# Stored data for newform 69.4.g.a, downloaded from the LMFDB on 19 April 2024.
{"label": "69.4.g.a", "space_label": "69.4.g", "level": 69, "weight": 4, "hecke_orbit": 1, "hecke_orbit_code": 412383969349, "dim": 220, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [], "char_order": 22, "char_parity": 1, "char_degree": 10, "char_conductor": 69, "char_orbit_label": "g", "char_is_real": false, "Nk2": 1104, "analytic_conductor": 4.071131790396103, "level_radical": 69, "self_twist_type": 0, "is_self_dual": false, "is_self_twist": false, "is_cm": false, "is_rm": false, "analytic_rank_proved": true, "char_values": [69, 22, [47, 28], [11, 1]], "inner_twist_count": 4, "level_primes": [3, 23], "conrey_indexes": [5, 11, 14, 17, 20, 38, 44, 53, 56, 65], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 22, "sato_tate_group": "3.2.3.c22", "trace_display": [0, -5, 0, -22], "traces": [220, 0, -5, 50, 0, -32, -22, 0, -5, -22, 0, 4, 30, 0, 363, 162, 0, -78, -22, 0, -671, 0, 0, -1258, -632, 0, -269, -22, 0, 1485, -138, 0, 957, 1892, 0, -518, 1166, 0, -401, -2332, 0, -11, -1738, 0, 0, -4326, 0, 1706, -3212, 0, -11, -346, 0, -2307, -1030, 0, -2123, 8656, 0, -451, 506, 0, 2079, 2524, 0, 5742, 1430, 0, 4875, 8092, 0, 6445, -114, 0, 9349, 1034, 0, 6684, -1870, 0, -5497, -4220, 0, -16753, -958, 0, -3785, 1386, 0, -18700, 0, 0, -14746, -6900, 0, -10367, 12650, 0, -4631, 8666, 0, 2915, 770, 0, 6457, -7414, 0, 13119, -5566, 0, 12705, -19030, 0, 0, -19618, 0, -2419, -23486, 0, -22803, -13616, 0, -6067, -14584, 0, 924, 13734, 0, 5709, 25322, 0, 27082, 23726, 0, 20163, 32934, 0, 52178, 21608, 0, 19034, 4684, 0, 37844, 10670, 0, 6947, 4730, 0, -20615, 9810, 0, -23903, 3840, 0, -38599, -10714, 0, -38841, 0, 0, -42698, 15198, 0, -5331, 16214, 0, -24376, 7988, 0, -4961, -17974, 0, -13544, -24442, 0, -7511, -20218, 0, 12749, -99418, 0, 0, -80042, 0, 30224, -31342, 0, -7711, -89878, 0, -5543, -10782, 0, 8943, 36062, 0, 25696, 47234, 0, 32175, 27280, 0, 95095, 72710, 0, 45631, 160824, 0, 65753, 42102, 0, 27207, 26378, 0, -5853, 18986, 0, -30241, 59130, 0, -65802, 17670, 0, -14728, -26158, 0, -111298, 0, 0, -89170, -100462, 0, -76035, -32516, 0, -30459, 6866, 0, -54208, -7942, 0, -26605, -39556, 0, -67780, -91234, 0, -42515, -81994, 0, 0, -57754, 0, 63619, -59230, 0, 76197, -36910, 0, 1973, 55210, 0, 77682, 21578, 0, 85415, 35882, 0, 153549, 1146, 0, 110242, 139326, 0, 86873, 87656, 0, 28443, 93598, 0, 119218, 78914, 0, -2927, 77352, 0, -17821, 53452, 0, -18931, 59486, 0, -20140, 82082, 0, -74569, 0, 0, -156612, -94390, 0, -54569, -77506, 0, -146916, -34974, 0, -86669, -123904, 0, -185400, -105226, 0, -69090, -164230, 0, -46123, -68530, 0, 0, -183394, 0, 116594, -36198, 0, 45001, -97194, 0, 52718, -13818, 0, 152603, -8336, 0, 236808, 18194, 0, 139337, 22908, 0, 169466, 63734, 0, 68425, 58452, 0, 64712, 106998, 0, 54153, 272580, 0, -86203, 129338, 0, -27233, 218476, 0, -121847, 83992, 0, -87797, 46794, 0, -146751, 0, 0, -84426, -127766, 0, -146984, -46750, 0, -235059, -158440, 0, -357533, -242110, 0, -195745, -292534, 0, -204462, -170434, 0, -27797, -239470, 0, 0, 11450, 0, 136095, -3950, 0, 209308, -151818, 0, 115691, 199656, 0, 334609, 30634, 0, 264077, 160490, 0, 239855, 113970, 0, 101926, 265650, 0, 125964, 116068, 0, 13204, 331932, 0, 214689, 255134, 0, -724, 553058, 0, 54916, 359402, 0, -16291, 251258, 0, -12586, 69938, 0, -109505, 0, 0, -61962, -150486, 0, -116255, -273658, 0, -428021, -248782, 0, -186043, -565972, 0, -464709, -276562, 0, -161625, -557788, 0, -164692, -130702, 0, 0, -90550, 0, 295340, -150150, 0, 187924, -170714, 0, 245059, 38354, 0, 227843, -160944, 0, 352605, 7766, 0, 203357, -113264, 0, 407506, 54362, 0, 24697, 144008, 0, -49827, 41478, 0, 82861, 502216, 0, -250794, 348062, 0, 57894, 425860, 0, -94171, 289674, 0, -13087, 196724, 0, -280335, 0, 0, -221760, -323096, 0, -419454, -281842, 0, -386661, -20756, 0, -537218, -136664, 0, -286553, -719686, 0, -299434, -189178, 0, -200255, -207394, 0, 0, -58760, 0, 242987, 20978, 0, 401610, -128398, 0, 110419, 184216, 0, 608102, 33978, 0, 372977, 