# Stored data for newform 900.3.p.a, downloaded from the LMFDB on 25 April 2024.
{"label": "900.3.p.a", "space_label": "900.3.p", "level": 900, "weight": 3, "hecke_orbit": 1, "hecke_orbit_code": 1030842483588, "dim": 4, "is_polredabs": true, "nf_label": "4.0.1089.1", "trace_hash": 2015456916840671388, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[7, [5476, 74, 75, -1, 1]]], "qexp_display": "q+(\\beta _{2}-\\beta _{3})q^{3}+(-\\beta _{1}+3\\beta _{3})q^{7}+(-1+\\cdots)q^{9}+\\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": 3, "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": "0.174", "prec": 17}, "analytic_rank_proved": true, "char_values": [900, 6, [451, 101, 577], [6, 1, 6]], "hecke_ring_generator_nbound": 7, "inner_twist_count": 2, "level_primes": [2, 3, 5], "conrey_indexes": [101, 401], "field_disc": 1089, "field_disc_factorization": [[3, 2], [11, 2]], "field_poly": [9, -3, -2, -1, 1], "hecke_ring_index_factorization": [[3, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.016", "prec": 17}, {"__RealLiteral__": 0, "data": "3.783", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "51.862", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1105.565", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "2.2.3.c6", "trace_display": [0, -3, 0, 1], "traces": [0, 4, 0, -3, 0, 0, 0, 1, 0, -15, 0, -36, 0, -5, 0, 0, 0, 0, 0, 2, 0, 99, 0, -99, 0, 0, 0, 0, 0, -63, 0, -7, 0, 36, 0, 0, 0, 64, 0, 57, 0, -18, 0, 46, 0, 0, 0, 81, 0, -51, 0, -27, 0, 0, 0, 0, 0, -51, 0, 126, 0, 41, 0, -141, 0, 0, 0, -116, 0, 99, 0, 0, 0, -86, 0, 0, 0, 279, 0, 83, 0, -63, 0, 81, 0, 0, 0, 63, 0, 0, 0, -302, 0, 159, 0, 0, 0, 196, 0, 171, 0, 441, 0, 199, 0, 0, 0, 0, 0, 332, 0, -246, 0, 297, 0, 0, 0, 75, 0, 126, 0, 172, 0, -387, 0, 0, 0, -116, 0, 0, 0, 63, 0, -148, 0, 0, 0, -396, 0, -88, 0, -81, 0, 0, 0, 0, 0, 126, 0, -117, 0, -355, 0, 387, 0, 0, 0, 223, 0, -432, 0, 0, 0, -512, 0, 0, 0, 27, 0, 177, 0, 141, 0, 459, 0, 0, 0, 333, 0, 0, 0, 404, 0, -297, 0, 0, 0, -369, 0, -333, 0, 117, 0, -98, 0, 0, 0, 0, 0, -520, 0, 471, 0, -1071, 0, 0, 0, -99, 0, -315, 0, -481, 0, -54, 0, 0, 0, -898, 0, 213, 0, 36, 0, -53, 0, 0, 0, 864, 0, 335, 0, -981, 0, 0, 0, 0, 0, -495, 0, -405, 0, 98, 0, 837, 0, 0, 0, 146, 0, -81, 0, 0, 0, 1386, 0, 0, 0, -162, 0, -578, 0, 819, 0, -225, 0, 0, 0, -216, 0, 0, 0, 140, 0, 78, 0, 0, 0, -593, 0, 105, 0, 639, 0, -731, 0, 0, 0, 0, 0, 382, 0, 198, 0, -369, 0, 0, 0, -1026, 0, 99, 0, -23, 0, -441, 0, 0, 0, 586, 0, -447, 0, -1287, 0, 586, 0, 0, 0, 153, 0, -315, 0, -513, 0, 0, 0, 0, 0, 48, 0, -405, 0, -313, 0, 354, 0, 0, 0, -20, 0, 891, 0, 0, 0, -250, 0, 0, 0, 702, 0, 17, 0, 117, 0, 1440, 0, 0, 0, -126, 0, 0, 0, -1146, 0, 930, 0, 0, 0, 193, 0, 792, 0, 1224, 0, 283, 0, 0, 0, 0, 0, 962, 0, -804, 0, 315, 0, 0, 0, 345, 0, 549, 0, 792, 0, -1467, 0, 0, 0, -728, 0, 0, 0, 36, 0, -463, 0, 0, 0, -1764, 0, 308, 0, 396, 0, 0, 0, 0, 0, 33, 0, -729, 0, -253, 0, -459, 0, 0, 0, 425, 0, -540, 0, 0, 0, -134, 0, 0, 0, -198, 0, -19, 0, 765, 0, 1458, 0, 0, 0, 1197, 0, 0, 0, -1368, 0, 891, 0, 0, 0, 208, 0, -1080, 0, 855, 0, 805, 0, 0, 0, 0, 0, -1898, 0, 705, 0, -828, 0, 0, 0, -144, 0, 189, 0, 514, 0, -2376, 0, 0, 0, 736, 0, 186, 0, -792, 0, -126, 0, 0, 0, 252, 0, -160, 0, -1053, 0, 0, 0, 0, 0, -495, 0, 2007, 0, 424, 0, 594, 0, 0, 0, -783, 0, -459, 0, 0, 0, -2336, 0, 0, 0, 288, 0, 625, 0, -792, 0, 1233, 0, 0, 0, 756, 0, 0, 0, 728, 0, -996, 0, 0, 0, 418, 0, 753, 0, 1008, 0, 701, 0, 0, 0, 0, 0, -230, 0, 2079, 0, -3402, 0, 0, 0, -63, 0, -1314, 0, -124, 