# Stored data for newform 825.3.b.a, downloaded from the LMFDB on 25 April 2024. {"label": "825.3.b.a", "space_label": "825.3.b", "level": 825, "weight": 3, "hecke_orbit": 1, "hecke_orbit_code": 68769809209, "dim": 4, "is_polredabs": true, "nf_label": "4.0.39744.5", "trace_hash": 1429897813550914935, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[2, [69, 0, 18, 0, 1]], [23, [454, -46, 1]]], "qexp_display": "q-\\beta _{3}q^{2}+\\beta _{1}q^{3}+(-5-2\\beta _{1})q^{4}+\\cdots", "char_order": 2, "char_parity": -1, "char_degree": 1, "char_conductor": 11, "char_orbit_label": "b", "char_is_real": true, "Nk2": 7425, "analytic_conductor": 22.479621809724495, "hecke_ring_index": 2, "level_radical": 165, "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": "0.504", "prec": 17}, "analytic_rank_proved": true, "char_values": [825, 2, [551, 727, 376], [2, 2, 1]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 2, "level_primes": [3, 5, 11], "conrey_indexes": [76], "field_disc": 39744, "field_disc_factorization": [[2, 6], [3, 3], [23, 1]], "field_poly": [22, 4, 12, -2, 1], "hecke_ring_index_factorization": [[2, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.019", "prec": 17}, {"__RealLiteral__": 0, "data": "3.818", "prec": 17}, {"__RealLiteral__": 0, "data": "1.760", "prec": 17}, {"__RealLiteral__": 0, "data": "72.108", "prec": 20}, {"__RealLiteral__": 0, "data": "80.088", "prec": 20}, {"__RealLiteral__": 0, "data": "1954.544", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "2.2.3.c2", "trace_display": [0, 0, 0, 0], "traces": [0, 4, 0, 0, -20, 0, 0, 0, 0, 12, 0, 20, -24, 0, 12, 0, 4, 0, 0, 0, 0, 0, 12, 92, 0, 0, 204, 0, 0, 0, 0, 80, 0, 12, 48, 0, -60, 64, 120, 0, 0, 0, -84, 0, -124, 0, 0, -100, 144, 100, 0, 0, 0, -28, 0, 0, 156, 0, 240, 40, 0, 0, 0, 0, 28, 0, 192, 136, 0, -60, 0, -284, 0, 0, 0, 0, 0, 180, 228, 0, 0, 36, -216, 0, 0, 0, -216, 0, -396, 304, 0, 24, -340, -216, 0, 0, 0, 376, 0, 60, 0, 0, 216, -272, -660, 0, 0, 0, -72, 0, 0, -24, 0, -208, -288, 0, 0, 0, 0, 168, 0, -260, -204, 0, 32, 0, 36, 0, 0, 0, 0, 0, -180, -408, 0, 0, -480, 200, 0, 0, 0, 36, 0, -252, 12, 0, -24, 120, -272, 0, 0, 0, 456, 0, -24, 0, 0, 760, -804, 132, 0, 0, 0, 112, 0, 0, -504, 0, 12, -572, 0, 0, 0, 0, 528, 0, 164, -504, 0, -200, 0, 176, 0, 0, 0, 0, 0, -384, 428, 0, 0, 364, 216, 0, 0, 0, -740, 0, 36, 200, 0, 0, -408, 288, 0, 0, 0, 276, 0, 696, 0, 0, -124, 12, -1224, 0, 0, 0, 1068, 0, 0, -456, 0, -440, -372, 0, 0, 0, 0, 920, 0, -156, -1296, 0, 612, 0, 808, 0, 0, 0, 0, 0, 