# Stored data for newform 112.5.k.a, downloaded from the LMFDB on 12 September 2026.
{"Nk2": 2800, "analytic_conductor": 11.577435865390564, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 16, "char_degree": 2, "char_is_minimal": true, "char_is_real": false, "char_orbit_index": 11, "char_orbit_label": "k", "char_order": 4, "char_parity": -1, "char_values": [112, 4, [15, 85, 17], [2, 1, 4]], "cm_discs": [], "conrey_index": 43, "dim": 96, "has_non_self_twist": 1, "hecke_cutters": [], "hecke_orbit": 1, "hecke_orbit_code": 687278653552, "inner_twist_count": 2, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 16, 6, -1, 4, 0]], "is_cm": false, "is_largest": true, "is_maximal": true, "is_rm": false, "is_self_dual": false, "is_self_twist": false, "is_twist_minimal": true, "label": "112.5.k.a", "level": 112, "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": [2, 7], "level_radical": 14, "minimal_twist": "112.5.k.a", "prim_orbit_index": 6, "related_objects": [], "relative_dim": 48, "rm_discs": [], "sato_tate_group": "4.2.3.c4", "self_twist_discs": [], "self_twist_type": 0, "space_label": "112.5.k", "trace_display": [0, 0, 0, 0], "traces": [96, 0, 0, 6, 0, -132, 0, 0, 0, -200, -96, 660, 0, -294, 0, 642, 0, -810, 1408, -2604, 0, -106, -1152, 3880, 0, 6828, 3648, 0, -864, 6360, 0, -3360, 0, -8204, 0, -17216, 1824, -3360, -5376, 180, 0, 0, -6176, 10926, 0, 12544, 0, -4940, 32928, -24066, -8064, -26160, 480, 7776, 23552, 6174, 0, 23270, -7488, 26048, 7552, 21132, 0, -13986, 4032, -47492, -9440, -28512, -19584, -15288, 0, 35642, 0, 12978, -32320, 9888, 4704, -4384, 0, 5100, -69984, -29372, 24000, 0, -22400, -1206, 98560, 42250, 0, -13544, 0, 18132, -17472, -6300, 0, 92728, 0, 0, -59552, 16616, 47808, -76632, 0, -6000, 0, -14070, -61920, -47792, -5408, -127920, 0, -39200, 6720, 52864, 95680, 54558, 64320, 17752, 0, 23200, 0, -52800, 110720, -44324, 0, 56840, 0, 97608, -16256, 179576, -129984, 139452, 0, 44970, -131840, -110612, 0, -98392, -145152, -67620, -33600, -15024, 0, -83608, 9792, 45312, 0, 164478, 32736, 313488, 296320, -237804, 0, -39102, 145536, -65960, -39680, 5196, 0, -64524, 0, 123752, -116960, -840, 112896, 64992, -520704, 88396, 0, -129864, -217024, -259910, 19008, 173324, 0, -116838, -70784, 43328, 71904, -1756, 81792, -79380, 322560, -207232, 0, -315296, 246208, -25116, 0, 347584, 0, 411772, 0, -88500, -168384, 2058, 58656, 300462, -342016, 84042, 0, -154704, -42336, -111024, -191744, -602052, 0, -6872, 54144, 14112, 372512, -152034, 61248, -229762, 392448, 269088, 0, -24006, 427904, 359520, 0, 167268, 0, -61446, -324000, -465424, -343680, -62320, -181376, 20352, 0, 542866, 0, 703212, -278912, 253920, 172800, 95648, 0, 32680, 0, -421650, 521088, 72804, 0, -953368, 330240, -808452, 0, 145136, -20928, 44982, -54400, -558024, 0, -276382, -81600, 100220, -148960, -234912, 75552, 311696, -450816, 667284, 0, 84084, -832128, 669790, 0, 719992, 0, -210288, 0, 24368, 762720, -770752, -280160, 226452, 877312, 214620, 0, 709104, 30592, 422136, 190016, 604664, 0, -1069018, 626208, -743472, -110208, -301220, 369600, -45276, 37632, -983346, 0, 134634, -715584, -576720, 