52470, 0, 660770, -21138, 0, 280137, 439846, 0, 200585, 225820, 0, 129128, 303868, 0, 251418, 330638, 0, -16541, 304766, 0, 17703, 389930, 0, 6919, 440436, 0, 104654, 134882, 0, -143759, 0, 0, -354978, -353610, 0, -204363, -603218, 0, -426888, -78478, 0, -357170, -646030, 0, -646535, -303490, 0, -362771, -470074, 0, -216381, -609334, 0, 0, -116522, 0, 551247, 91578, 0, 268323, -298630, 0, 269153, 193518, 0, 371987, -11722, 0, 643445, -101662, 0, 326953, 418968, 0, 287023, 227018, 0, 102271, 319548, 0, 145593, 340228, 0, 124859, 635690, 0, -539971, 338690, 0, -109201, 669928, 0, -194403, 416716, 0, -174613, 500148, 0, -582230, 0, 0, -486078, -416096, 0, -488780, -216370, 0, -470624, -455848, 0, -715143, -322366, 0, -454917, -412940, 0, -497992, -419518, 0, -104797, -719752, 0, 0, -214398, 0, 254953, -307852, 0, 462253, -133074, 0, 168949, 242042, 0, 687533, 10358, 0, 451627, 540078, 0, 811998, -24096, 0, 450978, 359238, 0, 545745, 583904, 0, 259077, 356158, 0, 626613, 439010, 0, 27979, 752950, 0, 156791, 358106, 0, -35354, 329362, 0, -149035, 59906, 0, -232001, 0, 0, -249112, -276898, 0, -137031, -476872, 0, -706167, -5746, 0, -358281, -550792, 0, -600542, -698698, 0, -260267, -625834, 0, -152075, -405922, 0, 0, -752224, 0, 241085, -244710, 0, 211629, -676840, 0, 196994, -307954, 0, 262691, 139798, 0, 574222, 52514, 0, 288783, -96336, 0, 675466, 235202, 0, 126487, 535588, 0, 36030, 75938, 0, 234388, 526724, 0, -205723, 274934, 0, -48019, 693146, 0, -434115, 70602, 0, -238843, -413314, 0, -935385, 0, 0, -555414, -922300, 0, -596977, -52162, 0, -453783, -74512, 0, -483945, -635998, 0, -373119, -523270, 0, -359662, -139304, 0, -79321, -618178, 0, 0, 39002, 0, 328205, -208494, 0, 178321, 52206, 0, 131615, 604170, 0, 594132, 245774, 0, 547074, 795740, 0, 658504, 674106, 0, 837540, 988878, 0, 773831, 589352, 0, 320528, 919394, 0, 601632, 698918, 0, 262159, 1186196, 0, -226754, 314468, 0, -84843, 551924, 0, 74351, 532334, 0, -176671, 0, 0, -522686, -20166, 0, -90214, 299750, 0, -334917, -260046, 0, -199089, -345268, 0, -434313, -724306, 0, -3049, -1563892, 0, 5863, -478786, 0, 0, -1013758, 0, 641093, -443538, 0, 157421, -951114, 0, -4165, -514026, 0, 155133, -270860, 0, 385792, 259094, 0, 284251, -207862, 0, 298012, 39842, 0, 183601, 260640, 0, 280278, 27506, 0, 85987, 515306, 0, -488996, -65230, 0, -480851, 265724, 0, -865656, 134546, 0, -484962, 1188, 0, -1128358, 0, 0, -885926, 116208, 0, -735568, -62216, 0, -765919, -123992, 0, -528385, 187814, 0, -312445, -308308, 0, -150844, -145486, 0, -235895, -277838, 0, 0, -651222, 0, 277571, 23250, 0, -55341, -368102, 0, -72319, 152538, 0, 670890, 595754, 0, 586157, 589490, 0, 801449, 262088, 0, 778459, 1106094, 0, 920064, 660704, 0, 550336, 218330, 0, 1066794, 281776, 0, 566413, -94138, 0, 82335, 21158, 0, -98681, -153800, 0, -200723, -379522, 0, -107910, 0, 0, -60022, -534870, 0, -208741, -405988, 0, -219945, 172674, 0, -143583, -934516], "weight_parity": 1, "has_non_self_twist": 1, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": false, "level_is_squarefree": true, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 3, 2, -1, 2, 0], [1, 1, 23, 4, -1, 22, 0], [1, 1, 69, 7, 1, 22, 0]], "char_orbit_index": 7, "prim_orbit_index": 7, "minimal_twist": "69.4.g.a", "char_is_minimal": true, "conrey_index": 5, "id": null, "is_polredabs": null, "nf_label": null, "trace_hash": null, "qexp_display": null, "fricke_eigenval": null, "atkin_lehner_string": null, "hecke_ring_index": null, "projective_image": null, "projective_image_type": null, "field_poly_is_cyclotomic": null, "field_poly_root_of_unity": null, "artin_degree": null, "artin_image": null, "field_poly_is_real_cyclotomic": null, "artin_field_label": null, "projective_field_label": null, "hecke_ring_index_proved": null, "trace_zratio": null, "hecke_ring_generator_nbound": null, "field_disc": null, "field_disc_factorization": null, "field_poly": null, "hecke_ring_index_factorization": null, "trace_moments": null, "atkin_lehner_eigenvals": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null}