# Stored data for newform 208.12.f.b, downloaded from the LMFDB on 12 June 2024.
{"Nk2": 29952, "analytic_conductor": 159.8153815563945, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 13, "char_degree": 1, "char_is_minimal": false, "char_is_real": true, "char_orbit_index": 6, "char_orbit_label": "f", "char_order": 2, "char_parity": 1, "char_values": [208, 2, [79, 53, 145], [2, 2, 1]], "cm_discs": [], "conrey_index": 129, "dim": 12, "field_disc": 10525681345696499214017613316607324434481663567730116775884705378880168026699850304119069696, "field_disc_factorization": [[2, 10], [3, 4], [23, 1], [41, 2], [7393, 1], [1053739, 2], [7798933, 2], [206195933, 2], [393211449411106531, 2]], "field_poly": [1497425476589715456, 0, 134825856231997440, 0, 380893885719552, 0, 340607607312, 0, 121088056, 0, 18433, 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": [[3, [-255121008509808, -14522233287672, 109163403621, 129598956, -665334, -244, 1]]], "hecke_orbit": 2, "hecke_orbit_code": 4503943426080976, "hecke_ring_generator_nbound": 13, "hecke_ring_index": 4968076718112768, "hecke_ring_index_factorization": [[2, 31], [3, 4], [13, 4]], "hecke_ring_index_proved": true, "inner_twist_count": 2, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 13, 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": "208.12.f.b", "level": 208, "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, 13], "level_radical": 26, "minimal_twist": "13.12.b.a", "prim_orbit_index": 2, "qexp_display": "q+(41-\\beta _{2})q^{3}-\\beta _{5}q^{5}+(\\beta _{1}+\\beta _{5}-\\beta _{6}+\\cdots)q^{7}+\\cdots", "related_objects": [], "relative_dim": 12, "rm_discs": [], "sato_tate_group": "11.2.3.c2", "self_twist_discs": [], "self_twist_type": 0, "space_label": "208.12.f", "trace_display": [0, 488, 0, 0], "trace_hash": 838072259157644317, "trace_moments": [{"__RealLiteral__": 0, "data": "0.053", "prec": 17}, {"__RealLiteral__": 0, "data": "10.351", "prec": 20}, {"__RealLiteral__": 0, "data": "1.971", "prec": 17}, {"__RealLiteral__": 0, "data": "586.108", "prec": 24}, {"__RealLiteral__": 0, "data": "390.840", "prec": 24}, {"__RealLiteral__": 0, "data": "49436.809", "prec": 30}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.508", "prec": 17}, "traces": [0, 12, 0, 488, 0, 0, 0, 0, 0, 654644, 0, 0, 0, 3208868, 0, 0, 0, 12198768, 0, 0, 0, 0, 0, -5810592, 0, 6102388, 0, 52613336, 0, -244463112, 0, 0, 0, 0, 0, 562027560, 0, 0, 0, 2199109744, 0, 0, 0, -2294519976, 0, 0, 0, 0, 0, -3573617796, 0, -7713246552, 0, -4602062760, 0, 6178744976, 0, 0, 0, 0, 0, -13775649944, 0, 0, 0, -7598401512, 0, 0, 0, -25419983328, 0, 0, 0, 0, 0, -68016370832, 0, -80478036048, 0, -18046097296, 0, -132677486692, 0, 0, 0, 0, 0, -94507900752, 0, 0, 0, -104793638664, 0, 0, 0, -145093149648, 0, 0, 0, 0, 0, 487944942840, 0, 17145058800, 0, 438857348040, 0, 282243232992, 0, 0, 0, 0, 0, -1069738095960, 0, 0, 0, 408569829460, 0, 0, 0, -565646006300, 0, 0, 0, 0, 0, -1091153183296, 0, 1317053106344, 0, -1658906089656, 0, -1705601758992, 0, 0, 0, 0, 0, 5179795600056, 0, 0, 0, -3158054475264, 0, 0, 0, 3217854110000, 0, 0, 0, 0, 0, 8226281492472, 0, -255724653552, 0, 2429987012040, 0, 8966881028544, 0, 0, 0, 0, 0, -13609112848944, 0, 0, 0, 8818620487404, 0, 0, 0, -14234397339000, 0, 0, 0, 0, 0, -23361314649816, 0, -4640462191656, 0, -19943751655024, 0, -20051040763944, 0, 0, 0, 0, 0, 18273751085520, 0, 0, 0, -25986631626072, 0, 0, 0, 1862995562144, 0, 0, 0, 0, 0, 27739625932144, 0, -21413908844352, 0, 21546939409440, 0, 29457474647528, 0, 0, 0, 0, 0, -61586340704112, 0, 0, 0, -5753100029352, 0, 0, 0, -10579799356988, 0, 0, 0, 0, 0, -61392292526928, 