227360, 623544, 0, 899272, -463680, -537960, -116800, -192570, 580160, 300792, 571392, 997208, 0, 20196, 172480, -301064, -140256, -1044124, 0, 596220, 0, 109564, -693504, -1184502, -251456, 447498, 239616, 807836, 0, -272928, -273632, 301272, -983200, 332852, 0, -313992, 504000, -829134, -510528, 758632, -465600, -718708, 0, 73182, 0, 217268, -650400, 64180, -498304, 218736, 0, 30326, -431040, 1234152, -898688, 174276, 0, -1259442, -41856, -1699772, 0, -166548, 903040, -224616, 1416576, -254128, 0, 194196, 0, 1354664, 32928, 1051624, 230560, 2510412, 1267456, 598252, 0, -62720, 360992, 200736, 572096, 801740, 0, 124448, 0, -20448, -202080, 160208, -772320, -451256, -628224, 0, 0, -305042, 340992, -1868030, -676800, -1121124, 0, -1259648, 0, 1236348, -1197312, 91668, -1712064, -373870, -1439616, -316952, 0, -187416, 1193728, -1338900, 0, -355260, 0, 2466696, 350336, 97012, 1492992, 2744, 904672, 1091994, -153856, -20642, 0, -2501176, 94080, 1168950, 1186304, -368504, 0, 37168, 0, -295764, 842496, 806330, 686400, -1321944, -2776064, -1615560, 0, -696608, 373344, -385644, 578816, -1846560, 0, -284592, 114432, 90072, 1124800, 992616, -1651072, 490264, 0, 771056, 0, -558084, 2547200, -571656, -1377792, 612500, 0, 1132626, 0, 1804968, 1798272, 3011176, -277536, 1236744, -1824000, 1087116, 0, 356192, -1275328, 342804, -216800, 970240, 0, -1911224, 148800, 1388796, 285376, 397672, 1059840, -36892, -1787264, -2942388, 0, -68600, -498144, -408320, 0, -1582344, 0, 1016748, 715008, -47560, -1631648, 418704, 3204416, -976420, -2293248, 483336, 0, 1036980, -1858880, -170088, 558720, 390328, 0, 503928, -327040, -499680, 2327808, -913164, -1476160, -262542, 3927296, 1772840, 0, -630810, 53696, -497856, -956480, 543200, 0, -1558556, 322464, -1971624, -2228352, -290668, -2179968, -2195144, -395776, -1151250, 0, -1101836, -32928, 2711232, -813408, -1048848, 0, 550508, 179520, -321048, 799648, -2143248, 2220032, -407610, 5462784, 647656, 0, 4555038, 3210880, 165860, 2534496, -1333484, 0, -449820, -2074240, -895488, -1276224, 343032, 1318400, 2818992, 0, -657816, 0, -239968, -2821664, 2944848, 38080, 307720, 0, -3510120, 184000, -832512, 255296, 2482608, 0, -3718952, 1023104, -1307640, 0, 1434720, 1027200, 226380, -4370240, 1220280, 0, -1536894, 1798080, 2051544, -727552, -5155482, -2781760, -3274024, -1227264, 3211148, 0, 1131606, -978656, 2965452, -1313664, -463200, 0, 3130932, 0, -3867824, 1134336, 1311876, 1131040, 1197552, 286976, 89670, 0, 5774272, 3672448, 306432, 4044864, -542368, 0, 1163120, -319520, 1186068, -4355584, -2720424, 2659200, 67032, -3141888, 3058884, 0, -1335630, 1583040, -2072716, 0, -2912388, 0, -5729116, 0, -3458228, 876480, -1671096, -1932544, -2682384, -871680, -4495200, 0, -2064444, 1160320, 2934982, -2218080, 4042124, 0, -35640, -245056, -1255380, 141024, -5003808, -2359808, 1824198, -7463680, -1850956, 0, 4309902, -3446080, -2986956, 792064, 3483968, 0, 289884, -856320, -814320, 3193408, 942232, 1683840, 2337392, 0, -1045512, 0, -1280288, 1098912, 4166052, 6112960, -100842, 0, -1749874, 897600, 4532008, 1295552, 2212464, 635040, 1989930, 452352, 4386092, 0, 