128, 24, 36, 36, -168, 0, 0, 96, 12, 96, 108, 0, 0, 0, -24, 0, -168, 24, -24, 0, 0, 32, -120, 36, -88, 24, 0, 0, -120, 0, 24, -144, 42, 0, 0, -48, -64, -48, -18, 84, 0, 0, 216, 120, -180, 24, 324, 0, 0, 48, 72, 48, 120, 0, 0, 0, 72, -28, 252, 132, -168, 0, 0, -96, 84, 36, 4, 0, 0, 0, -360, -96, -180, -120, 144, 0, 0, 48, 134, -48, -84, 144, 0, 0, 224, 0, 192, 144, -144, 0, 0, -96, -36, -264, -60, -108, 0, 0, 336, -228, -216, 24, 360, 0, 0, -160, -252, -144, -8, -192, 0, 0, 0, -96, 504, -288, -324, 0, 0, 0, 248, 168, -36, -240, 0, 0, -188, 240, 36, 128, -108, 0, 0, -96, 168, -252, 204, -72, 0, 0, 48, 72, 672, 144, -468, 0, 0, 432, -12, -48, -56, -120, 0, 0, -600, -36, 12, -96, 264, 0, 0, -48, -252, -624, 36, -192, 0, 0, 256, 216, 180, -12, -24, 0, 0, 192, -24, 72, 168, 432, 0, 0, -84, 48, -792, 24, 432, 0, 0, 0, -420, 72, -288, 336, 0, 0, 600, 48, 600, -144, 54, 0, 0, -168, -288, -288, -192, -96, 0, 0, 72, 96, -324, -32, 828, 0, 0, 480, 180, 144, 492, -72, 0, 0, -648, -176, 1164, 36, 312, 0, 0, -768, 228, -72, -208, -96, 0, 0, -264, -48, -1188, 120, -360, 0, 0, 0, 898, 360, -264, -48, 0, 0, -1152, -288, -108, 240, -504, 0, 0, 432, -252, -48, -96, -396, 0, 0, 336, 144, -336, 48, 816, 0, 0, 256, 36, 144, 360, 96, 0, 0, 2064, -36, 48, 144, -12, 0, 0, 0, -512, 384, -120, 384, 0, 0, 760, -384, 540, -216, -864, 0, 0, -480, 180, 36, -132, 360, 0, 0, -288, 48, -1092, -240, -1044, 0, 0, -504, 204, -72, 70, 456, 0, 0, -528, 48, -60, -48, 252, 0, 0, -288, 236, 864, 240, -96, 0, 0, -512, 240, -336, -300, -696, 0, 0, -288, -192, 528, 156, -432, 0, 0, 288, -96, 480, -72, -2088, 0, 0, 112, -444, 144, -288, -504, 0, 0, -384, 264, 168, 336, 180, 0, 0, 216, -144, -96, 696, 504, 0, 0, 128, -120, -504, 96, 1668, 0, 0, -336, 216, 336, -636, -72, 0, 0, -720, 8, -936, -312, 36, 0, 0, 2016, 1044, 240, 396, -432, 0, 0, -840, 144, -252, 360, 24, 0, 0, 384, -764, -72, -36, 360, 0, 0, 608, -240, 0, -432, 1008, 0, 0, -480, -504, 480, -744, 864, 0, 0, 648, 372, -672, -48, 1824, 0, 0, -536, -408, 0, 328, 96, 0, 0, 792, -168, -360, 816, 108, 0, 0, 480, -272, -480, 408, 384, 0, 0, 360, -144, 282, -224, -1452, 0, 0, 0, -36, 252, -960, -384, 0, 0, 216, 288, -420, 0, 600, 0, 0, -888, 1728, 144, 662, 360, 0, 0, -1680, 252, 540, 96, -612, 0, 0, 144, 752, 624, 96, 528, 0, 0, -1744, -120, -72, 372, 360, 0, 0, -1056, -672, -1392, -1500, -432, 0, 0, 936, 240, 2160, -336, -936, 0, 0, 912, -1380, -648, 632, 432, 0, 0, -696, 48, -1488, 528, 168, 0, 0, 240, -792, 624, 360, -2004, 0, 0, 2016, -816, 900, 160, -660, 0, 0, 1008, -12, -1008, 12, 288, 0, 0, -528, -16, 1236, -324, 1212, 0, 0, -288, 1248, 72, -76, 288, 0, 0, 216, 624, 552, 0, -108, 0, 0, 384, 226, -1392, 216, -1008, 0, 0, -640, -576, -384, -1584, 960, 0, 0, -720, -180, 96, -132, 36, 0, 0, 48, 72, 0, 0, -288, 0, 0, -992, -276, -288, -144, -336, 0, 0, 2616, -72, 1416, 216, -504, 0, 0, -864, -360, -816, 108, -816, 0, 0, 1168, -288, 126, 188, -4068, 0, 0, -960, 792, 1296, 2052, -72, 0, 0, -864, 256, -2304, -288, 504, 0, 0, 2184, 1488, 0, 756, -240, 0, 0, -936, -72, 3696, 96, 864, 0, 0, -672, 28, -1728, 192, 504, 0, 0, -576, 