# Stored data for newform 55.6.e.b, downloaded from the LMFDB on 16 June 2025.
{"Nk2": 1980, "analytic_conductor": 8.821110089713935, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 55, "char_degree": 2, "char_is_minimal": true, "char_is_real": false, "char_orbit_index": 5, "char_orbit_label": "e", "char_order": 4, "char_parity": 1, "char_values": [55, 4, [12, 46], [1, 2]], "cm_discs": [], "conrey_index": 32, "dim": 52, "has_non_self_twist": 1, "hecke_cutters": [[2, [215321154773083480612342333440000000000, 0, 0, 0, 137486121079236271824531514982400000000, 0, 0, 0, 10391833820542405383100041527296000000, 0, 0, 0, 136593023499946978309016080220160000, 0, 0, 0, 628272167335502479402788904960000, 0, 0, 0, 1276127441281929857591011840000, 0, 0, 0, 1383358676131774529162720000, 0, 0, 0, 880323681566082194589200, 0, 0, 0, 343539885297227163000, 0, 0, 0, 83201649184914825, 0, 0, 0, 12359132998700, 0, 0, 0, 1084701006, 0, 0, 0, 51268, 0, 0, 0, 1]]], "hecke_orbit": 2, "hecke_orbit_code": 4503874605940791, "inner_twist_count": 4, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 5, 3, -1, 4, 0], [1, 1, 11, 2, -1, 2, 0], [1, 1, 55, 5, 1, 4, 0]], "is_cm": false, "is_largest": true, "is_maximal": false, "is_rm": false, "is_self_dual": false, "is_self_twist": false, "is_twist_minimal": true, "label": "55.6.e.b", "level": 55, "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": true, "level_primes": [5, 11], "level_radical": 55, "minimal_twist": "55.6.e.b", "prim_orbit_index": 5, "related_objects": [], "relative_dim": 26, "rm_discs": [], "sato_tate_group": "5.2.3.c4", "self_twist_discs": [], "self_twist_type": 0, "space_label": "55.6.e", "trace_display": [0, 56, -48, 0], "traces": [52, 0, 56, 0, -48, 0, 0, 0, 0, 0, -364, 4792, 0, 0, 2564, -6416, 0, 0, 0, 18272, 0, 2680, -144, 0, -12248, 2432, 3644, 0, 0, 0, 9672, 0, 30576, 0, 0, -148776, 24152, 4400, 0, 0, 0, -43480, 0, 0, -4984, 0, -44148, 26416, 0, 0, 0, 0, 75596, 0, 59092, 304264, 0, -220200, 0, -240016, 0, 0, 0, 0, 0, 207000, -17888, 0, 0, -216880, 285704, 0, 0, 0, 278404, 0, -341160, 15160, 0, 616192, -397204, 349720, 0, 0, 0, -94768, 0, 539000, 0, 0, -864768, 242072, 15772, 0, 0, 0, -633128, 0, 0, -991288, 0, 1945040, -942364, 0, 0, 0, 0, -1328, 0, -680520, -95456, 0, -91464, 0, -599496, 0, 0, 0, 0, 0, 242652, -662760, 0, 0, 1270512, 1195232, 0, 0, 0, -477480, 0, -2526968, 1531040, 0, 1895048, -1934136, -1861928, 0, 0, 0, 2729344, 0, -202280, 0, 0, -2026368, 2897032, 2392816, 0, 0, 0, -540800, 0, 0, 817484, 0, 2686952, -1232040, 0, 0, 0, 0, 1216476, 0, -1567616, -1307568, 0, -4723480, 0, -3462200, 0, 0, 0, 0, 0, 5075368, 2877444, 0, 0, 5225416, 