# Stored data for newform 275.4.b.b, downloaded from the LMFDB on 08 December 2024. {"Nk2": 4400, "analytic_conductor": 16.22552525157867, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 5, "char_degree": 1, "char_is_minimal": false, "char_is_real": true, "char_orbit_index": 2, "char_orbit_label": "b", "char_order": 2, "char_parity": 1, "char_values": [275, 2, [177, 101], [1, 2]], "cm_discs": [], "conrey_index": 199, "dim": 4, "field_disc": 4624, "field_disc_factorization": [[2, 4], [17, 2]], "field_poly": [16, 0, 9, 0, 1], "field_poly_is_cyclotomic": false, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 0, "has_non_self_twist": 1, "hecke_cutters": [[2, [64, 0, 33, 0, 1]]], "hecke_orbit": 2, "hecke_orbit_code": 4503668413956371, "hecke_ring_generator_nbound": 3, "hecke_ring_index": 2, "hecke_ring_index_factorization": [[2, 1]], "hecke_ring_index_proved": true, "inner_twist_count": 2, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 5, 2, 1, 2, 0]], "is_cm": false, "is_largest": false, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": false, "is_self_twist": false, "is_twist_minimal": false, "label": "275.4.b.b", "level": 275, "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": [5, 11], "level_radical": 55, "minimal_twist": "55.4.a.b", "nf_label": "4.0.4624.1", "prim_orbit_index": 2, "qexp_display": "q+(\\beta _{1}+2\\beta _{2})q^{2}+(-\\beta _{1}-\\beta _{2})q^{3}+(-5+\\cdots)q^{4}+\\cdots", "related_objects": [], "relative_dim": 4, "rm_discs": [], "sato_tate_group": "3.2.3.c2", "self_twist_discs": [], "self_twist_type": 0, "space_label": "275.4.b", "trace_display": [0, 0, 0, 0], "trace_hash": 2060538329416328613, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.891", "prec": 17}, {"__RealLiteral__": 0, "data": "0.014", "prec": 17}, {"__RealLiteral__": 0, "data": "77.914", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "2110.835", "prec": 27}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.508", "prec": 17}, "traces": [0, 4, 0, 0, -34, 0, 38, 0, 0, 82, 0, -44, 0, 0, -22, 0, 594, 0, 0, 6, 0, -78, 0, 0, -614, 0, 180, 0, 0, 442, 0, 282, 0, 0, -1346, 0, -340, 0, 0, 20, 0, -288, 0, 0, 374, 0, -268, 0, 0, -630, 0, 742, 0, 0, 1550, 0, -2250, 0, 0, 172, 0, -310, 0, 0, -5618, 0, -418, 0, 0, 76, 0, 3174, 0, 0, -3182, 0, -5406, 0, 0, 2588, 0, 1132, 0, 0, 782, 0, -2232, 0, 0, 3554, 0, 2780, 0, 0, 1364, 0, 6086, 0, 0, -902, 0, -1856, 0, 0, 1100, 0, 2054, 0, 0, 1640, 0, 946, 0, 0, 3882, 0, -12206, 0, 0, -1174, 0, 484, 0, 0, 11526, 0, -1420, 0, 0, 2472, 0, 5202, 0, 0, -688, 0, 16738, 0, 0, -1856, 0, -1556, 0, 0, 8964, 0, -1476, 0, 0, -3810, 0, 8580, 0, 0, 242, 0, 1020, 0, 0, -2522, 0, -1812, 0, 0, -16116, 0, -684, 0, 0, 4588, 0, -2172, 0, 0, 10234, 0, -6534, 0, 0, -7216, 0, 1672, 0, 0, 1324, 0, -7266, 0, 0, -3654, 0, -17336, 0, 0, -10056, 0, -21420, 0, 0, 4418, 0, 1752, 0, 0, -18326, 0, 9656, 0, 0, -66, 