# Stored data for newform 900.3.p.c, downloaded from the LMFDB on 20 April 2024. {"label": "900.3.p.c", "space_label": "900.3.p", "level": 900, "weight": 3, "hecke_orbit": 3, "hecke_orbit_code": 9008230097224580, "dim": 12, "is_polredabs": true, "trace_hash": 1661261833722676311, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[7, [6345361, 2508924, 4581591, 41720, 2054970, 219204, 222711, -14346, 11340, 50, 141, -6, 1]]], "qexp_display": "q-\\beta _{1}q^{3}+(-\\beta _{1}-\\beta _{3}+\\beta _{4}+\\beta _{6})q^{7}+\\cdots", "char_order": 6, "char_parity": -1, "char_degree": 2, "char_conductor": 9, "char_orbit_label": "p", "char_is_real": false, "Nk2": 8100, "analytic_conductor": 24.52322379242672, "hecke_ring_index": 729, "level_radical": 30, "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": "0.175", "prec": 17}, "analytic_rank_proved": true, "char_values": [900, 6, [451, 101, 577], [6, 1, 6]], "hecke_ring_generator_nbound": 17, "inner_twist_count": 2, "level_primes": [2, 3, 5], "conrey_indexes": [101, 401], "field_disc": 3079184492160000000000, "field_disc_factorization": [[2, 16], [3, 6], [5, 10], [7, 2], [367, 2]], "field_poly": [531441, -118098, -72171, 43740, -9720, -3078, 2709, -342, -120, 60, -11, -2, 1], "hecke_ring_index_factorization": [[3, 6]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.009", "prec": 17}, {"__RealLiteral__": 0, "data": "11.055", "prec": 20}, {"__RealLiteral__": 0, "data": "5.303", "prec": 17}, {"__RealLiteral__": 0, "data": "487.296", "prec": 24}, {"__RealLiteral__": 0, "data": "775.453", "prec": 24}, {"__RealLiteral__": 0, "data": "33623.642", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 6, "sato_tate_group": "2.2.3.c6", "trace_display": [0, -2, 0, 6], "traces": [0, 12, 0, -2, 0, 0, 0, 6, 0, 26, 0, 48, 0, 30, 0, 0, 0, 0, 0, 72, 0, -128, 0, 78, 0, 0, 0, 106, 0, 150, 0, -12, 0, -96, 0, 0, 0, 12, 0, 40, 0, 90, 0, -114, 0, 0, 0, -12, 0, 48, 0, -144, 0, 0, 0, 0, 0, 158, 0, 48, 0, -78, 0, 212, 0, 0, 0, 168, 0, -150, 0, 0, 0, 24, 0, 0, 0, 258, 0, 120, 0, 434, 0, -114, 0, 0, 0, 330, 0, 0, 0, 120, 0, -82, 0, 0, 0, -96, 0, -120, 0, 228, 0, -354, 0, 0, 0, 0, 0, 60, 0, 388, 0, -912, 0, 0, 0, -220, 0, -348, 0, -198, 0, -450, 0, 0, 0, 0, 0, 352, 0, -744, 0, 246, 0, 0, 0, 432, 0, 12, 0, -156, 0, 0, 0, 0, 0, -342, 0, 234, 0, 96, 0, 378, 0, 0, 0, -264, 0, 624, 0, 0, 0, -132, 0, 0, 0, 276, 0, -426, 0, 16, 0, 1392, 0, 0, 0, -120, 0, 0, 0, -828, 0, 1034, 0, 0, 0, 168, 0, 478, 0, 1212, 0, 450, 0, 0, 0, 0, 0, 552, 0, 478, 0, 30, 0, 0, 0, -552, 0, -12, 0, 336, 0, -1314, 0, 0, 0, 36, 0, -704, 0, -1020, 0, 144, 0, 0, 0, -522, 0, 18, 0, -1140, 0, 0, 0, 0, 0, 20, 0, -804, 0, -450, 0, -92, 0, 0, 0, -300, 0, -1272, 0, 0, 0, 276, 0, 0, 0, 204, 0, 456, 0, 390, 0, 1662, 0, 0, 0, 1266, 0, 0, 0, -1104, 0, 310, 0, 0, 0, -438, 0, -8, 0, 1938, 0, 546, 0, 0, 0, 0, 0, -1188, 0, 388, 0, -1530, 0, 0, 0, -186, 0, 300, 0, 624, 0, -1896, 0, 0, 0, -2364, 0, 556, 0, -528, 0, -786, 0, 0, 0, -2262, 0, -60, 0, -1986, 0, 0, 0, 0, 0, -640, 0, -402, 0, 324, 0, 2426, 0, 0, 0, -252, 0, -900, 0, 0, 0, -1296, 0, 0, 0, -846, 0, 558, 0, 1720, 0, 2160, 0, 0, 0, 36, 0, 0, 0, 900, 0, 292, 0, 0, 0, -126, 0, -1440, 0, 1608, 0, -132, 0, 0, 0, 