# Stored data for newform 225.5.g.l, downloaded from the LMFDB on 25 June 2026.
{"Nk2": 5625, "analytic_conductor": 23.258241693864974, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 5, "char_degree": 2, "char_is_minimal": true, "char_is_real": false, "char_orbit_index": 7, "char_orbit_label": "g", "char_order": 4, "char_parity": -1, "char_values": [225, 4, [101, 127], [4, 1]], "cm_discs": [], "conrey_index": 82, "dim": 4, "field_disc": 2304, "field_disc_factorization": [[2, 8], [3, 2]], "field_poly": [9, 0, 0, 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, [36, -72, 72, -12, 1]]], "hecke_orbit": 12, "hecke_orbit_code": 49540008301822177, "hecke_ring_generator_nbound": 7, "hecke_ring_index": 1, "hecke_ring_index_factorization": [], "hecke_ring_index_proved": true, "inner_twist_count": 2, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 5, 3, -1, 4, 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": "225.5.g.l", "level": 225, "level_is_powerful": true, "level_is_prime": false, "level_is_prime_power": false, "level_is_prime_square": false, "level_is_square": true, "level_is_squarefree": false, "level_primes": [3, 5], "level_radical": 15, "minimal_twist": "75.5.f.a", "nf_label": "4.0.2304.2", "prim_orbit_index": 3, "qexp_display": "q+(3-3\\beta _{2}+2\\beta _{3})q^{2}+(12\\beta _{1}-14\\beta _{2}+\\cdots)q^{4}+\\cdots", "related_objects": [], "relative_dim": 2, "rm_discs": [], "sato_tate_group": "4.2.3.c4", "self_twist_discs": [], "self_twist_type": 0, "space_label": "225.5.g", "trace_display": [12, 0, 0, 72], "trace_hash": 285335434010247348, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.903", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "51.738", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1005.341", "prec": 27}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.248", "prec": 17}, "traces": [0, 4, 12, 0, 0, 0, 0, 72, -264, 0, 0, 24, 0, -144, 0, 0, -2320, 600, 0, 0, 0, 0, -1800, 888, 0, 0, 792, 0, -1152, 0, 0, 3244, -6192, 0, 0, 0, 0, -2448, -1068, 0, 0, -6864, 0, 5544, 0, 0, -2496, 5616, 0, 0, 0, 0, 7920, 1848, 0, 0, -10320, 0, -5544, 0, 0, 15020, 15636, 0, 0, 0, 0, 13320, -8112, 0, 0, 21552, 0, -19728, 0, 0, -25048, -504, 0, 0, 0, 0, -13536, 8592, 0, 0, 18984, 0, 62064, 0, 0, -4356, -34512, 0, 0, 0, 0, 11520, 20136, 0, 0, 9024, 0, -25776, 0, 0, -5136, -29304, 0, 0, 0, 0, -43488, -43488, 0, 0, -75504, 0, -61128, 0, 0, 87596, 69828, 0, 0, 0, 0, -45360, 54816, 0, 0, 66960, 0, 8640, 0, 0, -77568, 18672, 0, 0, 0, 0, 86976, -65448, 0, 0, -147264, 0, 52128, 0, 0, -13412, -56328, 0, 0, 0, 0, -8352, -51240, 0, 0, 28056, 0, -9720, 0, 0, 29040, -312, 0, 0, 0, 0, -8064, 78312, 0, 0, 255648, 0, 26928, 0, 0, 4, 15876, 0, 0, 0, 0, 5472, 98496, 0, 0, 180504, 0, 1008, 0, 0, 87632, -2256, 0, 0, 0, 0, 81360, 3960, 0, 0, -147936, 0, -35712, 0, 0, -89596, -71472, 0, 0, 0, 0, 61344, -46668, 0, 0, -44856, 0, 4536, 0, 0, -135360, 88968, 0, 0, 0, 0, -203184, 45576, 0, 0, -564048, 0, -67464, 0, 0, 