0, -2830, 0, 0, 2864, 0, -25646, 0, 0, 1196, 0, 4660, 0, 0, -918, 0, -2192, 0, 0, -1760, 0, 858, 0, 0, 4200, 0, 17340, 0, 0, -2436, 0, 16584, 0, 0, -11526, 0, 10524, 0, 0, 2916, 0, -9324, 0, 0, 10480, 0, 38930, 0, 0, -20554, 0, 5440, 0, 0, 6754, 0, 14502, 0, 0, -20220, 0, -3712, 0, 0, 11784, 0, -2788, 0, 0, 11748, 0, -12408, 0, 0, -34238, 0, -1980, 0, 0, -8062, 0, 8720, 0, 0, 13140, 0, 16942, 0, 0, 3080, 0, 25368, 0, 0, 49086, 0, -20708, 0, 0, -6256, 0, 11986, 0, 0, -15838, 0, -35564, 0, 0, -4862, 0, -256, 0, 0, 14654, 0, -7858, 0, 0, -16500, 0, -32, 0, 0, -12246, 0, -12654, 0, 0, 5272, 0, -3102, 0, 0, 62520, 0, 31580, 0, 0, -10384, 0, 1460, 0, 0, -11796, 0, -35326, 0, 0, 37032, 0, 6998, 0, 0, 18020, 0, 7170, 0, 0, -13860, 0, -28782, 0, 0, 14806, 0, -39476, 0, 0, 25556, 0, -3248, 0, 0, -57638, 0, 11610, 0, 0, 20408, 0, -6092, 0, 0, 26520, 0, 3740, 0, 0, -882, 0, -43230, 0, 0, -38964, 0, 20502, 0, 0, -32076, 0, -14784, 0, 0, -4984, 0, 24820, 0, 0, 29360, 0, 7020, 0, 0, -64454, 0, 35338, 0, 0, -220, 0, -31728, 0, 0, -39342, 0, 33660, 0, 0, 21640, 0, -24390, 0, 0, -33626, 0, -3756, 0, 0, 9240, 0, 3168, 0, 0, 16500, 0, -53706, 0, 0, 30094, 0, 16010, 0, 0, 141678, 0, 81522, 0, 0, 29600, 0, 18066, 0, 0, 34276, 0, -45594, 0, 0, 63744, 0, 35260, 0, 0, -4114, 0, 35264, 0, 0, 10158, 0, -25638, 0, 0, -7380, 0, -83430, 0, 0, -5200, 0, 7842, 0, 0, -47604, 0, 2948, 0, 0, -37588, 0, 7124, 0, 0, -91516, 0, -45288, 0, 0, -14836, 0, -62056, 0, 0, -29818, 0, 50274, 0, 0, 46092, 0, 11584, 0, 0, 37418, 0, 46992, 0, 0, 6930, 0, 30918, 0, 0, -210562, 0, -3340, 0, 0, -12424, 0, 54978, 0, 0, 20632, 0, 150008, 0, 0, -29520, 0, -8162, 0, 0, 28220, 0, 76596, 0, 0, -41972, 0, -39690, 0, 0, 51972, 0, -83396, 0, 0, -11086, 0, 55260, 0, 0, 29060, 0, -60572, 0, 0, -89082, 0, -14824, 0, 0, -17050, 0, 40358, 0, 0, 47022, 0, -24736, 0, 0, 14892, 0, 21468, 0, 0, -9826, 0, 19400, 0, 0, 51956, 0, 24750, 0, 0, -29128, 0, 2692, 0, 0, -7740, 0, -74460, 0, 0, -71982, 0, -37866, 0, 0, 38118, 0, 44642, 0, 0, 61956, 0, -111870, 0, 0, -16252, 0, -105294, 0, 0, -1892, 0, -3510, 0, 0, -18420, 0, 124308, 0, 0, 11778, 0, 808, 0, 0, 79596, 0, -58652, 0, 0, 8332, 0, 3410, 0, 0, -82926, 0, -98498, 0, 0, 61112, 0, 1924, 0, 0, -90780, 0, 68594, 0, 0, 34580, 0, -1708, 0, 0, -64692, 0, -151130, 0, 0, -47110, 0, 3274, 0, 0, 61798, 0, -39292, 0, 0, -43760, 0, 47240, 0, 0, 28542, 0, 28016, 0, 0, -90138, 0, -12104, 0, 0, 35292, 0, 4598, 0, 0, 4396, 0, -36024, 0, 0, -24648, 0, -39916, 0, 0, -3080, 0, -7620, 0, 0, 93954, 0, -132028, 0, 0, 31600, 0, 34778, 0, 0, 7820, 0, 29750, 0, 0, -836, 0, -12192, 0, 0, 184008, 0, -8556, 0, 0, -31624, 0, 50684, 0, 0, -19440, 0, 213992, 0, 0, 118908, 0, -34914, 0, 0, 147420, 0, 39134, 0, 0, -51942, 0, 87488, 0, 0, -17260, 0, -6018, 0, 0, 21652, 0, 70664, 0, 0, -25840, 0, 32580, 0, 0, 19152, 0, -58162, 0, 0, 35002, 0, 218358, 0, 0, 74840, 0, 66528, 0, 