# Stored data for newform 825.4.c.e, downloaded from the LMFDB on 25 April 2024. {"label": "825.4.c.e", "space_label": "825.4.c", "level": 825, "weight": 4, "hecke_orbit": 5, "hecke_orbit_code": 18014536015545145, "dim": 2, "is_polredabs": true, "nf_label": "2.0.4.1", "trace_hash": 1398327285919886232, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[2, [1, 0, 1]], [7, [1296, 0, 1]]], "qexp_display": "q+iq^{2}-3iq^{3}+7q^{4}+3q^{6}+6^{2}iq^{7}+\\cdots", "char_order": 2, "char_parity": 1, "char_degree": 1, "char_conductor": 5, "char_orbit_label": "c", "char_is_real": true, "Nk2": 13200, "analytic_conductor": 48.67657575473601, "hecke_ring_index": 1, "level_radical": 165, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 4, "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": "0.508", "prec": 17}, "analytic_rank_proved": true, "char_values": [825, 2, [551, 727, 376], [2, 1, 2]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 2, "level_primes": [3, 5, 11], "conrey_indexes": [199], "field_disc": -4, "field_disc_factorization": [[-1, 1], [2, 2]], "field_poly": [1, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.020", "prec": 17}, {"__RealLiteral__": 0, "data": "1.949", "prec": 17}, {"__RealLiteral__": 0, "data": "0.021", "prec": 17}, {"__RealLiteral__": 0, "data": "16.169", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "166.180", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "3.2.3.c2", "trace_display": [0, 0, 0, 0], "traces": [0, 2, 0, 0, 14, 0, 6, 0, 0, -18, 0, 22, 0, 0, -72, 0, 82, 0, 0, -280, 0, 216, 0, 0, 90, 0, 4, 0, 0, -300, 0, -256, 0, 0, -132, 0, -126, 0, 0, -12, 0, -236, 0, 0, 154, 0, -136, 0, 0, -1906, 0, 396, 0, 0, -54, 0, -1080, 0, 0, 1480, 0, 244, 0, 0, 334, 0, 66, 0, 0, 408, 0, -1976, 0, 0, 628, 0, -1960, 0, 0, -2200, 0, 162, 0, 0, 1512, 0, 344, 0, 0, 940, 0, 144, 0, 0, 648, 0, 966, 0, 0, -198, 0, 3004, 0, 0, 60, 0, 164, 0, 0, 4380, 0, -1884, 0, 0, -840, 0, -2100, 0, 0, -4752, 0, 242, 0, 0, -1792, 0, 648, 0, 0, -1032, 0, -2616, 0, 0, 248, 0, -1980, 0, 0, -360, 0, -1944, 0, 0, -738, 0, 4, 0, 0, -2860, 0, -3896, 0, 0, -792, 0, -84, 0, 0, -492, 0, -4896, 0, 0, -1652, 0, -1736, 0, 0, 4386, 0, 2520, 0, 0, -900, 0, 902, 0, 0, 760, 0, -1076, 0, 0, -2040, 0, -768, 0, 0, -1944, 0, 2824, 0, 0, -2372, 0, -13342, 0, 0, 480, 0, -744, 0, 0, 2772, 0, 64, 0, 0, -3080, 0, 10184, 0, 0, -2232, 0, -810, 0, 