0, -117, 0, 0, 0, 490, 0, 147, 0, -405, 0, -360, 0, 0, 0, 828, 0, 442, 0, -3240, 0, 0, 0, 0, 0, 786, 0, -1251, 0, 764, 0, 1740, 0, 0, 0, -1145, 0, -1197, 0, 0, 0, 688, 0, 0, 0, 2556, 0, 1004, 0, 891, 0, 1008, 0, 0, 0, 315, 0, 0, 0, 2240, 0, 1563, 0, 0, 0, -276, 0, 774, 0, 288, 0, -1154, 0, 0, 0, 0, 0, 72, 0, 426, 0, -2745, 0, 0, 0, -123, 0, 603, 0, -2161, 0, -1008, 0, 0, 0, 1386, 0, 1485, 0, -1629, 0, 673, 0, 0, 0, -3087, 0, -395, 0, -864, 0, 0, 0, 0, 0, -1245, 0, 1368, 0, 1331, 0, 1683, 0, 0, 0, -261, 0, 1377, 0, 0, 0, 1220, 0, 0, 0, 369, 0, 29, 0, 1365, 0, -99, 0, 0, 0, -243, 0, 0, 0, 1090, 0, 3168, 0, 0, 0, 1207, 0, -540, 0, -1035, 0, -551, 0, 0, 0, 0, 0, 2294, 0, -318, 0, 351, 0, 0, 0, -459, 0, 1602, 0, 299, 0, -3159, 0, 0, 0, 3064, 0, -2970, 0, -4185, 0, 974, 0, 0, 0, -1503, 0, -1453, 0, 675, 0, 0, 0, 0, 0, 1386, 0, 1179, 0, -738, 0, 1323, 0, 0, 0, 1117, 0, 225, 0, 0, 0, 686, 0, 0, 0, 1755, 0, 756, 0, 3096, 0, 1665, 0, 0, 0, 1836, 0, 0, 0, -1054, 0, -2184, 0, 0, 0, 23, 0, 1578, 0, 2061, 0, 553, 0, 0, 0, 0, 0, 1784, 0, -2079, 0, -999, 0, 0, 0, 639, 0, 1431, 0, 1405, 0, -639, 0, 0, 0, -6956, 0, 1245, 0, -2178, 0, -2345, 0, 0, 0, -1647, 0, 1046, 0, -1242, 0, 0, 0, 0, 0, 456, 0, -2979, 0, -1181, 0, 1173, 0, 0, 0, 1519, 0, 531, 0, 0, 0, 1942, 0, 0, 0, -2277, 0, -2702, 0, 2970, 0, 486, 0, 0, 0, -99, 0, 0, 0, 288, 0, 1173, 0, 0, 0, -326, 0, -3357, 0, 243, 0, -783, 0, 0, 0, 0, 0, -4924, 0, -291, 0, 72, 0, 0, 0, -2985, 0, -1377, 0, 123, 0, -1683, 0, 0, 0, 2224, 0, 396, 0, 531, 0, -99, 0, 0, 0, 1188, 0, -338, 0, -153, 0, 0, 0, 0, 0, -567, 0, -495, 0, 561, 0, 1017, 0, 0, 0, -575, 0, -1053, 0, 0, 0, 506, 0, 0, 0, -1368, 0, -2952, 0, -2136, 0, 3663, 0, 0, 0, 2133, 0, 0, 0, 1292, 0, -4059, 0, 0, 0, 1819, 0, 2376, 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": "36.3.g.a", "char_is_minimal": true, "conrey_index": 101, "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, 0], [0, 0, 1, -1], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -1, 0, 3], [0, 0, 0, 0], [-1, -8, -2, 1], [0, 0, 0, 0], [-10, 7, 4, -2], [0, 0, 0, 0], [-4, 1, -3, 3], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-7, 16, 1, -2], [0, 0, 0, 0], [-1, 0, -3, 0], [0, 0, 0, 0], [26, 1, 2, -3], [0, 0, 0, 0], [-16, -17, 1, 1], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-15, 24, -6, 0], [0, 0, 0, 0], [-28, 7, -14, 7], [0, 0, 0, 0], [-8, -1, -9, 9], [0, 0, 0, 0], [21, -39, -9, 12], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [10, 0, -12, 0], [0, 0, 0, 0], [4, 23, 3, 1], [0, 0, 0, 0], [-7, 1, -8, -8], [0, 0, 0, 0], [0, 23, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [24, -15, -6, 3], [0, 0, 0, 0], [-27, 24, -3, 3], [0, 0, 0, 0], [6, -24, 6, 9], [0, 0, 0, 0], [16, -16, 8, -16], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-24, 24, 2, 1], [0, 0, 0, 0], [25, 17, 8, 8], [0, 0, 0, 0], [0, 25, 0, -9], [0, 0, 0, 0], [-10, -17, 22, -23], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-67, 49, -18, 18], [0, 0, 0, 0], [0, 9, -33, 15], [0, 0, 0, 0], [-14, 32, 2, -4], [0, 0, 0, 0], [-17, 0, 9, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [38, 55, -17, -17], [0, 0, 0, 0], [0, 49, 0, -15], [0, 0, 0, 0], [-24, 24, 15, 15], [0, 0, 0, 0], [24, -15, -6, 3], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-42, 105, 0, 21], [0, 0, 0, 0], [-56, 128, 8, -16], [0, 0, 0, 0], [-80, 0, -9, 0], [0, 0, 0, 0], [8, 73, 9, -1], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 95, 0, 6], [0, 0, 0, 0], [-3, 111, 3, -33], [0, 0, 0, 0]]}