408, -900, 12, 2112, 0, 0, 768, -600, -192, -420, 432, 0, 0, -108, -576, 4344, -48, -2880, 0, 0, -288, 384, 252, -2056, -1344, 0, 0, 984, 288, -2232, 864, 576, 0, 0, 192, -488, 672, -96, 720, 0, 0, -3896, -648, -108, -432, 3804, 0, 0, 48, 324, -2064, -1824, 96, 0, 0, -1656, -112, -2172, -360, 2232, 0, 0, -1728, -840, -720, 324, 576, 0, 0, 2880, -144, -456, 600, -1476, 0, 0, 144, 288, -576, -504, -24, 0, 0, 1728, -192, 972, 1344, 1080, 0, 0, 1728, -1164, 648, 396, -108, 0, 0, -624, 624, 1056, 48, 2496, 0, 0, 1008, -1764, 1152, 560, 1248, 0, 0, 3240, 72, -1680, -96, 624, 0, 0, 192, 432, -432, -216, 1680, 0, 0, 236, 912, 396, -256, -1716, 0, 0, -864, 1188, -1212, 1536, -360, 0, 0, 720, -24, -1020, 144, -84, 0, 0, -1512, 132, 0, -180, -2736, 0, 0, -2496, -360, 2400, -192, 792, 0, 0, 96, 1316, 1872, -444, -144, 0, 0, -4832, 336, 1728, -828, -3048, 0, 0, 288, 108, -216, 48, -720, 0, 0, 1008, 1104, -2160, 84, -2232, 0, 0, -192, -264, -648, 1360, 1584, 0, 0, -600, 48, -1872, -288, 288, 0, 0, 792, -968, 576, -324, 1668, 0, 0, 2896, 864, -504, 0, 1596, 0, 0, 1680, 336, 1728, -72, -144, 0, 0, -1632, -576, 372, 432, -1260, 0, 0, 2208, -516, -384, -432, -384, 0, 0, -3816, -144, 828, -600, -1080, 0, 0, -192, 670, 3936, -252, -1200, 0, 0, 3488, -288, -3096, 288, 600, 0, 0, -912, -48, 96, -444, -432, 0, 0, 24, -1260, 552, 168, -2088, 0, 0, 1152, -696, 0, -1832, 576, 0, 0, 1680, -384, -1944, -1752, 360, 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.c.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, -1, -2, -2], [0, -2, 0, -1], [0, 0, 0, 0], [0, 0, 0, 2], [3, 0, 3, 0], [4, 2, 2, -2], [0, 3, -6, 3], [2, 0, -2, 0], [-8, -4, -16, -2], [0, 0, 0, 0], [-6, 0, 0, 3], [-4, 0, -4, 0], [-4, 11, -2, -11], [0, 3, 0, 3], [2, -8, -2, -16], [4, 4, 8, 2], [0, 0, 0, 0], [-6, 0, 0, -6], [-6, -9, -6, 0], [0, 2, 0, -2], [0, -12, 7, -12], [4, -8, -4, -16], [-3, 0, -6, 0], [0, 0, 0, 0], [30, 0, 0, 0], [-6, -6, -6, 0], [-24, 12, -12, -12], [0, -4, 0, -4], [-6, -3, 6, -6], [22, -4, 44, -2], [0, 0, 0, 0], [-6, 0, 0, 0], [20, 36, 20, 0], [32, 2, 16, -2], [0, 6, 24, 6], [-4, 4, 4, 8], [-14, -14, -28, -7], [0, 0, 0, 0], [-32, 0, 0, -30], [12, -6, 12, 0], [12, 3, 6, -3], [0, -6, -18, -6], [-28, -4, 28, -8], [4, 0, 8, 0], [0, 0, 0, 0], [24, 0, 0, 7], [6, -33, 6, 0], [32, 4, 16, -4], [0, 12, -54, 12], [0, -3, 0, -6], [-6, 0, -12, 0], [0, 0, 0, 0], [-6, 0, 0, 24], [0, 30, 0, 0], [-56, -20, -28, 20], [0, -6, -12, -6], [-4, 4, 4, 8], [24, -24, 48, -12], [0, 0, 0, 0], [8, 0, 0, 0], [-60, -36, -60, 0], [12, -6, 6, 6], [0, 12, 44, 12], [4, 22, -4, 44], [6, 18, 12, 9], [0, 0, 0, 0], [-30, 0, 0, 57], [0, -6, 0, 0], [8, -26, 4, 26], [0, 20, 72, 20], [7, 12, -7, 24], [4, 32, 8, 16], [0, 0, 0, 0], [-12, 0, 0, 24], [-32, 72, -32, 0], [-16, -4, -8, 4], [0, 0, 9, 0], [14, -14, -14, -28], [-32, 40, -64, 20], [0, 0, 0, 0], [54, 0, 0, -60], [60, -32, 60, 0], [-60, 0, -30, 0], [0, 12, -12, 12], [54, 21, -54, 42], [6, 12, 12, 6], [0, 0, 0, 0], [12, 0, 0, -18], [36, -36, 36, 0], [16, -28, 8, 28], [0, -54, -60, -54], [0, 4, 0, 8], [-44, 20, -88, 10], [0, 0, 0, 0], [18, 0, 0, 9], [-14, 24, -14, 0]]}