# Stored data for newform 7.4.c.a, downloaded from the LMFDB on 20 April 2024. {"label": "7.4.c.a", "space_label": "7.4.c", "level": 7, "weight": 4, "hecke_orbit": 1, "hecke_orbit_code": 137506062343, "dim": 2, "is_polredabs": true, "nf_label": "2.0.3.1", "trace_hash": 2120677302297852475, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [], "qexp_display": "q+(-2+2\\zeta_{6})q^{2}-7\\zeta_{6}q^{3}+4\\zeta_{6}q^{4}+\\cdots", "char_order": 3, "char_parity": 1, "char_degree": 2, "char_conductor": 7, "char_orbit_label": "c", "char_is_real": false, "Nk2": 112, "analytic_conductor": 0.4130133700401843, "hecke_ring_index": 1, "level_radical": 7, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 6, "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": 0, "analytic_rank_proved": true, "char_values": [7, 3, [3], [1]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 2, "level_primes": [7], "conrey_indexes": [2, 4], "field_disc": -3, "field_disc_factorization": [[-1, 1], [3, 1]], "field_poly": [1, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.971", "prec": 17}, {"__RealLiteral__": 0, "data": "0.013", "prec": 17}, {"__RealLiteral__": 0, "data": "11.453", "prec": 20}, {"__RealLiteral__": 0, "data": "0.312", "prec": 17}, {"__RealLiteral__": 0, "data": "103.377", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "3.2.3.c3", "trace_display": [-2, -7, -7, 28], "traces": [0, 2, -2, -7, 4, -7, 28, 28, -48, -22, -14, 5, 28, -28, 14, 98, 16, 21, -44, -49, -56, -245, -20, 159, 168, 76, 28, -70, 140, 116, -98, -147, -160, 35, -84, 49, -176, -219, -98, 98, 168, 700, 392, -248, -20, -154, 318, -525, -224, 98, -304, 147, -56, -303, 70, -70, -672, 686, -116, 105, 196, 413, 588, 154, 896, 98, 70, -415, -84, -2226, -490, -864, 528, 1113, -438, 532, -392, 175, -392, 103, 112, 839, -700, 2184, -196, -294, 248, -406, -120, 329, 616, -392, 1272, -1029, -1050, -343, -1120, -1764, 1078, -220, -304, -1379, 294, 679, 672, 1372, 1212, -457, -140, 1125, 70, 3066, -112, -3076, -686, 1113, 232, 308, -420, 735, -2352, 1306, 826, -2450, 588, -2814, -1540, 144, 384, 868, 196, -2149, 280, 343, 1660, 245, -504, 1125, 2226, 504, -784, 7350, 864, -70, 352, -406, -4452, -4459, -1752, 201, 1064, -1619, 1176, -924, -280, 2058, -392, -679, 206, -2121, 2240, -1113, -3356, 467, 1400, 245, -2184, 2408, 5880, -4002, 294, -1078, -496, 2821, 1624, 2660, 160, 735, 658, 3253, 616, 3164, -196, -5782, -3816, -1533, -2058, -105, -4200, -980, 1372, -2557, -3136, 397, 1764, -1372, 2548, 5828, 220, -3339, -1824, -2905, 5516, 1624, 1176, -2450, 1358, 3498, -224, -490, 686, 3560, 1212, 3024, -914, 868, 1680, -5145, -4500, 7791, -140, -294, -3066, -2800, -5600, -3344, 3076, 2205, 1372, -287, -4452, -245, -2784, -4587, 616, -3675, -420, -1442, -1176, 3336, 784, 3409, 2612, 4928, 3304, 3773, 9800, 686, 3528, -7644, 2814, -9520, -2464, 1590, -144, 1029, 4352, 805, -3472, 1533, 784, -1276, -4298, 257, -840, 4242, -3430, -4606, 1660, -3591, 490, -1393, 672, 3430, -4500, -380, -4452, -415, -504, 6468, -1176, -9908, -7350, 4277, -1728, -2401, 280, 9800, 7040, 4472, -812, 6174, -4452, 15484, 1372, -1470, 5256, -175, 402, -2226, 4256, -3472, 