1656272, 0, 0, 0, -3847636, 0, -1670600, -346784, 0, 2190040, -5305128, -11101808, 0, 0, 0, 8181016, 0, 1610680, 0, 0, -8772256, 11546720, 6071840, 0, 0, 0, -7138964, 0, 0, 5151440, 0, 2093752, -11375348, 0, 0, 0, 0, -6180640, 0, -1711008, -3641568, 0, -1664, 0, -8618164, 0, 0, 0, 0, 0, 3529600, 7360760, 0, 0, 4894504, 9701904, 0, 0, 0, 5675744, 0, -3773200, 5897668, 0, 2810472, -23729600, -7676720, 0, 0, 0, 15859304, 0, 3770016, 0, 0, 152016, 9785332, 26592280, 0, 0, 0, -14652560, 0, 0, -4303416, 0, 9507924, -6462544, 0, 0, 0, 0, -1165760, 0, 4664412, -16695056, 0, -8562560, 0, -28228640, 0, 0, 0, 0, 0, 5185632, 8845440, 0, 0, 566120, 25845944, 0, 0, 0, 2305464, 0, -15774356, -6290440, 0, 23326744, -5406768, 5609760, 0, 0, 0, 13854432, 0, -7867760, 0, 0, -11688896, 20253240, 7914216, 0, 0, 0, -11671528, 0, 0, -20819448, 0, -1510840, -11978480, 0, 0, 0, 0, -11249640, 0, 10852360, -19055528, 0, -9309572, 0, -22351076, 0, 0, 0, 0, 0, -2932096, 11321760, 0, 0, 7388748, -19238768, 0, 0, 0, 41412600, 0, -16503080, 24506056, 0, 16106624, -3022264, 13854320, 0, 0, 0, 26271252, 0, -13556104, 0, 0, -3173800, -9707768, 38825056, 0, 0, 0, -32358296, 0, 0, -38886616, 0, -2285200, 18459320, 0, 0, 0, 0, -41162344, 0, 24857960, 19064232, 0, -19330464, 0, -56815920, 0, 0, 0, 0, 0, 25908840, 24557812, 0, 0, -15437608, -45530128, 0, 0, 0, 23966220, 0, -4221568, 79010800, 0, 10527200, 67130944, 53546872, 0, 0, 0, 9954496, 0, -20391000, 0, 0, -10056928, -2140000, 26528028, 0, 0, 0, -21154720, 0, 0, -37342360, 0, -23333976, 24810456, 0, 0, 0, 0, -106646320, 0, 35915760, -50732876, 0, -948704, 0, -17083036, 0, 0, 0, 0, 0, 23246800, 3099112, 0, 0, -8968640, -144771800, 0, 0, 0, 87126184, 0, -9549080, 37095896, 0, 23004628, 7219832, 63426192, 0, 0, 0, 2439544, 0, -46138600, 0, 0, 61989896, -65935684, 79319320, 0, 0, 0, -16347880, 0, 0, -35722056, 0, -37002648, 62196120, 0, 0, 0, 0, -61633760, 0, 62973336, -17774264, 0, -76742440, 0, -79534008, 0, 0, 0, 0, 0, 22882000, 13142872, 0, 0, -122502160, -95238368, 0, 0, 0, 53318784, 0, 7121892, 67566160, 0, 68537880, 7282272, 205459040, 0, 0, 0, 125967432, 0, -144201584, 0, 0, 117922848, -37574240, 104342320, 0, 0, 0, -2267036, 0, 0, -152024592, 0, -111228760, 63226692, 0, 0, 0, 0, -211631424, 0, 98599640, -48368800, 0, -39608240, 0, -59377112, 0, 0, 0, 0, 0, 1967600, 47443520, 0, 0, -47732276, -138934768, 0, 0, 0, 284278840, 0, -37840360, 134610932, 0, -34346616, 118004456, 113598952, 0, 0, 0, 66290832, 0, -81744644, 0, 0, 159172432, -67092668, 245411216, 0, 0, 0, -152823528, 0, 0, -132412000, 0, -83175056, 71340000, 0, 0, 0, 0, -151475372, 0, 113960192, -233109200, 0, -6687200, 