1468260, -948224, 1556534, 1361376, 5726824, 0, 5732166, 539904, 3369168, 987840, -3444112, -2933728, -1333944, -1410432, 5062992, 0, 2283400, -688896, 1164042, -2558400, -1422888, 0, 2940404, 0, -3671130, -5251840, 2742688, -4613280, -4318736, 1750784, -863184, 0, 1943264, 591552, -5921472, -1732672, -6499392, 0, -1012696, 3447168, 4624240, 3594784, 618984, 925696, 724122, 8772480, 2170360, 0, -55866, -5734144, -9365244, 1020768, -1058600, 0, -2658492, 1930880, -601608, 2363712, -2893744, 3255584, 1092222, 2911232, -4620864, 0, -11351264, -1412768, 4372392, 2036736, 3425156, 0, -846892, 0, -3571512, -673408, -3540304, -4417920, 9785538, 5246208, -6972612, 0, -742238, 513792, -5711056, -7716736, 5070816, 0, 220206, -2296896, -6267256, -908672, 950538, -5386304, 4575904, 696192, 5061114, 0, -6659556, -4605440, 1053820, 1191360, -1311632, 0, 869382, -4111040, 5810680, -5024064, 12775340, 0, 1346856, -7408896, 522788, 0, -2329024, -89600, 3114342, 9688448, 93968, 0, 8507360, 0, 7656156, -2104256, 849144, 5384736, -6526728, 4477184, 2164380, 0, 2553684, 3265632, 3511280, 838528, -4279368, 0, 4766144, 0, -5390992, 2974336, 8351196, -716032, -153068, 8296704, -899640, 0, -1730958, 1898752, -3889314, -6681984, -10501788, 0, 3320562, 0, 5312744, -1732032, 1278496, -5753792, 622104, -1238528, 4021498, 0, -8053168, 5027648, -13085040, 0, 4887152, 0, 1707640, 1561280, 709764, -3218304, -2564660, 1406976, -6022024, -6608896, -905418, 0, -11684824, 1947456, 3630840, 4632928, 1522008, 0, -7125552, -2952000, -277830, 2481952, -5408160, 9845312, 9711186, -8881152, -7259772, 0, 8416752, -4806816, -5789392, -2399040, -352212, 0, 211974, -229120, -6584776, -2305920, 7743098, -4905088, -1369692, -5958400, -7189512, 0, -5124088, 4631520, -693552, -9446272, -235200, 0, -11557856, 0, -158220, 11729728, 10657672, 235200, 942224, 13862400, 3830592, 0, 4114284, 7657728, 5067580, -1950432, 7190340, 0, 4601174, -5518080, 21940840, 482944, -7638072, 11660032, 3591200, -4382208, 3854992, 0, 5296410, -5422976, 8802352, 2472000, -6598944, 0, 4205664, -1517824, -8486804, 1954656, 1526736, 5755392, -6282492, -541184, 181496, 0, 16817926, -424832, -3226176, 4810560, -10598420, 0, -1207224, -1877920, 9685944, 1570400, -7688632, -658944, -5488, -5739648, 1202178, 0, -5965160, -13632576, -20307820, -2352000, 1336608, 0, -1712132, 1400832, -12256156, 5090752, -893172, -5464992, -9962418, 4551936, -13440888, 0, -14044620, -4264960, 15747464, -6466176, 5774008, 0, -10461684, 5418240, -3955672, -9227136, -14224368, 11147840, 597342, 6737152, -11180800], "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, "field_disc": null, "field_disc_factorization": null, "field_poly": null, "field_poly_is_cyclotomic": null, "field_poly_is_real_cyclotomic": null, "field_poly_root_of_unity": null, "fricke_eigenval": null, "hecke_ring_generator_nbound": null, "hecke_ring_index": null, "hecke_ring_index_factorization": null, "hecke_ring_index_proved": null, "is_polredabs": null, "nf_label": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp_display": null, "trace_hash": null, "trace_moments": null, "trace_zratio": null}