6476, -9653, 784, 2891, 924, -14728, 140, -9506, -2058, -9975, -2352, 4753, 2716, -5390, 824, 3477, -4242, 290, -3136, 6398, 11130, -2058, -3356, -1064, 934, 7875, -16800, 3675, -980, -3341, 4368, -4818, -2408, 5810, -3136, 14732, 4002, 10766, -588, 735, 4312, -6860, 5952, 7791, 5642, -7415, 1624, -7756, -4256, 980, 800, -1267, 1470, 3024, 2632, -1029, -13012, -4685, 3696, 4458, -3164, -18284, -1960, -15582, 5782, 4641, -2544, -7700, 6132, -10605, -8232, 8797, -210, 9849, 12600, -1624, -490, 27360, 1372, -504, -5114, -9765, -5376, -980, -1588, 2728, -3528, -1731, 1372, 6678, -2352, 30086, -5828, 721, -440, -10983, 13356, 9604, 2432, -6603, -5810, 2058, 5516, -11746, 812, -2190, -3528, -10955, -4900, 7875, 5432, 3675, -13992, -7644, 2240, -1764, 490, 13272, 6860, -33260, -3560, -11550, 7272, -1596, -12096, -2891, -3656, -490, 1736, -4923, -560, 17948, 8232, 5684, -4500, 7791, 15582, 4179, 1680, 11858, 1176, 12927, 6132, 2303, 2800, -2814, 12544, -5652, 3344, 1750, -6152, -11333, -8820, -686, -16464, -8479, -574, -735, -4452, 18676, 2450, -8032, 928, -7203, -9174, 5859, 2464, -14525, 14700, -4753, -2520, -620, 1442, -7448, 588, 13332, -3336, -6503, -7840, 3066, -13636, -31164, 10448, 6174, 9856, 16049, -9912, -6538, -8918, 17728, 9800, 1218, 1372, 770, -4704, -12096, 30576, 10211, -5628, -8428, 9520, -3360, -3696, 19306, -1590, 14007, 288, 9457, -4116, 38955, -11264, 1715, 1610, 4753, -3472, -5250, -15330, -39494, -2352, 18081, -2552, -20377, -17192, -3724, -1028, 3087, -560, -13114, -4242, -4620, -5488, -9800, 4606, -3199, 9960, 22771, 14364, 3185, 1960, 6193, -2786, -11074, 3360, -15750, -5488, -36928, -4500, 9086, -760, -2842, 53424, -721, 1660, -10731, 1008, 9413, -6468, 3472, 3920, 1470, 9908, -3199, 14700, 10766, -17108, 29365, 20736, -21583, -4802, -20267, 280, 35798, 4900, 24168, -9856, -13951, 8944, 2779, -3248, 30576, -24696, 1515, -26712, 2156, -15484, -41944, -15092, 14406, 1470, -20398, 3504, 189, 700, -4116, 1608, -23373, -4452, 10281, -12768, -12180, -1736, 18260, 6476, 9142, -19306, -4949, 15680, -14210, -11564, 7350, -1848, 15797, 14728, 34300, -4200, -18756, 9506, 24353, 4116, -5565, 39900, -2303, 3136, 349, 9506, 1715, 2716, -9198, 8624, -25280, -2472, -12460, 6954, -504, -16968, -1372, -1160, 9504, 2688, 1041, -6398, 19096, 17808, -12152, 2058, 3241, -20136, -525, 4256, 7203, 3736, 8853, 15750, -15043, 5600, -48972, -36750, 14088, -980, 12089, -6682, -2058, -52416, -12005, 19272, 9222, 4816, 9800, -5810, 4130, 7840, 1964, -14732, -2660, -8004, 30513, -43064, -24696, 7056, 15435, 1470, -11475, 4312, -15750, 25382, 4018, -1984, 4242, 15582, 28315, 22568, -3080, 29660, -1764, 9744, 7350, 7756, 64218, 2128, 21228, -980, -10731, 2240, -25725, 5068, -48265, 5880, -10299, 6048, 2266, -7896, -46746, 10290, 980, -13012, -11676, -9370, -32529, -4928, -4753, -17832, 23863, 6328, 4408, 18284, 58912, 9408, -23686, 15582, -2604, -11564, -27867, -18564, 4802, -50880, 2075, -15400, -19539, 6132, -9604, 16968, 2496, 24696, 1407, 17594, -24024, -840, 3199, -39396, -28093, 8400, 33320, 1624, 22666, -4900, 71908, -27360, -5565, 8232, 861, 2016, 39375, -20456, 3234, -19530, -1470, 30464, 