0, -232846880, 0, 0, 0, 0, 0, -18224336, 61003372, 0, 0, -36778456, -112294112, 0, 0, 0, 191830632, 0, -15762960, 174276336, 0, 79786400, -14306696, 235911080, 0, 0, 0, 85868344, 0, -170408280, 0, 0, 83363872, -65408320, 106595056, 0, 0, 0, -71305288, 0, 0, -181853280, 0, -229403488, 51608056, 0, 0, 0, 0, -284873240, 0, 263543224, -17269296, 0, -101649520, 0, -266191760, 0, 0, 0, 0, 0, 59624400, 335781400, 0, 0, -96040152, -339664784, 0, 0, 0, 346026680, 0, -70135640, 93460116, 0, 105404164, -71437736, 213004004, 0, 0, 0, -37455496, 0, -231829560, 0, 0, 173467400, 67791360, 403918480, 0, 0, 0, -221335640, 0, 0, -175351452, 0, -143426720, 70630752, 0, 0, 0, 0, -102603028, 0, 187502040, -30489664, 0, -154646240, 0, -600236984, 0, 0, 0, 0, 0, 238098400, 164290272, 0, 0, -28025440, -267181568, 0, 0, 0, 289910944, 0, -99157248, 474031040, 0, 233301384, -12016000, 248870960, 0, 0, 0, 175065232, 0, -243783960, 0, 0, 169198504, 176713472, 273259972, 0, 0, 0, -181324428, 0, 0, -459212080, 0, -212464240, 129584480, 0, 0, 0, 0, -576797504, 0, 327192520, -142044656, 0, -174180524, 0, -346658536, 0, 0, 0, 0, 0, 91123072, 172136280, 0, 0, 18456664, -203290600, 0, 0, 0, 425648080, 0, -335468920, 214728640, 0, 221005228, -61046696, 145916872, 0, 0, 0, 333547216, 0, -191623560, 0, 0, 88696464, 54683984, 708986560, 0, 0, 0, -377148280, 0, 0, -97864496, 0, 51834640, -49324960, 0, 0, 0, 0, -305726424, 0, 39691824, -286100736, 0, -393662392, 0, -635681880, 0, 0, 0, 0, 0, 285213800, 134291068, 0, 0, -63290680, -18055348, 0, 0, 0, 349858392, 0, -119086880, 322531656, 0, 260564840, -238023256, 272085624, 0, 0, 0, 541671264, 0, -272946560, 0, 0, 69692800, 110481520, 529019836, 0, 0, 0, -350827768, 0, 0, -725780480, 0, 168354480, -33362212, 0, 0, 0, 0, -592175000, 0, 94994472, -175637696, 0, -398578484, 0, -525582432, 0, 0, 0, 0, 0, 232757980, 257505792, 0, 0, -93606476, -611304072, 0, 0, 0, 876388336, 0, -500195920, 418093280, 0, 150826124, -451685600, 273185532, 0, 0, 0, 414935272, 0, -128736280, 0, 0, -42055696, 241683600, 973957120, 0, 0, 0, -231843640, 0, 0, -144729356, 0, 127799596, 65158360, 0, 0, 0, 0, -294623568, 0, 245189320, -618291136, 0, -339923680, 0, -655958496, 0, 0, 0, 0, 0, 589848032, -56687008, 0, 0, 188698640, -246876856, 0, 0, 0, 183288484, 0, -343095680, 794429720, 0, 984403784, -530040244, 482514920, 0, 0, 0, 519399600, 0, -518337440, 0, 0, -136628728, 561217016, 738928480, 0, 0, 0, -481663288, 0, 0, -582230848, 0, -183677440, -2582984, 0, 0, 0, 0, -818477000, 0, 475612280, -216183528, 0, -652354948, 0, -698251656, 0, 0, 0, 0, 0], "weight": 6, "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}