0, -17051418839856, 0, -31470925146952, 0, -40832063342096, 0, 0, 0, 0, 0, 4083246988400, 0, 0, 0, -28978759522752, 0, 0, 0, 445444193472, 0, 0, 0, 0, 0, 69344169319200, 0, -11237931747672, 0, -32282453204472, 0, 25472039650224, 0, 0, 0, 0, 0, 9753746824344, 0, 0, 0, 4020648052200, 0, 0, 0, -102413446442808, 0, 0, 0, 0, 0, 130857265522400, 0, -115689323400048, 0, 215136126541008, 0, 222809935555596, 0, 0, 0, 0, 0, -216541886777344, 0, 0, 0, 85516542765888, 0, 0, 0, -14045342652192, 0, 0, 0, 0, 0, -356292717540976, 0, -145150067929584, 0, 7264837678336, 0, -285229481063040, 0, 0, 0, 0, 0, 336838844494320, 0, 0, 0, -292961917455532, 0, 0, 0, 344587888415448, 0, 0, 0, 0, 0, 248073793396608, 0, 49995931865296, 0, 439946554177776, 0, 417442231467936, 0, 0, 0, 0, 0, -640563676161384, 0, 0, 0, 326133718069120, 0, 0, 0, -214186420017496, 0, 0, 0, 0, 0, -289679172406236, 0, -229045257525704, 0, -501423453632736, 0, -360043597637568, 0, 0, 0, 0, 0, 465899299480840, 0, 0, 0, -738275609358456, 0, 0, 0, -173260549601312, 0, 0, 0, 0, 0, 195376001725712, 0, -442884112459896, 0, 766125961746048, 0, 1055963242946424, 0, 0, 0, 0, 0, -310522058371536, 0, 0, 0, 185744290520256, 0, 0, 0, 488827519040112, 0, 0, 0, 0, 0, 1141936197496608, 0, -476278822658896, 0, -416529422551384, 0, 1446400097290632, 0, 0, 0, 0, 0, -105027793679400, 0, 0, 0, 149557735816944, 0, 0, 0, -121937315099552, 0, 0, 0, 0, 0, -836536974037824, 0, 1667584626792620, 0, 975277491374712, 0, 273654334794544, 0, 0, 0, 0, 0, 2797168153804352, 0, 0, 0, 391483310206560, 0, 0, 0, 1182805392597960, 0, 0, 0, 0, 0, 3678461568941328, 0, -417942709215360, 0, 1396731784536000, 0, 504455491024864, 0, 0, 0, 0, 0, -3580711137038856, 0, 0, 0, 598222357340088, 0, 0, 0, -1389299998542576, 0, 0, 0, 0, 0, -3810592819242024, 0, 5341699439576640, 0, -1280400589806336, 0, -3514502755428120, 0, 0, 0, 0, 0, 4233222412648944, 0, 0, 0, -1449419975549416, 0, 0, 0, 4036953684478752, 0, 0, 0, 0, 0, 7389210278559088, 0, -4820314678293456, 0, -2413907209756224, 0, -929579643699936, 0, 0, 0, 0, 0, -4759584006332724, 0, 0, 0, 541561315800336, 0, 0, 0, -8345733573500232, 0, 0, 0, 0, 0, -13661848133303696, 0, 513850905539784, 0, 1452597396483240, 0, -1113535586825320, 0, 0, 0, 0, 0, 3431278670141736, 0, 0, 0, 2486577599942384, 0, 0, 0, 4153260252592776, 0, 0, 0, 0, 0, 4495291691377296, 0, -1758334575128296, 0, -11742594923665104, 0, -877430471203296, 0, 0, 0, 0, 0, 2606229644287344, 0, 0, 0, -7146765681164928, 0, 0, 0, -1228520489039808, 0, 0, 0, 0, 0, -9038901494654280, 0, 7919706908151808, 0, 5956020643178496, 0, 199168779258880, 0, 0, 0, 0, 0, -3252148422206208, 0, 0, 0, 10130528698606056, 0, 0, 0, -708135385128816, 0, 0, 0, 0, 0, 2491598194416000, 0, -12084227326060272, 0, -17529987949765028, 0, -14722509482019168, 0, 0, 0, 0, 0, 6390677492629720, 0, 0, 0, -11857943823430276, 0, 0, 0, -3127294139805816, 0, 0, 0, 0, 0, -3444631118055168, 0, 13298490901270048, 0, 28251577589616816, 0, 18075518270385288, 0, 0, 0, 0, 0, -5974529411483616, 0, 0, 0, 18057200607330144, 0, 0, 0, 12640302232514208, 0, 0, 0, 0, 0, 3762173453948112, 0, -9451012066074464, 0, -28789943776173432, 0, -30601013201187792, 0, 0, 0, 0, 0, 25342803511523392, 0, 0, 0, -11059741419603240, 0, 0, 0, -11955140499857088, 0, 0, 0, 0, 0, -26032215283139400, 0, 20142535265359656, 0, 24659071514800944, 0, 29966778191599608, 0, 0, 0, 0, 0, -27956516870897216, 0, 0, 0, 24063833377004096, 0, 0, 0, 19909360958311392, 0, 0, 0, 0, 0, 7112407460564328, 0, -20115452741771632, 0, -50446379804722324, 0, -26426210835953640, 0, 0, 0, 0, 0, 18587180799535488, 0, 0, 0, -38282514285363504, 0, 0, 0, -17276560821358640, 