49420, -490, -11270, -1588, -16499, 5456, 11172, 42336, 42924, 6924, -17150, -2744, -2160, -6678, -4060, -8624, 9506, -30086, -16471, 11656, 1799, -2884, -43064, 5280, -5782, -21966, -14847, 13356, -72940, 4802, -22050, 12160, 7238, -13206, -5565, -23240, 38955, -8232, -25137, 33096, -35751, 11746, -32984, 8120, 19502, 2190, 3269, -2352, 6076, 43820, -2156, -19600, 41473, 15750, 25065, -16296, 5320, -5880, 19464, -13992, -27755, -15288, -2905, -12544, 13377, 7056, -8428, -980, 5145, -13272, 42224, -32928, -42050, 33260, 34678, 7120, 14007, 46200, -9142, -9696, 29939, -3192, 34821, -12096, -42476, 28910, 15092, 10968, 35609, -980, -2177, 6944, -85750, 19692, 32247, 5600, 19747, -17948, -62608, -4116, 1030, -5684, 5810, -27000, 19404, -31164, -39396, 62328, -27631, 8358, -54194, -560, 48804, -28028, -39224, 1176, 5145, 25854, -2261, -73584, 2016, -9212, -4195, -5600, -25725, 2814, -45542, -2688, 31164, 5652, -8526, -6688, 6363, -7000, 30380, 73824, -11074, -22666, 23833, -8820, 60676, 6860, 63648, 5488, 5460, -16958, 20237, -2296, 15043, 2940, 16819, -26712, 51548, -18676, 12096, 3920, -33288, 8032, 14938, -9280, -1799, 28812, 26411, -36696, -69825, 11718, -735, -7392, 28308, 23240, -66542, 14700, -12047, -9506, 55650, 3360, -1715, 2480, 24379, -2884, -15582, 7448, -48678, -17640, -104660, -13332, -17899, 6672, 2030, 26012, 39375, 43904, 8182, 6132, -10054, -13636, -5558, -15582, -24832, -31344, 7203, 12348, -36813, 39424, 7056, -64196, -7448, -6608, -34995, 6538, 3290, -2744, -49500, -17728, 14301, 58800, -20398, -4872, 102900, 5488, -19716, 1540, 2665, -23520, 46774, -6048, 46746, 30576, -24871, 20422, 7665, 67536], "weight_parity": 1, "has_non_self_twist": 1, "level_is_prime": true, "level_is_prime_power": true, "level_is_square": false, "level_is_squarefree": true, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 7, 3, 1, 3, 0]], "char_orbit_index": 3, "prim_orbit_index": 3, "minimal_twist": "7.4.c.a", "char_is_minimal": true, "conrey_index": 2, "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], [1, 0], [-2, 2], [0, -7], [0, 4], [-7, 7], [14, 0], [21, -14], [-24, 0], [-22, 22], [0, -14], [0, 5], [28, -28], [-14, 0], [-14, 42], [49, 0], [16, -16], [0, 21], [0, -44], [-49, 49], [-28, 0], [-98, -49], [-10, 0], [159, -159], [0, 168], [0, 76], [28, -28], [-35, 0], [56, 28], [58, 0], [-98, 98], [0, -147], [0, -160], [35, -35], [-42, 0], [-49, 147], [-88, 0], [-219, 219], [0, -98], [0, 98], [168, -168], [350, 0], [294, -196], [-124, 0], [-20, 20], [0, -154], [0, 318], [-525, 525], [-112, 0], [245, -392], [-152, 0], [147, -147], [0, -56], [0, -303], [70, -70], [-35, 0], [-504, 336], [343, 0], [-116, 116], [0, 105], [0, 196], [413, -413], [294, 0], [-154, 462], [448, 0], [98, -98], [0, 70], [0, -415], [-84, 84], [-1113, 0], [-196, -98], [-432, 0], [528, -528], [0, 1113], [0, -438], [532, -532], [-196, 0], [70, 35], [-196, 0], [103, -103], [0, 112], [0, 839], [-700, 700], [1092, 0], [196, -588], [-147, 0], [248, -248], [0, -406], [0, -120], [329, -329], [308, 0], [-294, 196], [636, 0], [-1029, 1029], [0, -1050], [0, -343], [-1120, 1120], [-882, 0], [294, 490], [-110, 0], [-304, 304]]}