0, 0, -1344, 0, 1270, 0, -4098, 0, 0, 0, -358, 0, -570, 0, -1668, 0, -2880, 0, 0, 0, 504, 0, -1228, 0, -2124, 0, 840, 0, 0, 0, 948, 0, -888, 0, -2904, 0, 0, 0, 0, 0, -148, 0, -960, 0, 72, 0, 4170, 0, 0, 0, 648, 0, 240, 0, 0, 0, 300, 0, 0, 0, 3918, 0, -516, 0, 2592, 0, 2064, 0, 0, 0, 1770, 0, 0, 0, 1440, 0, 1892, 0, 0, 0, 390, 0, 1980, 0, 2178, 0, -1410, 0, 0, 0, 0, 0, 3636, 0, 136, 0, -4152, 0, 0, 0, -1128, 0, 1932, 0, -780, 0, -2724, 0, 0, 0, 1644, 0, 952, 0, -3468, 0, -330, 0, 0, 0, -3798, 0, 696, 0, -4350, 0, 0, 0, 0, 0, -1842, 0, 54, 0, 72, 0, 2156, 0, 0, 0, 138, 0, 1656, 0, 0, 0, 3720, 0, 0, 0, 2964, 0, -396, 0, 3288, 0, 4770, 0, 0, 0, 1938, 0, 0, 0, -516, 0, 1958, 0, 0, 0, -1218, 0, 214, 0, 1920, 0, 0, 0, 0, 0, 0, 0, -720, 0, 1176, 0, -3192, 0, 0, 0, -1144, 0, 1272, 0, 1272, 0, -4824, 0, 0, 0, 600, 0, 520, 0, -3774, 0, -348, 0, 0, 0, 774, 0, 1608, 0, -1296, 0, 0, 0, 0, 0, 1538, 0, 1224, 0, -576, 0, 1952, 0, 0, 0, -48, 0, -570, 0, 0, 0, -1308, 0, 0, 0, 360, 0, 36, 0, 3414, 0, 4122, 0, 0, 0, 2964, 0, 0, 0, -1464, 0, -1654, 0, 0, 0, 2040, 0, 2088, 0, 3114, 0, -192, 0, 0, 0, 0, 0, 2856, 0, 44, 0, -894, 0, 0, 0, -2008, 0, 2256, 0, 1860, 0, -8340, 0, 0, 0, 660, 0, 808, 0, -2724, 0, -774, 0, 0, 0, -294, 0, -1584, 0, -2856, 0, 0, 0, 0, 0, -412, 0, 300, 0, -1380, 0, 1068, 0, 0, 0, 1710, 0, -600, 0, 0, 0, -3168, 0, 0, 0, -1812, 0, -630, 0, 580, 0, 3354, 0, 0, 0, 1980, 0, 0, 0, 1152, 0, 2270, 0, 0, 0, 1860, 0, -1132, 0, 6492, 0, 1260, 0, 0, 0, 0, 0, -5280, 0, 2180, 0, -4626, 0, 0, 0, 120, 0, -5442, 0, 888, 0, -3066, 0, 0, 0, -372, 0, 2364, 0, -1806, 0, 240, 0, 0, 0, 600, 0, 1230, 0, -5820, 0, 0, 0, 0, 0, 2152, 0, -4680, 0, 2088, 0, 2670, 0, 0, 0, -1206, 0, -3864, 0, 0, 0, 1020, 0, 0, 0, 3738, 0, -312, 0, -1842, 0, 4476, 0, 0, 0, 540, 0, 0, 0, 3504, 0, 2054, 0, 0, 0, -1704, 0, 20, 0, 1614, 0, 756, 0, 0, 0, 0, 0, -2820, 0, 5644, 0, -5796, 0, 0, 0, -2986, 0, 3744, 0, -2196, 0, -5406, 0, 0, 0, 3684, 0, -374, 0, -5952, 0, 2946, 0, 0, 0, -5214, 0, -564, 0, -4950, 0, 0, 0, 0, 0, -6422, 0, 5340, 0, 240, 0, 3188, 0, 0, 0, -1818, 0, -120, 0, 0, 0, -960, 0, 0, 0, -1866, 0, 2550, 0, 312, 0, 2838, 0, 0, 0, -1380, 0, 0, 0, -744, 0, 5374, 0, 0, 0, -1020, 0, 1860, 0, 2376, 0, -714, 0, 0, 0, 0, 0, 7176, 0, -86, 0, -5220, 0, 0, 0, 884, 0, 60, 0, -972, 0, -3030, 0, 0, 0, -960, 0, -2192, 0, -4974, 0, -720, 0, 0, 0, -3324, 0, -480, 0, -4176, 0, 0, 0, 0, 0, -330, 0, -3708, 0, 3462, 0, 3552, 0, 0, 0, 1758, 0, -2424, 0, 0, 0, -2736, 0, 0, 0, 7218, 0, -1512, 0, 5710, 0, 2766, 0, 0, 0, 4380, 0, 0, 0, 840, 0, 5048, 0, 0, 0, -1632, 0, -764, 0], "weight_parity": -1, "has_non_self_twist": 1, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": true, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 9, 4, -1, 6, 0]], "char_orbit_index": 16, "prim_orbit_index": 4, "minimal_twist": "180.3.o.b", "char_is_minimal": true, "conrey_index": 101, "id": null, "nf_label": 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, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 0, -1, 1, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, 1, 0, 1, -1, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [5, 1, 1, 3, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [5, 