# Stored data for newform 448.4.i.d, downloaded from the LMFDB on 25 April 2024.
{"label": "448.4.i.d", "space_label": "448.4.i", "level": 448, "weight": 4, "hecke_orbit": 4, "hecke_orbit_code": 13511348705034688, "dim": 2, "is_polredabs": true, "nf_label": "2.0.3.1", "trace_hash": 317016416860238181, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[3, [1, -1, 1]], [11, [1225, 35, 1]]], "qexp_display": "q+(1-\\zeta_{6})q^{3}+7\\zeta_{6}q^{5}+(1+18\\zeta_{6})q^{7}+\\cdots", "char_order": 3, "char_parity": 1, "char_degree": 2, "char_conductor": 7, "char_orbit_label": "i", "char_is_real": false, "Nk2": 7168, "analytic_conductor": 26.432855682571795, "hecke_ring_index": 1, "level_radical": 14, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 6, "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": "0.000", "prec": 17}, "analytic_rank_proved": true, "char_values": [448, 3, [127, 197, 129], [3, 3, 1]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 2, "level_primes": [2, 7], "conrey_indexes": [65, 193], "field_disc": -3, "field_disc_factorization": [[-1, 1], [3, 1]], "field_poly": [1, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.032", "prec": 17}, {"__RealLiteral__": 0, "data": "1.946", "prec": 17}, {"__RealLiteral__": 0, "data": "0.173", "prec": 17}, {"__RealLiteral__": 0, "data": "11.433", "prec": 20}, {"__RealLiteral__": 0, "data": "1.867", "prec": 17}, {"__RealLiteral__": 0, "data": "103.063", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "3.2.3.c3", "trace_display": [0, 1, 7, 20], "traces": [0, 2, 0, 1, 0, 7, 0, 20, 0, 26, 0, -35, 0, -132, 0, 14, 0, -59, 0, -137, 0, 37, 0, -7, 0, 76, 0, 106, 0, -212, 0, 75, 0, 35, 0, -119, 0, 11, 0, -66, 0, -996, 0, 520, 0, -182, 0, -171, 0, -286, 0, 59, 0, -417, 0, -490, 0, -274, 0, 17, 0, 51, 0, -442, 0, -462, 0, -439, 0, -14, 0, 1568, 0, -295, 0, -76, 0, -1295, 0, -495, 0, -649, 0, 1864, 0, -826, 0, -106, 0, 873, 0, -1320, 0, -75, 0, 959, 0, -580, 0, -1820, 0, -1085, 0, 1553, 0, 140, 0, -129, 0, -965, 0, 22, 0, -100, 0, 49, 0, -1716, 0, -2183, 0, 106, 0, -498, 0, 2814, 0, -1872, 0, 260, 0, 755, 0, 2329, 0, 371, 0, 2357, 0, 56, 0, -342, 0, 2310, 0, -742, 0, 397, 0, 2295, 0, -1109, 0, -3068, 0, 1050, 0, 1559, 0, 417, 0, 119, 0, 2251, 0, -245, 0, -5576, 0, 4318, 0, 3562, 0, 1579, 0, 2812, 0, -17, 0, -2451, 0, 2340, 0, 102, 0, -77, 0, -2065, 0, 1060, 0, -1275, 0, -35, 0, -924, 0, 5468, 0, 2243, 0, 439, 0, -2120, 0, -3486, 0, 182, 0, 9590, 0, 2344, 0, 784, 0, 1820, 0, 2775, 0, 295, 