# Stored data for newform 825.4.c.i, downloaded from the LMFDB on 06 May 2024.
{"label": "825.4.c.i", "space_label": "825.4.c", "level": 825, "weight": 4, "hecke_orbit": 9, "hecke_orbit_code": 36028934525027129, "dim": 4, "is_polredabs": true, "nf_label": "4.0.17424.1", "trace_hash": 62224430183666126, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[2, [64, 0, 17, 0, 1]], [7, [1024, 0, 68, 0, 1]]], "qexp_display": "q+\\beta _{1}q^{2}+3\\beta _{2}q^{3}+(-1+\\beta _{3})q^{4}+\\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": 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": "0.508", "prec": 17}, "analytic_rank_proved": true, "char_values": [825, 2, [551, 727, 376], [2, 1, 2]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 2, "level_primes": [3, 5, 11], "conrey_indexes": [199], "field_disc": 17424, "field_disc_factorization": [[2, 4], [3, 2], [11, 2]], "field_poly": [64, 0, 17, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.076", "prec": 17}, {"__RealLiteral__": 0, "data": "3.934", "prec": 17}, {"__RealLiteral__": 0, "data": "1.930", "prec": 17}, {"__RealLiteral__": 0, "data": "78.224", "prec": 20}, {"__RealLiteral__": 0, "data": "68.386", "prec": 20}, {"__RealLiteral__": 0, "data": "2204.347", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "3.2.3.c2", "trace_display": [0, 0, 0, 0], "traces": [0, 4, 0, 0, -2, 0, 6, 0, 0, -36, 0, 44, 0, 0, 64, 0, -238, 0, 0, 108, 0, 12, 0, 0, -54, 0, 188, 0, 0, -444, 0, -80, 0, 0, -964, 0, 18, 0, 0, 456, 0, -988, 0, 0, -22, 0, 224, 0, 0, 1236, 0, -156, 0, 0, -54, 0, 480, 0, 0, -784, 0, -2208, 0, 0, -1426, 0, 66, 0, 0, -1344, 0, 912, 0, 0, -1404, 0, -648, 0, 0, 460, 0, 324, 0, 0, 192, 0, -2904, 0, 0, -1944, 0, -680, 0, 0, 1648, 0, -1482, 0, 0, -396, 0, -548, 0, 0, 2532, 0, -4308, 0, 0, -2200, 0, -288, 0, 0, 1944, 0, 1740, 0, 0, 2032, 0, 484, 0, 0, -3392, 0, -576, 0, 0, 396, 0, -6336, 0, 0, -5944, 0, -7164, 0, 0, 4220, 0, -384, 0, 0, 2142, 0, -8908, 0, 0, -2500, 0, 4820, 0, 0, 704, 0, 564, 0, 0, 504, 0, 448, 0, 0, 428, 0, -10344, 0, 0, 900, 0, -972, 0, 0, -5220, 0, -2618, 0, 0, 9456, 0, -5864, 0, 0, -2016, 0, 10176, 0, 0, -108, 0, 6064, 0, 0, -12676, 0, -750, 0, 0, -1680, 0, 5568, 0, 0, -2892, 0, 5584, 0, 0, 1188, 0, -13308, 0, 0, -1992, 0, 486, 0, 0, 3552, 0, 9896, 0, 0, 32, 0, -3804, 0, 0, 6768, 0, 132, 0, 0, -1692, 0, 392, 0, 0, -5304, 0, -5984, 0, 0, 2820, 0, -1284, 0, 0, -2088, 0, -7648, 0, 0, -4528, 0, 2194, 0, 0, 3000, 0, 3996, 0, 0, -594, 0, 1728, 0, 0, 760, 0, 15932, 0, 0, -1556, 0, 672, 0, 0, 720, 0, 12708, 0, 0, -6528, 0, 2068, 0, 