504, 0, 0, 0, 408, -312, 0, 0, 0, 928, 0, 400, 1212, 0, -524, 1088, 960, 0, 0, 0, 168, 0, -264, 0, 0, 216, -680, -1028, 0, 0, 0, 384, 0, 0, -252, 0, 1824, 240, 0, 0, 0, 0, 1396, 0, 1248, 624, 0, 724, 0, 504, 0, 0, 0, 0, 0, 36, 1752, 0, 0, 1176, -2916, 0, 0, 0, 144, 0, -588, -504, 0, -188, -1452, 232, 0, 0, 0, -1396, 0, -816, 0, 0, 696, 576, -180, 0, 0, 0, -600, 0, 0, 752, 0, 192, 216, 0, 0, 0, 0, -792, 0, 184, 360, 0, -1704, 0, -1152, 0, 0, 0, 0, 0, 732, 8, 0, 0, -1952, -72, 0, 0, 0, -428, 0, 240, -888, 0, 876, -440, -628, 0, 0, 0, 600, 0, 456, 0, 0, -1728, -252, 848, 0, 0, 0, -556, 0, 0, 1392, 0, -2888, -332, 0, 0, 0, 0, -264, 0, -372, -128, 0, 648, 0, -1040, 0, 0, 0, 0, 0, 296, -504, 0, 0, -144, 2368, 0, 0, 0, 300, 0, 312, -512, 0, -976, 1008, -300, 0, 0, 0, 1080, 0, -996, 0, 0, 432, 1096, 1752, 0, 0, 0, -936, 0, 0, 300, 0, 992, -264, 0, 0, 0, 0, -1016, 0, -1032, 2624, 0, 2136, 0, -432, 0, 0, 0, 0, 0, -384, -608, 0, 0, 888, -1624, 0, 0, 0, -576, 0, -2136, -996, 0, -696, -84, -504, 0, 0, 0, 2352, 0, 820, 0, 0, 232, -1548, 624, 0, 0, 0, -1056, 0, 0, -2512, 0, -888, -1552, 0, 0, 0, 0, 468, 0, -684, -1752, 0, -1004, 0, -912, 0, 0, 0, 0, 0, -464, 360, 0, 0, -272, 720, 0, 0, 0, 504, 0, 732, 300, 0, 120, 744, 672, 0, 0, 0, -600, 0, 620, 0, 0, -2004, 888, 720, 0, 0, 0, -712, 0, 0, 672, 0, -192, 2244, 0, 0, 0, 0, 120, 0, -72, -672, 0, 420, 0, 288, 0, 0, 0, 0, 0, 3252, 324, 0, 0, 84, -632, 0, 0, 0, -384, 0, -8, 1896, 0, 3264, 776, -1200, 0, 0, 0, -224, 0, 576, 0, 0, 1968, 3552, -3476, 0, 0, 0, 408, 0, 0, -1560, 0, -1512, 192, 0, 0, 0, 0, -2736, 0, 792, -256, 0, -1624, 0, -180, 0, 0, 0, 0, 0, -1008, -2648, 0, 0, -352, 2796, 0, 0, 0, -492, 0, 1728, -852, 0, 2320, 288, 184, 0, 0, 0, -3292, 0, -304, 0, 0, -1808, 620, 1908, 0, 0, 0, -552, 0, 0, -1000, 0, -1224, 2280, 0, 0, 0, 0, -192, 0, -1956, 396, 0, 408, 0, 6364, 0, 0, 0, 0, 0, -3216, -64, 0, 0, 48, 480, 0, 0, 0, 1304, 0, 540, -6552, 0, -1968, -816, 324, 0, 0, 0, 684, 0, 356, 0, 0, -1152, 2280, 1832, 0, 0, 0, 2920, 0, 0, 2200, 0, 7824, 1660, 0, 0, 0, 0, -2656, 0, 1992, -488, 0, 108, 0, -1920, 0, 0, 0, 0, 0, 680, -648, 0, 0, 1080, -1008, 0, 0, 0, 1140, 0, 2064, 1512, 0, 3920, 332, -1152, 0, 0, 0, -2240, 0, -24, 0, 0, 2556, 840, -2468, 0, 0, 0, -2688, 0, 0, -456, 0, -1204, -648, 0, 0, 0, 0, 2928, 0, -1408, 24, 0, 1540, 0, 2136, 0, 0, 0, 0, 0, -1188, 144, 0, 0, -4936, -1972, 0, 0, 0, 912, 0, 1848, -816, 0, -24, 588, 3528, 0, 0, 0, -1824, 0, -192, 0, 0, 5136, -5688, 72, 0, 0, 0, 2728, 0, 0, 3648, 0, -1020, -232, 0, 0, 0, 