94556, 240324, 0, 0, 0, 0, 114408, -414840, 0, 0, 106752, 0, 310464, 0, 0, 397888, -8544, 0, 0, 0, 0, 179712, 212040, 0, 0, -43320, 0, -440928, 0, 0, -267064, -344544, 0, 0, 0, 0, -177264, -40632, 0, 0, -161592, 0, 58536, 0, 0, -247968, -120024, 0, 0, 0, 0, -449568, 95520, 0, 0, 424320, 0, 217224, 0, 0, 192444, 39684, 0, 0, 0, 0, -185976, 410544, 0, 0, 256584, 0, -324720, 0, 0, -798800, -153024, 0, 0, 0, 0, -51336, 86136, 0, 0, 307368, 0, 213120, 0, 0, -11032, -14784, 0, 0, 0, 0, 319536, -259464, 0, 0, -441048, 0, 298440, 0, 0, 742080, 167760, 0, 0, 0, 0, 838944, -483336, 0, 0, 457248, 0, 94680, 0, 0, 132096, 349356, 0, 0, 0, 0, 95256, 48288, 0, 0, 58416, 0, -323856, 0, 0, 262368, 248184, 0, 0, 0, 0, 411480, -367440, 0, 0, -237480, 0, -414288, 0, 0, 274224, 432624, 0, 0, 0, 0, -764496, 507516, 0, 0, -664080, 0, 86904, 0, 0, -217440, 101376, 0, 0, 0, 0, -320544, -157680, 0, 0, -329184, 0, 373608, 0, 0, 282952, -704964, 0, 0, 0, 0, 282744, 1101456, 0, 0, 95736, 0, 136080, 0, 0, 179272, -569400, 0, 0, 0, 0, 115560, -275856, 0, 0, 639672, 0, 448128, 0, 0, -591552, 144576, 0, 0, 0, 0, 231552, -350052, 0, 0, 701232, 0, -817776, 0, 0, 784656, -596904, 0, 0, 0, 0, -1801008, 590184, 0, 0, -334896, 0, -256032, 0, 0, 73584, -567660, 0, 0, 0, 0, -350280, -1833432, 0, 0, 233520, 0, 67968, 0, 0, -2731696, 399096, 0, 0, 0, 0, 602496, 493224, 0, 0, 984672, 0, 806112, 0, 0, -724656, 878784, 0, 0, 0, 0, 1184976, 337104, 0, 0, -239304, 0, -619416, 0, 0, 1220112, 480696, 0, 0, 0, 0, -450000, 490536, 0, 0, -3200112, 0, 565128, 0, 0, -1447636, -486120, 0, 0, 0, 0, 400752, -584256, 0, 0, -828264, 0, 112320, 0, 0, 152528, 726480, 0, 0, 0, 0, -566712, -125208, 0, 0, 1891032, 0, -2181312, 0, 0, 1528916, -47952, 0, 0, 0, 0, -466560, 476508, 0, 0, 298056, 0, 643824, 0, 0, 1312752, 465576, 0, 0, 0, 0, 1634112, -484824, 0, 0, 1617744, 0, -352296, 0, 0, 244756, 353556, 0, 0, 0, 0, -496800, 419760, 0, 0, -1422792, 0, 806688, 0, 0, 2352960, -375528, 0, 0, 0, 0, 535320, -87120, 0, 0, -1802232, 0, 2344176, 0, 0, 1083668, -2043120, 0, 0, 0, 0, 281808, 1359504, 0, 0, -571344, 0, 483984, 0, 0, -310656, -1448880, 0, 0, 0, 0, 2058048, 132960, 0, 0, 2965056, 0, -64584, 0, 0, -2625272, -93576, 0, 0, 0, 0, -1193760, -1704048, 0, 0, -1841784, 0, 24912, 0, 0, -2085200, 1292184, 0, 0, 0, 0, -2805912, 60240, 0, 0, 1859160, 0, -2187360, 0, 0, 1648456, 2729616, 0, 0, 0, 0, -1036656, 1263864, 0, 0, 403800, 0, -170640, 0, 0, -2888352, 189576, 0, 0, 0, 0, 1135008, -242184, 0, 0, 1497840, 0, -2630448, 0, 0, -924576, 1156896, 0, 0, 0, 0, 902808, -696600, 0, 0, 1677480, 0, -1528416, 0, 0, 912384, -1573992, 0, 0, 0, 0, -105696, -527184, 0, 0, -1902936, 0, 3294720, 0, 0, 659416, -1131840, 0, 0, 0, 0, 620928, -1439340, 0, 0, 211968, 0, -577800, 0, 0, -738528, 1034208, 0, 0, 0, 0, -1447056, -1710840, 0, 0, -2954352, 0, 3077712, 0, 0, -1611648, -361584, 0, 0, 0, 0, 692424, 2498880, 0, 0, -1502784, 0, 313776, 0, 0, 4082296, -1689504, 0, 0, 0, 0, -893088, 1008576, 0, 0, 1439352, 