0, 0, 0, 0, 0, -25310938345018512, 0, 22862672249110032, 0, 62628444589330536, 0, 6385062822241336, 0, 0, 0, 0, 0, 19310104146655416, 0, 0, 0, 16165767511014576, 0, 0, 0, 29296177348254408, 0, 0, 0, 0, 0, 58893660418789416, 0, -37965943086191328, 0, -29404668057709136, 0, -6421365962383440, 0, 0, 0, 0, 0, -44479972583531472, 0, 0, 0, -22849131292620360, 0, 0, 0, -47959709181148008, 0, 0, 0, 0, 0, -35497782320452704, 0, 29739128371158240, 0, -8329375765006320, 0, 19343790476400576, 0, 0, 0, 0, 0, 37433297265650208, 0, 0, 0, 9365621813708784, 0, 0, 0, 3929575036909344, 0, 0, 0, 0, 0, 107409577705371640, 0, -79092345723349040, 0, -11938809704040408, 0, 70979987139840176, 0, 0, 0, 0, 0, -33320001703825644, 0, 0, 0, -2870846697710784, 0, 0, 0, -27390928055911568, 0, 0, 0, 0, 0, -134906748635839392, 0, 108532092657408408, 0, 70557177965265824, 0, 3226455889307376, 0, 0, 0, 0, 0, 99841883916915344, 0, 0, 0, -15268574814268464, 0, 0, 0, 81781803669095400, 0, 0, 0, 0, 0, 147399883810401888, 0, 39526129692089288, 0, -803302183610304, 0, 91990774645815024, 0, 0, 0, 0, 0, -41373334136815152, 0, 0, 0, -34255561377701664, 0, 0, 0, -42431339007550224, 0, 0, 0, 0, 0, -150984874778150536, 0, 7065578729108184, 0, 35367548180443632, 0, 54678692035040800, 0, 0, 0, 0, 0, 105986990831969792, 0, 0, 0, -59825626389751560, 0, 0, 0, 100142564417014688, 0, 0, 0, 0, 0, 121416547554351792, 0, -193530351664764720, 0, 47048134054888504, 0, 17952205866528632, 0, 0, 0, 0, 0, -66941971610664600, 0, 0, 0, -18942055830734400, 0, 0, 0, -26939685083721936, 0, 0, 0, 0, 0, -52545007401297600, 0, 10987934820040116, 0, 82013347901665392, 0, -19661899115968176, 0, 0, 0, 0, 0, -34555826505934920, 0, 0, 0, 64915420158104048, 0, 0, 0, 108275334867500000, 0, 0, 0, 0, 0, -84118160747289512, 0, -47960064669947928, 0, -130228166253405504, 0, -132877242865946832, 0, 0, 0, 0, 0, -22152883816822584, 0, 0, 0], "weight": 12, "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, "nf_label": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [41, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [54567, 0, -41, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 12, 0, 0, 0, 9, -2, 1, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [267655, -3, -749, 0, 0, -13, -4, -2, -1, 0, 1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -45, 0, 0, 0, -156, 15, 0, 0, 0, 5, -5], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1015567, -1, 2968, 30, 4, 1, 0, 1, 2, 5, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -307, 0, 0, 0, -178, -74, 39, 0, 0, 25, 5], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -19, 0, 0, 0, 765, 126, 157, 0, 0, 11, -14], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-487243, 2, 9147, -53, 7, -2, 0, -2, -4, 17, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [500308, -10, 24724, -28, -28, 10, 0, 10, 20, 3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4382136, 12, 6820, 85, 24, -12, 0, -12, -24, 3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-20382113, -33, 30641, 49, 75, 33, 0, 33, 66, 63, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1450, 0, 0, 0, -308, -2506, -726, 0, 0, -116, 149], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 5051, 0, 0, 0, -23343, -2478, 2080, 0, 0, 33, -12], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [46886195, -10, -150435, -1160, -350, 10, 0, 10, 20, 80, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 4556, 0, 0, 0, -35380, -1454, -1644, 0, 0, -665, 104], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [183366039, -8159, -322079, 1729, -377, -43043, -873, 1520, 188, 143, 