0, -12, 0, 264, 0, 0, -11592, 0, -2796, 0, 0, 5300, 0, 2376, 0, 0, -36, 0, 10360, 0, 0, 13040, 0, -4876, 0, 0, 1708, 0, -708, 0, 0, 5208, 0, -10536, 0, 0, 88, 0, -238, 0, 0, 22608, 0, 2700, 0, 0, 990, 0, 10080, 0, 0, -8820, 0, -2616, 0, 0, -3252, 0, 2856, 0, 0, 2304, 0, 1044, 0, 0, -13832, 0, 44, 0, 0, 1114, 0, 7116, 0, 0, -5718, 0, 9420, 0, 0, 272, 0, 12384, 0, 0, -11480, 0, 1188, 0, 0, -192, 0, 11304, 0, 0, -1292, 0, -15400, 0, 0, -3300, 0, 6696, 0, 0, 1134, 0, 6104, 0, 0, 23328, 0, -14536, 0, 0, -2432, 0, 8856, 0, 0, 8388, 0, -2816, 0, 0, 5160, 0, -7716, 0, 0, -9220, 0, 108, 0, 0, 4440, 0, 6580, 0, 0, 8320, 0, 25482, 0, 0, 1008, 0, 732, 0, 0, 2124, 0, 5904, 0, 0, -1452, 0, 9720, 0, 0, 3080, 0, -264, 0, 0, 8730, 0, -1276, 0, 0, 21180, 0, -8976, 0, 0, -7372, 0, -1386, 0, 0, -30240, 0, 22804, 0, 0, 21028, 0, 10800, 0, 0, 1020, 0, 9756, 0, 0, 1224, 0, 644, 0, 0, -4840, 0, -16356, 0, 0, 2460, 0, -5928, 0, 0, -132, 0, -13536, 0, 0, 9216, 0, 30660, 0, 0, 6520, 0, 17154, 0, 0, -13188, 0, -7616, 0, 0, -30580, 0, -2596, 0, 0, 88, 0, -12600, 0, 0, -3564, 0, 13564, 0, 0, -12300, 0, -11436, 0, 0, 8928, 0, 3876, 0, 0, -6600, 0, -33264, 0, 0, -3840, 0, -1256, 0, 0, 1694, 0, 486, 0, 0, -18312, 0, 35464, 0, 0, -560, 0, -10496, 0, 0, 11160, 0, 7296, 0, 0, 9720, 0, -1496, 0, 0, 44780, 0, 144, 0, 0, 11148, 0, -7224, 0, 0, 23148, 0, 1764, 0, 0, -18312, 0, 4944, 0, 0, 15086, 0, -13320, 0, 0, 2820, 0, 3720, 0, 0, -20966, 0, -35996, 0, 0, -21252, 0, 432, 0, 0, -2196, 0, 42000, 0, 0, -452, 0, -2520, 0, 0, -688, 0, 4356, 0, 0, -13608, 0, -3016, 0, 0, 140, 0, -24696, 0, 0, 8496, 0, -3006, 0, 0, 3828, 0, -62496, 0, 0, 60, 0, -9316, 0, 0, 35840, 0, 22116, 0, 0, -594, 0, -20020, 0, 0, 22200, 0, 30484, 0, 0, -27272, 0, 9012, 0, 0, -32400, 0, -1296, 0, 0, -12952, 0, -11880, 0, 0, -52040, 0, -3672, 0, 0, -492, 0, -11276, 0, 0, 41448, 0, -47056, 0, 0, -3012, 0, -3444, 0, 0, 17784, 0, -37996, 0, 0, -34272, 0, 18480, 0, 0, 16280, 0, -27648, 0, 0, 13140, 0, -9676, 0, 0, -29880, 0, 9004, 0, 0, -26040, 0, -5652, 0, 0, 22848, 0, 2684, 0, 0, 14508, 0, 30702, 0, 0, -85392, 0, -264, 0, 0, 17640, 0, 43920, 0, 0, -328, 0, -3656, 0, 0, -4552, 0, -13500, 0, 0, 34308, 0, 46364, 0, 0, 3674, 0, 9204, 0, 0, 67700, 0, 19800, 0, 0, -14256, 0, 5320, 0, 0, 14280, 0, 2304, 0, 0, -7532, 0, 726, 0, 0, -1458, 0, 22704, 0, 0, 10048, 0, -21896, 0, 0, -23240, 0, 1680, 0, 0, -11520, 0, 21684, 