0, 3894, 0, -4048, 0, 3952, 0, -2571, 0, 895, 0, -595, 0, -1787, 0, 1197, 0, -990, 0, 10200, 0, 4177, 0, 2080, 0, -4781, 0, 9042, 0, 932, 0, -9360, 0, 490, 0, -413, 0, 1749, 0, -187, 0, -2756, 0, -4473, 0, -5838, 0, 1746, 0, 1975, 0, -8439, 0, -2442, 0, 2660, 0, 527, 0, 3900, 0, -404, 0, 7949, 0, -959, 0, -9960, 0, 1432, 0, -290, 0, -636, 0, 238, 0, -1855, 0, 462, 0, 5200, 0, 1085, 0, -357, 0, -16264, 0, 3106, 0, -929, 0, 209, 0, -6734, 0, 7131, 0, 3710, 0, -258, 0, 16166, 0, -5016, 0, 965, 0, 2907, 0, 6571, 0, -286, 0, -6146, 0, -22932, 0, -50, 0, 2625, 0, -12580, 0, -49, 0, 9777, 0, -23828, 0, -6996, 0, -9123, 0, 5488, 0, -1003, 0, 8149, 0, -11910, 0, 212, 0, -4130, 0, 9671, 0, -12948, 0, -15429, 0, -4109, 0, 1407, 0, 13992, 0, -6976, 0, -936, 0, 8717, 0, -4900, 0, 6760, 0, 163, 0, 826, 0, 1510, 0, 3465, 0, 999, 0, -2740, 0, 14757, 0, -4950, 0, -9086, 0, -770, 0, 133, 0, -2357, 0, 629, 0, 6524, 0, 28, 0, -12840, 0, -20532, 0, 4446, 0, 4484, 0, -867, 0, -2310, 0, -15213, 0, -2756, 0, -1484, 0, -959, 0, -2763, 0, -17758, 0, -5849, 0, -6111, 0, 4590, 0, 9164, 0, 17430, 0, 1109, 0, 7854, 0, -11551, 0, -3127, 0, 18988, 0, 20320, 0, 525, 0, 1307, 0, -16243, 0, -1559, 0, -9100, 0, -20824, 0, -21684, 0, 18287, 0, -726, 0, -140, 0, -2030, 0, -14953, 0, 4502, 0, 28704, 0, 6254, 0, -6370, 0, 15680, 0, 5531, 0, -2788, 0, -16800, 0, -15190, 0, 2159, 0, -2385, 0, -10915, 0, -7261, 0, -10871, 0, 11970, 0, 3158, 0, 9153, 0, 13807, 0, 1292, 0, 4425, 0, 12118, 0, 884, 0, 65736, 0, 903, 0, 2451, 0, -13895, 0, 8175, 0, 1170, 0, -13510, 0, 9312, 0, -1326, 0, 14522, 0, 8415, 0, 77, 0, 7003, 0, -34320, 0, -4130, 0, 19753, 0, -350, 0, -24013, 0, 6897, 0, -24915, 0, -2550, 0, -1064, 0, -127, 0, 35, 0, 18640, 0, -14595, 0, 12012, 0, 18088, 0, -20550, 0, 2734, 0, 10701, 0, -8260, 0, -2243, 0, 20799, 0, -2804, 0, -22828, 0, -742, 0, 6525, 0, -3922, 0, 11286, 0, 15051, 0, -6972, 0, 22300, 0, -3415, 0, -371, 0, -14841, 0, 349, 0, 4795, 0, -1298, 0, 42368, 0, 1172, 0, -6552, 0, 18876, 0, 20384, 0, 10705, 0, 13720, 0, 3640, 0, 14463, 0, 595, 0, 1275, 0, 5979, 0, -5285, 0, -15340, 0, -13880, 0, 13399, 0, -3894, 0, 35483, 0, 742, 0, -2024, 0, -3570, 0, 59020, 0, 4028, 0, -26001, 0, -5800, 0, 2571, 0, 8805, 0, 32998, 0, 1790, 0, 27522, 0, -28685, 0, -18200, 0, 196, 0, 29382, 0, -3574, 0, 6292, 0, 1507, 0, -1197, 0, -40145, 0, 1259, 0, 12870, 0, -1050, 0, 32340, 0, 5100, 0, 16425, 0, -26401, 0, -4177, 0, -8056, 0, 12064, 0, -30886, 0, -15340, 0, 15243, 0, -2002, 0, -15365, 0, 