# Stored data for newform 294.3.g.c, downloaded from the LMFDB on 24 April 2024.
{"label": "294.3.g.c", "space_label": "294.3.g", "level": 294, "weight": 3, "hecke_orbit": 3, "hecke_orbit_code": 9007611621933350, "dim": 4, "is_polredabs": true, "nf_label": "4.0.576.2", "trace_hash": 911455217819900233, "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}+(-2+\\cdots)q^{5}+\\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": "0.043", "prec": 17}, {"__RealLiteral__": 0, "data": "4.005", "prec": 17}, {"__RealLiteral__": 0, "data": "0.269", "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]]}