# Stored data for newform 405.4.a.h, downloaded from the LMFDB on 04 September 2025.
{"Nk2": 6480, "analytic_conductor": 23.89577355232495, "analytic_rank": 1, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[3, 1], [5, -1]], "atkin_lehner_string": "+-", "char_conductor": 1, "char_degree": 1, "char_is_minimal": true, "char_is_real": true, "char_orbit_index": 1, "char_orbit_label": "a", "char_order": 1, "char_parity": 1, "char_values": [405, 1, [326, 82], [1, 1]], "cm_discs": [], "conrey_index": 1, "dim": 3, "field_disc": 2292, "field_disc_factorization": [[2, 2], [3, 1], [191, 1]], "field_poly": [1, -13, -1, 1], "field_poly_is_cyclotomic": false, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 0, "fricke_eigenval": -1, "has_non_self_twist": 0, "hecke_cutters": [[2, [-3, -17, 1, 1]]], "hecke_orbit": 8, "hecke_orbit_code": 31525197458702741, "hecke_ring_generator_nbound": 2, "hecke_ring_index": 3, "hecke_ring_index_factorization": [[3, 1]], "hecke_ring_index_proved": true, "inner_twist_count": 1, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "is_cm": false, "is_largest": false, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": true, "is_self_twist": false, "is_twist_minimal": false, "label": "405.4.a.h", "level": 405, "level_is_powerful": false, "level_is_prime": false, "level_is_prime_power": false, "level_is_prime_square": false, "level_is_square": false, "level_is_squarefree": false, "level_primes": [3, 5], "level_radical": 15, "minimal_twist": "45.4.e.b", "nf_label": "3.3.2292.1", "prim_orbit_index": 1, "qexp_display": "q+\\beta _{2}q^{2}+(3-\\beta _{1}-\\beta _{2})q^{4}+5q^{5}+\\cdots", "related_objects": [], "relative_dim": 3, "rm_discs": [], "sato_tate_group": "3.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "405.4.a", "trace_display": [-1, 0, 15, -43], "trace_hash": 160427886204265263, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "2.858", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "22.161", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "268.430", "prec": 24}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, "traces": [0, 3, -1, 0, 11, 15, 0, -43, -27, 0, -5, 14, 0, 40, -27, 0, -13, -166, 0, -164, 55, 0, -376, 171, 0, 75, 434, 0, -517, -335, 0, -352, -77, 0, -52, -215, 0, 402, -178, 0, -135, 187, 0, -602, 982, 0, -201, 665, 0, 430, -25, 0, -456, -730, 0, 70, 705, 0, 217, -298, 0, -1439, -1614, 0, -1569, 200, 0, -1849, -710, 0, -135, 70, 0, -368, -320, 0, 204, -948, 0, -382, -65, 0, -575, -831, 0, -830, 1580, 0, -1428, 1719, 0, -710, -1623, 0, -2077, -820, 0, -282, 2164, 0, 275, -186, 0, -2598, 690, 0, 2366, 879, 0, -1533, -1880, 0, 2921, 1088, 0, 855, -3307, 0, 4310, 2904, 0, 1835, 2123, 0, 2456, 375, 0, -3023, 3597, 0, 2170, -1554, 0, 1438, -1071, 0, 1488, -1164, 0, -888, -2585, 0, 496, -5200, 0, -1675, -784, 0, 5014, 4771, 0, -1466, 438, 0, 8598, -1760, 0, 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