0, -2441376, 0, 0, -522212, -1391760, 0, 0, 0, 0, -1584576, 551388, 0, 0, 1600008, 0, 2604168, 0, 0, -2360880, -1793640, 0, 0, 0, 0, -2170944, 1050864, 0, 0, -285072, 0, -742032, 0, 0, 878932, 1498872, 0, 0, 0, 0, 1565496, 96288, 0, 0, -601824, 0, -300960, 0, 0, 7784928, -403824, 0, 0, 0, 0, 1473624, 145776, 0, 0, -1511112, 0, -2250864, 0, 0, 504036, -376968, 0, 0, 0, 0, 228672, -3043380, 0, 0, 602208, 0, 1678824, 0, 0, -526272, 2056416, 0, 0, 0, 0, 3738240, 2463264, 0, 0, 2187840, 0, -2534256, 0, 0, 570624, 1480032, 0, 0, 0, 0, -1015776, 1815312, 0, 0, 2063592, 0, 929520, 0, 0, -2917672, 1194696, 0, 0, 0, 0, 4173696, -5832, 0, 0, -5856576, 0, 2535840, 0, 0, -1071496, 3705264, 0, 0, 0, 0, -86544, -2345436, 0, 0, 3785736, 0, -2673936, 0, 0, -1733760, 2777352, 0, 0, 0, 0, -1517040, -469296, 0, 0, -3350112, 0, 2357640, 0, 0, 389184, -685584, 0, 0, 0, 0, -1136160, -5017560, 0, 0, 2721096, 0, -500400, 0, 0, -12278192, 145440, 0, 0, 0, 0, -775728, 1137408, 0, 0, -1627488, 0, 961344, 0, 0, 1573508, -7784784, 0, 0, 0, 0, 1110528, -1031268, 0, 0], "weight": 5, "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], [3, 0, -3, 2], [0, 0, 0, 0], [0, 12, -14, 12], [0, 0, 0, 0], [0, 0, 0, 0], [18, 0, -18, 1], [-66, 68, -66, 0], [0, 0, 0, 0], [0, 0, 0, 0], [6, 78, 0, -78], [0, 0, 0, 0], [-36, -69, -36, 0], [0, 39, -114, 39], [0, 0, 0, 0], [-580, 144, 0, -144], [150, 0, -150, -2], [0, 0, 0, 0], [0, 114, 139, 114], [0, 0, 0, 0], [0, 0, 0, 0], [-450, 0, 450, -456], [222, 326, 222, 0], [0, 0, 0, 0], [0, 0, 0, 0], [198, -135, 0, 135], [0, 0, 0, 0], [-288, 446, -288, 0], [0, 282, 102, 282], [0, 0, 0, 0], [811, -246, 0, 246], [-1548, 0, 1548, -936], [0, 0, 0, 0], [0, 294, -888, 294], [0, 0, 0, 0], [0, 0, 0, 0], [-612, 0, 612, -124], [-267, 406, -267, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-1716, -294, 0, 294], [0, 0, 0, 0], [1386, 595, 1386, 0], [0, -1020, 5532, -1020], [0, 0, 0, 0], [-624, 534, 0, -534], [1404, 0, -1404, -1230], [0, 0, 0, 0], [0, 36, 1750, 36], [0, 0, 0, 0], [0, 0, 0, 0], [1980, 0, -1980, 102], [462, 676, 462, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-2580, 1290, 0, -1290], [0, 0, 0, 0], [-1386, 1488, -1386, 0], [0, 1584, -1926, 1584], [0, 0, 0, 0], [3755, -1032, 0, 1032], [3909, 0, -3909, 3098], [0, 0, 0, 0], [0, -3600, 5624, -3600], [0, 0, 0, 0], [0, 0, 0, 0], [3330, 0, -3330, 1767], [-2028, 3572, -2028, 0], [0, 0, 0, 0], [0, 0, 0, 0], [5388, -930, 0, 930], [0, 0, 0, 0], [-4932, 1204, -4932, 0], [0, -1596, 4416, -1596], [0, 0, 0, 0], [-6262, -72, 0, 72], [-126, 0, 126, -2802], [0, 0, 0, 0], [0, 3180, 2090, 3180], [0, 0, 0, 0], [0, 0, 0, 0], [-3384, 0, 3384, -1668], [2148, 938, 2148, 0], [0, 0, 0, 0], [0, 0, 0, 0], [4746, -987, 0, 987], [0, 0, 0, 0], [15516, -9888, 15516, 0], [0, -1884, -1524, -1884], [0, 0, 0, 0], [-1089, -1206, 0, 1206], [-8628, 0, 8628, 764], [0, 0, 0, 0], [0, -882, -1044, -882], [0, 0, 0, 0], [0, 0, 0, 0], [2880, 0, -2880, 1757], [5034, -3284, 5034, 0], [0, 0, 0, 0], [0, 0, 0, 0]]}