0, -10724, 0, -7104, 0, 0, 2250, 0, -10596, 0, 0, 17024, 0, 5544, 0, 0, -10584, 0, 8676, 0, 0, -8952, 0, 22752, 0, 0, 27476, 0, -2672, 0, 0, -4884, 0, 17496, 0, 0, -162, 0, 25304, 0, 0, -3040, 0, 6520, 0, 0, 6192, 0, 672, 0, 0, 18864, 0, -880, 0, 0, -19272, 0, -7380, 0, 0, 42480, 0, -4104, 0, 0, -1176, 0, 1236, 0, 0, 12448, 0, -13828, 0, 0, -2432, 0, -8460, 0, 0, 8892, 0, 8280, 0, 0, -10604, 0, 10512, 0, 0, 31736, 0, 27564, 0, 0, -6966, 0, 20324, 0, 0, 5376, 0, -5824, 0, 0, -5500, 0, 198, 0, 0, -3240, 0, 40864, 0, 0, 10372, 0, -7104, 0, 0, 7104, 0, 16464, 0, 0, -2016, 0, 16924, 0, 0, -4144, 0, -40520, 0, 0, -28812, 0, 19584, 0, 0, 5016, 0, -7896, 0, 0, -1280, 0, -1540, 0, 0, 28292, 0, -11124, 0, 0, -4212, 0, 6272, 0, 0, 8264, 0, -10868, 0, 0, -2136, 0, 11016, 0, 0, 1404, 0, 31812, 0, 0, 37044, 0, 29844, 0, 0, 8176, 0, 4632, 0, 0, 8016, 0, 832, 0, 0, -23752, 0, 15264, 0, 0, -242, 0, 486, 0, 0, -6888, 0, -4792, 0, 0, -15120, 0, -19264, 0, 0, -6416, 0, -9432, 0, 0, -4320, 0, 2464, 0, 0, -14568, 0, 15448, 0, 0, -53764, 0, -8712, 0, 0, -21060, 0, -11712, 0, 0, -1848, 0, -39952, 0, 0, -1508, 0, 7056, 0, 0, -3708, 0, -26760, 0, 0, 13596, 0, 42088, 0, 0, 508, 0, 7296, 0, 0, 19872, 0, -39312, 0, 0, -7052, 0, 4424, 0, 0, 17688, 0, -1716, 0, 0, 4944, 0, 6920, 0, 0, 33636, 0, -36916, 0, 0, -15808, 0, 12834, 0, 0, -31656, 0, 22080, 0, 0, -52884, 0, -67428, 0, 0, 59616, 0, 6468, 0, 0, -594, 0, 21116, 0, 0, 46960, 0, -1096, 0, 0, 17984, 0, -31116, 0, 0, 7776, 0, -7808, 0, 0, -28600, 0, 5280, 0, 0, 5848, 0, 12096, 0, 0, -21588, 0, -54764, 0, 0, -44808, 0, -27728, 0, 0, -8188, 0, -12924, 0, 0, -8208, 0, -70440, 0, 0, 7168, 0, -27216, 0, 0, -8624, 0, -20832, 0, 0, 4620, 0, 58324, 0, 0, -26048, 0, 27112, 0, 0, -77976, 0, 12636, 0, 0, -22584, 0, -24288, 0, 0, -31396, 0, -20514, 0, 0, 30088, 0, -35496, 0, 0, 5832, 0, 41728, 0, 0, 27408, 0, -72856, 0, 0, -62344, 0, -25884, 0, 0, 1908, 0, 26116, 0, 0, -15686, 0, -22524, 0, 0, -89264, 0, -4140, 0, 0, -2496, 0, 24, 0, 0, 66624, 0, -5200, 0, 0, -26108, 0, 726, 0, 0, -2916, 0, -83424, 0, 0, 98080, 0, -55328, 0, 0, 68308, 0, -1944, 0, 0, 73152, 0, -88660, 0, 0, -7680, 0, -12800, 0, 0, 30744, 0, -1728, 0, 0, -14784, 0, 48204, 0, 0, -10160, 0, 94736, 0, 0, -59048, 0, 50136, 0, 0, 26136, 0, -107676, 0, 0, -25488, 0, 10032, 0, 0, -74466, 0, 5544, 0, 0, 15576, 0, -4968, 0, 0, -41804, 0, -9456, 0, 0, 45856, 0, 17496, 0, 0, -17832, 0, -120448, 0, 0, 37716, 0, 84724, 0, 0, -15444, 0, -11508, 0, 0, 6120, 0, 81404, 0, 0, 15216, 0, -12544, 0, 0, 89504, 0, 7464, 0, 0, -13272, 0, -7128, 0, 