10053, 0, 18084, 0, -48768, 0, -16065, 0, 24232, 0, 2193, 0, 11589, 0, -4680, 0, -15526, 0, -29124, 0, 245, 0, 22765, 0, -35705, 0, -10738, 0, -1122, 0, 7532, 0, 3498, 0, -26861, 0, -5700, 0, 220, 0, 68226, 0, -27440, 0, -11236, 0, 21826, 0, 2097, 0, 4473, 0, -1000, 0, -3366, 0, -2919, 0, 70668, 0, 20178, 0, -22698, 0, -10325, 0, 1813, 0, -1975, 0, -42535, 0, 61352, 0, -16878, 0, -15757, 0, -35620, 0, 29172, 0, 37343, 0, 2815, 0, 5320, 0, -18552, 0, 18571, 0, -527, 0, -23423, 0, -19516, 0, 3975, 0, -58096, 0, -26306, 0, -202, 0, 15113, 0, -1802, 0, -7949, 0, 77, 0, -64180, 0, 49868, 0, 24537, 0, -20825, 0, -18426, 0, -22847, 0, -11053, 0, 2864, 0, 34650, 0, 28974, 0, -7540, 0, 28140, 0, -42737, 0, -318, 0, 12324, 0, 15496, 0, 119, 0, -25923, 0, -18720, 0, -22715, 0, -23427, 0, -34314, 0, 924, 0, -7950, 0, -24603, 0, 9620, 0, 8190, 0, -31935, 0, -56420, 0, -6816, 0, -32620, 0, 357, 0, -12835, 0, 13909, 0, -8132, 0, -103488, 0, 1672, 0, -40378, 0, 24537, 0, 93571, 0, 929, 0, 14455, 0, -65516, 0, 418, 0, -38561, 0, 3486, 0, -6307, 0, -39661, 0, 19470, 0, 14262, 0, -93236, 0, 8925, 0, -3710, 0, 87209, 0, 24166, 0, 3354, 0, -490, 0, -29632, 0, 8083, 0, 16875, 0, 560, 0, 5016, 0, 15837, 0, -61110, 0, -50180, 0, 9915, 0, 19138, 0, -3420, 0, -1820, 0, -43681, 0, 13142, 0, 31402, 0, -47113, 0, 583, 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, 7, 3, 1, 3, 0]], "char_orbit_index": 9, "prim_orbit_index": 3, "minimal_twist": "14.4.c.b", "char_is_minimal": false, "conrey_index": 65, "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, 0], [1, -1], [0, 0], [0, 7], [0, 0], [1, 18], [0, 0], [0, 26], [0, 0], [-35, 35], [0, 0], [-66, 0], [0, 0], [7, 0], [0, 0], [-59, 59], [0, 0], [0, -137], [0, 0], [19, -1], [0, 0], [0, -7], [0, 0], [76, -76], [0, 0], [53, 0], [0, 0], [-106, 0], [0, 0], [75, -75], [0, 0], [0, 35], [0, 0], [-126, 133], [0, 0], [0, 11], [0, 0], [-66, 66], [0, 0], [-498, 0], [0, 0], [260, 0], [0, 0], [-182, 182], [0, 0], [0, -171], [0, 0], [-323, 360], [0, 0], [0, 59], [0, 0], [-417, 417], [0, 0], [-245, 0], [0, 0], [-137, 0], [0, 0], [17, -17], [0, 0], [0, 51], [0, 0], [-468, 494], [0, 0], [0, -462], [0, 0], [-439, 439], [0, 0], [-7, 0], [0, 0], [784, 0], [0, 0], [-295, 295], [0, 0], [0, -76], [0, 0], [-665, 35], [0, 0], [0, -495], [0, 0], [-649, 649], [0, 0], [932, 0], [0, 0], [-413, 0], [0, 0], [-106, 106], [0, 0], [0, 873], [0, 0], [-66, -1188], [0, 0], [0, -75], [0, 0], [959, -959], [0, 0], [-290, 0], [0, 0], [-910, 0], [0, 0]]}