488, -59], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -31871, 0, 0, 0, 51169, 8118, -1290, 0, 0, 943, 476], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-191040218, 166, -511042, 793, 854, -166, 0, -166, -332, -577, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -12165, 0, 0, 0, -68994, -12150, 1545, 0, 0, 2205, -450], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1617, 0, 0, 0, -54568, 12485, 5786, 0, 0, 137, 2096], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-297396725, -407, -1220301, 5851, 1166, 407, 0, 407, 814, -990, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-641479383, 306, -3875025, 2202, 5202, -306, 0, -306, -612, 1278, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-382396393, -770, -3313309, -10479, -403, 770, 0, 770, 1540, 1183, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [513221851, 1650, 5022373, -7281, -2761, -1650, 0, -1650, -3300, -2299, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 90682, 0, 0, 0, -217008, -9144, -22690, 0, 0, 7708, -4744], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -175060, 0, 0, 0, -345377, 29968, 31471, 0, 0, 274, 2377], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1150312095, 354, 7020487, -1011, -515, -354, 0, -354, -708, -3615, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 484136, 0, 0, 0, -570618, 25488, -8456, 0, 0, -4966, -977], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-636296972, 79880, 9307029, -19513, -598, -785876, 5150, -5225, -2060, -962, 9665, 5870], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -87519, 0, 0, 0, 425232, 62700, -37389, 0, 0, 14141, 3151], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2120917923, -990, 7756209, 7443, 8199, 990, 0, 990, 1980, 3735, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -7829, 0, 0, 0, -346927, -142649, -6446, 0, 0, 5566, -7772], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -743607, 0, 0, 0, -765147, 108882, 88146, 0, 0, -8739, -16608], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-5668835062, 5290, 2456014, -63958, 1292, -5290, 0, -5290, -10580, -9842, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-6713523483, 3575, 21059171, -18073, 16753, -3575, 0, -3575, -7150, -13189, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1508664536, 4840, 14551072, -88006, -12344, -4840, 0, -4840, -9680, 3462, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-11054148120, -4146, -6771251, -137669, 780, 4146, 0, 4146, 8292, 10101, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -2471665, 0, 0, 0, -454722, -46786, -7615, 0, 0, -12817, -4711], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1862415, 0, 0, 0, -1393110, -224640, 268425, 0, 0, 66750, -34350], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-7884324459, 594, 26014827, -2247, 79353, -594, 0, -594, -1188, 15579, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -2315100, 0, 0, 0, 857656, -675080, -309914, 0, 0, -132848, 17056], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-8731820754, -1231494, -3014754, 25129, -1300, 1046071, -748892, 301931, -13244, -28977, -24274, 3253], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -3021316, 0, 0, 0, 6625809, 1124622, 206344, 0, 0, 14657, -17000], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-12104243748, -15060, 39860796, -374502, -23532, 15060, 0, 15060, 30120, 12342, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1853177, 0, 0, 0, -2340799, -1142978, 448002, 0, 0, -7353, 72600], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 5021579, 0, 0, 0, -2890800, -163980, 231661, 0, 0, 126467, -84701], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]}