0, -146200, 0, -51980, 0, 0, -55668, 0, -14360, 0, 0, -113512, 0, 59466, 0, 0, -69536, 0, 36982, 0, 0, 156502, 0, 11336, 0, 0, -52508, 0, -29756, 0, 0, 40142, 0, 1424, 0, 0, 16180, 0, 2964, 0, 0, 248846, 0, -144880, 0, 0, -28468, 0, -38800, 0, 0, -8052, 0, -24684, 0, 0, 49604, 0, -95520, 0, 0, -340, 0, 77096, 0, 0, 64784, 0, -12452, 0, 0, -41890, 0, -177674, 0, 0, -110058, 0, 31174, 0, 0, 141040, 0, 18780, 0, 0, -61508, 0, 9462, 0, 0, -10918, 0, -38828, 0, 0, 55136, 0, -35692, 0, 0, -8602, 0, -174060, 0, 0, 20670, 0, 171180, 0, 0, 39082, 0, 38360, 0, 0, 62764, 0, 8454, 0, 0, -143676, 0, 24552, 0, 0, -6360, 0, -38650, 0, 0, 14924, 0, 159460, 0, 0, -172056, 0, 133430, 0, 0, -80988, 0, 5396, 0, 0, 78378, 0, -33320, 0, 0, -68168, 0, 81414, 0, 0, -39094, 0, 54020, 0, 0, -138780, 0, -311678, 0, 0, 13488, 0, -70896, 0, 0, 2246, 0, -39780, 0, 0, 33970, 0], "weight": 4, "weight_parity": 1, "id": null, "artin_degree": null, "artin_field": null, "artin_field_label": null, "artin_image": null, "atkin_lehner_eigenvals": null, "atkin_lehner_string": null, "embedded_related_objects": null, "fricke_eigenval": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp": [[0, 0, 0, 0], [1, 0, 0, 0], [0, 1, 2, 0], [0, -1, -1, 0], [-5, 0, 0, -7], [0, 0, 0, 0], [7, 0, 0, 5], [0, -9, 4, 0], [0, -25, -22, 0], [22, 0, 0, -3], [0, 0, 0, 0], [-11, 0, 0, 0], [0, 19, 26, 0], [0, 10, -10, 0], [-15, 0, 0, 19], [0, 0, 0, 0], [117, 0, 0, 63], [0, 17, 42, 0], [0, 10, 32, 0], [-21, 0, 0, 45], [0, 0, 0, 0], [-19, 0, 0, -1], [0, -11, -22, 0], [0, -4, 11, 0], [-119, 0, 0, -69], [0, 0, 0, 0], [50, 0, 0, -10], [0, -43, -40, 0], [0, -11, 78, 0], [75, 0, 0, 71], [0, 0, 0, 0], [129, 0, 0, -117], [0, 169, 310, 0], [0, 11, 11, 0], [-269, 0, 0, -135], [0, 0, 0, 0], [-26, 0, 0, -118], [0, -43, 129, 0], [0, 159, 138, 0], [10, 0, 0, -10], [0, 0, 0, 0], [-150, 0, 0, 156], [0, -23, -42, 0], [0, 156, 24, 0], [55, 0, 0, 77], [0, 0, 0, 0], [-62, 0, 0, -10], [0, -100, -13, 0], [0, -243, -306, 0], [-270, 0, 0, 225], [0, 0, 0, 0], [135, 0, 0, 101], [0, 90, -20, 0], [0, -169, -13, 0], [283, 0, 0, 209], [0, 0, 0, 0], [-577, 0, 0, 29], [0, -69, -114, 0], [0, 359, 434, 0], [122, 0, 0, -158], [0, 0, 0, 0], [-137, 0, 0, 119], [0, -339, -210, 0], [0, -222, 130, 0], [-1093, 0, 0, -623], [0, 0, 0, 0], [-77, 0, 0, -55], [0, 150, -29, 0], [0, -673, -742, 0], [10, 0, 0, 18], [0, 0, 0, 0], [763, 0, 0, 61], [0, -418, -268, 0], [0, 58, 32, 0], [-731, 0, 0, -129], [0, 0, 0, 0], [-1155, 0, 0, -393], [0, 99, -44, 0], [0, -30, -20, 0], [590, 0, 0, 114], [0, 0, 0, 0], [385, 0, 0, -204], [0, 474, 324, 0], [0, 270, -72, 0], [123, 0, 0, 145], [0, 0, 0, 0], [-300, 0, 0, -516], [0, -217, -288, 0], [0, 275, 242, 0], [867, 0, 0, 43], [0, 0, 0, 0], [870, 0, 0, -350], [0, -134, -76, 0], [0, 105, 222, 0], [178, 0, 0, 326], [0, 0, 0, 0], [1127, 0, 0, 789], [0, 454, 197, 0], [0, 630, 360, 0], [-242, 0, 0, 33], [0, 0, 0, 0]]}