0, -28736, 0, 21556, 0, 0, 24936, 0, -14832, 0, 0, -22116, 0, -10752, 0, 0, -35328, 0, 32712, 0, 0, 30792, 0, -3360, 0, 0, 13338, 0, 52004, 0, 0, 5060, 0, -30400, 0, 0, 72576, 0, -26724, 0, 0, -36972, 0, -22784, 0, 0, 36104, 0, 32584, 0, 0, -9320, 0, 3564, 0, 0, -63348, 0, -22560, 0, 0, -148992, 0, -124536, 0, 0, 23676, 0, -53952, 0, 0, 4932, 0, -127680, 0, 0, 65388, 0, -44964, 0, 0, -67708, 0, -60852, 0, 0, 2112, 0, 92096, 0, 0, -63216, 0, 35748, 0, 0, -111864, 0, -22788, 0, 0, -17520, 0, 47292, 0, 0, 46648, 0, -31944, 0, 0, 21536, 0, -5520, 0, 0, 38772, 0, 3840, 0, 0, -7864, 0, 239364, 0, 0, -2948, 0, -21504, 0, 0, 49248, 0, -134240, 0, 0, -24400, 0, 143388, 0, 0, -21384, 0, 19800, 0, 0, 14724, 0, 110040, 0, 0, 14784, 0, 19984, 0, 0, 14592, 0, -31032, 0, 0, 2592, 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": "33.4.a.d", "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, 0, 0], [1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 3, 0], [-1, 0, 0, 1], [0, 0, 0, 0], [3, 0, 0, -3], [0, -2, -2, 0], [0, 7, 8, 0], [-9, 0, 0, 0], [0, 0, 0, 0], [11, 0, 0, 0], [0, 3, 0, 0], [0, -8, -42, 0], [16, 0, 0, 0], [0, 0, 0, 0], [-63, 0, 0, 7], [0, 30, 28, 0], [0, -9, 0, 0], [36, 0, 0, -18], [0, 0, 0, 0], [0, 0, 0, 6], [0, 11, 0, 0], [0, 0, 112, 0], [-3, 0, 0, -21], [0, 0, 0, 0], [30, 0, 0, 34], [0, 0, -27, 0], [0, 0, -16, 0], [-134, 0, 0, 46], [0, 0, 0, 0], [32, 0, 0, -104], [0, -7, 120, 0], [0, 0, 33, 0], [-242, 0, 0, 2], [0, 0, 0, 0], [9, 0, 0, -9], [0, 44, 46, 0], [0, 36, -144, 0], [102, 0, 0, 24], [0, 0, 0, 0], [-246, 0, 0, -2], [0, 0, 48, 0], [0, 86, 10, 0], [-11, 0, 0, 11], [0, 0, 0, 0], [112, 0, 0, -112], [0, -48, 8, 0], [0, 21, -168, 0], [311, 0, 0, -4], [0, 0, 0, 0], [6, 0, 0, -90], [0, -34, -64, 0], [0, 128, 22, 0], [-27, 0, 0, 27], [0, 0, 0, 0], [112, 0, 0, 16], [0, -54, 54, 0], [0, -134, 368, 0], [-196, 0, 0, 0], [0, 0, 0, 0], [-578, 0, 0, 52], [0, 32, -832, 0], [0, 18, 18, 0], [-321, 0, 0, -71], [0, 0, 0, 0], [33, 0, 0, -33], [0, 152, -388, 0], [0, -2, 240, 0], [-336, 0, 0, 0], [0, 0, 0, 0], [320, 0, 0, -184], [0, -63, -72, 0], [0, 252, -170, 0], [-350, 0, 0, -2], [0, 0, 0, 0], [-180, 0, 0, 36], [0, -22, -22, 0], [0, 102, 192, 0], [152, 0, 0, -74], [0, 0, 0, 0], [81, 0, 0, 0], [0, -246, -16, 0], [0, 324, 336, 0], [48, 0, 0, 0], [0, 0, 0, 0], [-764, 0, 0, 76], [0, 138, -264, 0], [0, 77, 88, 0], [-490, 0, 0, 8], [0, 0, 0, 0], [-128, 0, 0, -84], [0, 112, 0, 0], [0, -312, -216, 0], [440, 0, 0, -56], [0, 0, 0, 0], [-381, 0, 0, 21], [0, 420, 802, 0], [0, 311, -32, 0], [-99, 0, 0, 0], [0, 0, 0, 0]]}