1, -1, 6, 0, -1, 2, -1, 0, -1, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, -3, 1, 3, 2, 1, -1, 1, 1, 2, -2, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [6, 0, -1, 1, 0, -1, 3, -3, 2, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-13, -1, 0, -6, -2, 2, -3, 1, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, 0, -1, -3, 1, -1, 3, -2, 2, 1, -1, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [13, 0, -1, 5, -2, -1, 2, -1, -1, 0, 2, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [18, -2, 0, 7, -2, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, 1, -1, -1, 0, -1, -1, -1, 0, -1, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-12, -3, -2, -12, -1, -2, 3, 0, 1, -1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, -1, 4, -2, 2, 4, 1, 1, -2, 0, 0, -4], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, -1, -1, 9, 6, 3, 6, -4, 2, 3, -4, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [7, 1, 1, -4, 2, -1, 3, 3, -4, 1, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 4, -6, 25, -6, 0, -1, -6, -1, -5, 1, 7], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, -1, 2, -6, -2, 8, -8, 5, 2, 4, 2, -4], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [9, -11, 3, -1, -1, 6, -7, 9, 0, 6, 0, -3], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-11, 5, 2, -6, -3, 3, 1, 5, 2, 0, -4, -7], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-8, 6, 1, -13, -2, 1, 0, -2, 1, 2, -2, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [9, -11, 10, -21, 2, 4, -6, 9, 1, 5, 1, -5], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, -4, 4, -2, 10, 2, 8, -2, -4, -2, 2, -6], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-9, -13, 3, 10, 5, 0, -14, -6, 2, 4, -2, -2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [24, 13, 0, 13, -4, -2, -3, 0, -3, -3, 3, -3], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [24, 9, 3, 30, 4, 9, -3, -2, 0, 9, -3, -6], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-16, -14, 9, -18, 4, 5, -13, 13, 0, 4, 0, -9], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [8, -8, -3, 5, 2, -3, 9, 5, 0, -6, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, 10, -4, 6, -2, -2, 8, -2, 0, 0, -4], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [16, 5, 2, -11, 9, 0, 14, 0, 0, 0, 0, -2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, -2, 9, -29, 5, 0, -4, 10, -2, 5, 2, -13], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [44, -12, 4, 7, -1, 1, 4, 4, -2, 3, -2, 7], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-15, -11, -2, -13, -2, -2, -19, 9, 1, -1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [46, -7, 0, 24, -4, 4, 7, 2, 0, 2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [9, 10, 4, 18, -4, 4, -8, 0, -2, 8, 4, -4], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [10, 12, -8, 18, 10, -2, 33, -23, 4, 0, 0, 5], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-17, -4, 5, -18, 3, -3, -1, -1, -1, 0, 2, 5], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-13, -30, 0, 16, 15, 0, -12, -13, -1, 1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, -1, 9, 21, 2, 7, -17, 5, 0, 5, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]}