0, 1032, 0, -1464, -648, 0, -3164, 0, 292, 0, 0, 0, 0, 0, 1488, 1556, 0, 0, 1592, 1644, 0, 0, 0, 648, 0, 1752, -16, 0, -1056, -5064, -52, 0, 0, 0, -288, 0, 1188, 0, 0, -4884, 1128, 4200, 0, 0, 0, 1284, 0, 0, 1816, 0, -3416, 4728, 0, 0, 0, 0, 1344, 0, 180, 2584, 0, 984, 0, -2916, 0, 0, 0, 0, 0, -672, -1608, 0, 0, -564, 712, 0, 0, 0, 172, 0, 1272, -2328, 0, -5560, 1968, 648, 0, 0, 0, 672, 0, -300, 0, 0, -816, 1392, 4408, 0, 0, 0, -1764, 0, 0, -1980, 0, 408, -2208, 0, 0, 0, 0, -6008, 0, -120, 5024, 0, 1056, 0, -708, 0, 0, 0, 0, 0, -912, -3480, 0, 0, 1644, 2808, 0, 0, 0, -2112, 0, -4488, -720, 0, -4160, -216, -792, 0, 0, 0, 2000, 0, 1736, 0, 0, -3816, -3220, 888, 0, 0, 0, -600, 0, 0, 704, 0, 288, -936, 0, 0, 0, 0, -72, 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, 11, 2, -1, 2, 0]], "char_orbit_index": 2, "prim_orbit_index": 2, "minimal_twist": "33.3.c.a", "char_is_minimal": true, "conrey_index": 76, "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, 0, 0, -1], [0, 1, 0, 0], [-5, -2, 0, 0], [0, 0, 0, 0], [0, 0, 1, -1], [0, 0, 1, 0], [0, 0, -2, 3], [3, 0, 0, 0], [0, 0, 0, 0], [5, 1, -2, 1], [-6, -5, 0, 0], [0, 0, -1, 6], [3, -7, 0, 0], [0, 0, 0, 0], [1, 12, 0, 0], [0, 0, -2, 2], [0, 0, 0, -3], [0, 0, 4, 2], [0, 0, 0, 0], [0, 0, -1, -2], [3, 16, 1, -6], [23, -5, 0, 0], [0, 0, -1, 7], [0, 0, 0, 0], [51, 19, 0, 0], [0, 3, 0, 0], [0, 0, -3, 4], [0, 0, -4, 8], [0, 0, 0, 0], [20, -18, 0, 0], [0, 0, 4, -1], [3, 5, 1, 5], [12, 18, 0, 0], [0, 0, 0, 0], [-15, -6, 0, 0], [16, -2, 0, 0], [30, -24, 0, 0], [0, 0, -5, 8], [0, 0, 0, 0], [0, 0, -6, -4], [-21, 3, 0, 0], [0, 0, -12, -2], [-31, -15, 8, -15], [0, 0, 0, 0], [0, 0, -5, -18], [-25, 3, 0, 0], [36, 1, 0, 0], [25, 10, 0, 0], [0, 0, 0, 0], [0, 0, 0, 6], [0, 0, 15, -46], [-7, 11, 0, 0], [0, 0, 3, -3], [0, 0, 0, 0], [39, 1, 0, 0], [0, 0, -6, -6], [60, 44, 0, 0], [10, -42, 0, 0], [0, 0, 0, 0], [0, 0, -11, -2], [0, 0, -18, -2], [0, 0, 3, 0], [7, 18, 0, 0], [0, 0, 0, 0], [48, 3, 5, -8], [34, 0, 0, 0], [0, 0, 10, -22], [-15, 23, 0, 0], [0, 0, 0, 0], [-71, 1, 0, 0], [0, 0, -6, 9], [0, 0, 10, -4], [0, 0, -2, -14], [0, 0, 0, 0], [0, 0, -8, 2], [45, -13, 4, -2], [57, 51, 0, 0], [0, 0, 5, -24], [0, 0, 0, 0], [9, 0, 0, 0], [-54, 34, 0, 0], [0, 0, 6, -16], [0, 0, -1, 10], [0, 0, 0, 0], [-54, 80, 0, 0], [0, 0, -4, 16], [-99, -22, -11, 22], [76, 18, 0, 0], [0, 0, 0, 0], [6, 32, 0, 0], [-85, -21, 0, 0], [-54, 20, 0, 0], [0, 0, 3, 22], [0, 0, 0, 0], [0, 0, -3, -9], [94, 42, 0, 0], [0, 0, 10, -35], [15, 3, -6, 3], [0, 0, 0, 0]]}