0, 0, -80352, 0, -75616, 0, 0, -600, 0, -13608, 0, 0, 4488, 0, 8564, 0, 0, 19768, 0, -18936, 0, 0, -48820, 0, -33444, 0, 0, -3096, 0, -35580, 0, 0, 33040, 0, -21736, 0, 0, -78146, 0, -7848, 0, 0, -14832, 0, -100656, 0, 0, 14868, 0, 3360, 0, 0, 42768, 0, -8460, 0, 0, -5208, 0, -512, 0, 0, -79860, 0, 4824, 0, 0, 6908, 0, 16236, 0, 0, -1296, 0, -12036, 0, 0, 960, 0, -53280, 0, 0, 88180, 0, 1356, 0, 0, -1080, 0, -21560, 0, 0, 47560, 0, -3778, 0, 0, 71288, 0, -5832, 0, 0, 9048, 0, 42704, 0, 0, -8784, 0, -33480, 0, 0, -9560, 0, -25488, 0, 0, -8694, 0, -956, 0, 0, -24200, 0, -496, 0, 0, 19040, 0, -84, 0, 0, 27948, 0, -10236, 0, 0, 1848, 0, 13624, 0, 0, 3168, 0, 1782, 0, 0, -8580, 0, -104760, 0, 0, 38400, 0, 10824, 0, 0, -41940, 0, -11688, 0, 0, -27036, 0, -73256, 0, 0, 25708, 0, 37100, 0, 0, 42600, 0, 38856, 0, 0, 16632, 0, -12816, 0, 0, -62900, 0, 266840, 0, 0, -20952, 0, -540, 0, 0, 33828, 0, 40844, 0, 0, 60680, 0, 3784, 0, 0, -8, 0, 9036, 0, 0, -1476, 0, 91280, 0, 0, -117072, 0, -26814, 0, 0, -34132, 0, -14688, 0, 0, -55440, 0, 7704, 0, 0, -16832, 0, 10004, 0, 0, 10340, 0, -39420, 0, 0, -10620, 0, 19800, 0, 0, 23392, 0, -47456, 0, 0, 71136, 0, 36456, 0, 0, 16956, 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, 5, 2, 1, 2, 0]], "char_orbit_index": 3, "prim_orbit_index": 2, "minimal_twist": "165.4.a.b", "char_is_minimal": false, "conrey_index": 199, "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], [0, 1], [0, -3], [7, 0], [0, 0], [3, 0], [0, 36], [0, 15], [-9, 0], [0, 0], [11, 0], [0, -21], [0, -2], [-36, 0], [0, 0], [41, 0], [0, 66], [0, -9], [-140, 0], [0, 0], [108, 0], [0, 11], [0, 68], [45, 0], [0, 0], [2, 0], [0, 27], [0, 252], [-150, 0], [0, 0], [-128, 0], [0, 161], [0, -33], [-66, 0], [0, 0], [-63, 0], [0, -314], [0, -140], [-6, 0], [0, 0], [-118, 0], [0, 108], [0, -172], [77, 0], [0, 0], [-68, 0], [0, -324], [0, -123], [-953, 0], [0, 0], [198, 0], [0, -14], [0, -82], [-27, 0], [0, 0], [-540, 0], [0, 420], [0, -150], [740, 0], [0, 0], [122, 0], [0, -128], [0, -324], [167, 0], [0, 0], [33, 0], [0, -124], [0, 462], [204, 0], [0, 0], [-988, 0], [0, -135], [0, -2], [314, 0], [0, 0], [-980, 0], [0, 396], [0, -6], [-1100, 0], [0, 0], [81, 0], [0, -118], [0, 868], [756, 0], [0, 0], [172, 0], [0, 450], [0, 165], [470, 0], [0, 0], [72, 0], [0, 476], [0, 384], [324, 0], [0, 0], [483, 0], [0, 1186], [0, -953], [-99, 0], [0, 0]]}