# Stored data for newform 49.10.c.a, downloaded from the LMFDB on 21 August 2025.
{"Nk2": 4900, "analytic_conductor": 25.236755972029783, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 7, "char_degree": 2, "char_is_minimal": false, "char_is_real": false, "char_orbit_index": 3, "char_orbit_label": "c", "char_order": 3, "char_parity": 1, "char_values": [49, 3, [3], [2]], "cm_discs": [-7], "conrey_index": 18, "dim": 2, "field_disc": -3, "field_disc_factorization": [[-1, 1], [3, 1]], "field_poly": [1, -1, 1], "field_poly_is_cyclotomic": true, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 6, "has_non_self_twist": 1, "hecke_cutters": [[2, [25, -5, 1]], [3, [0, 1]]], "hecke_orbit": 1, "hecke_orbit_code": 137606725681, "hecke_ring_generator_nbound": 4, "hecke_ring_index": 1, "hecke_ring_index_factorization": [], "hecke_ring_index_proved": true, "inner_twist_count": 4, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 7, 2, -1, 2, -7], [1, 1, 7, 3, 1, 3, 0], [1, 1, 7, 4, -1, 6, 0]], "is_cm": true, "is_largest": false, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": false, "is_self_twist": true, "is_twist_minimal": true, "label": "49.10.c.a", "level": 49, "level_is_powerful": true, "level_is_prime": false, "level_is_prime_power": true, "level_is_prime_square": true, "level_is_square": true, "level_is_squarefree": false, "level_primes": [7], "level_radical": 7, "minimal_twist": "49.10.a.a", "nf_label": "2.0.3.1", "prim_orbit_index": 3, "qexp_display": "q+5\\zeta_{6}q^{2}+(487-487\\zeta_{6})q^{4}+4995q^{8}+\\cdots", "related_objects": [], "relative_dim": 1, "rm_discs": [], "sato_tate_group": "9.2.1.d3", "self_twist_discs": [-7], "self_twist_type": 1, "space_label": "49.10.c", "trace_display": [5, 0, 0, 0], "trace_hash": 258309293207336630, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.914", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "17.192", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "211.512", "prec": 24}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.506", "prec": 17}, "traces": [0, 2, 5, 0, 487, 0, 0, 0, 9990, 19683, 0, 42908, 0, 0, 0, 0, -224369, 0, -98415, 0, 0, 0, 429080, -1396040, 0, 1953125, 0, 0, 0, 15142852, 0, 0, 3679285, 0, 0, 0, 19171242, -22743450, 0, 0, 0, 0, 0, 74203560, -20896196, 0, 6980200, 0, 0, 0, 19531250, 0, 0, 58133290, 0, 0, 0, 0, 37857130, 0, 0, 0, 0, 0, -192961006, 0, 0, -262469860, 0, 0, 0, -826135264, 98316585, 0, 113717250, 0, 0, 0, 0, 603893176, 0, -387420489, 0, 0, 0, 0, 185508900, 0, 214325460, 0, 0, 0, -1359742960, 0, 0, 0, 0, 0, 0, 1689116328, -951171875, 0, 0, 0, 0, 0, 581332900, -1862391820, 0, -209637234, 0, 0, 0, 5198919940, 0, 0, 3687284462, 0, 0, 0, 0, 516851227, 0, 0, 0, 0, 0, 8580596000, -2366196435, 0, 0, 0, 0, 0, -2624698600, 0, 0, -6089507510, 0, 0, 0, 0, -2065338160, 0, 4416255027, 0, 0, 0, -22152120300, 7538658314, 0, -4766148648, 0, 0, 0, 0, 0, 0, -3019465880, 0, 0, 0, -3874204890, 17486436980, 0, 0, 0, 0, 0, -21208998746, 0, 0, 18068566860, 0, 0, 0, -19254450104, 0, 0, -26806410724, 0, 0, 0, 0, -6973219800, 0, 0, 0, 0, 0, 0, -17600930888, 0, -2290735890, 0, 0, 0, 79789923980, 4222790820, 0, 9755859375, 0, 0, 0, 0, 0, 0, 27478255320, 0, 0, 0, 73369141416, -28310912230, 0, 9311959100, 0, 0, 0, -2096372340, 0, 0, 0, 0, 0, 0, 76886718750, 12997299850, 0, 0, 0, 0, 0, 75638545740, -73670275030, 0, 0, 0, 0, 0, -198408779488, 0, 0, -2584256135, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -119802568640, 21451490000, 0, -37567035361, 0, 0, 0, 0, 149028377958, 0, -14859963680, 0, 0, 0, 0, 127822821820, 0, 0, 0, 0, 0, -60895075100, -83804687500, 0, 75480859690, 0, 0, 0, -414323704756, 0, 0, -201163936784, 0, 0, 0, 144838733310, 118587876497, 0, 0, 0, 0, 0, 0, -113603532750, 0, -37693291570, 0, 0, 0, -47661486480, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 588191953424, -327479448830, 0, 324874746808, 0, 0, 0, 0, 188673778143, 0, -87432184900, 0, 0, 0, 0, -111156785028, 0, 447659326350, 0, 0, 0, 690837530940, -53022496865, 0, 0, 0, 0, 0, 370646782200, 0, 0, -444996652900, 0, 0, 0, 0, -157870760780, 0, 0, 0, 0, 0, -268064107240, -592645690184, 0, 322687697779, 0, 0, 0, 0, 0, 0, -313228098760, 0, 0, 0, 0, 551473419530, 0, 0, 0, 0, 0, -508307032152, 0, 0, 88004654440, 0, 0, 0, -22907358900, 730274335740, 0, -692557443706, 0, 0, 0, 0, 199474809950, 0, 411299825868, 0, 0, 0, -876441406250, 305042218402, 0, 0, 0, 0, 0, -1951751905200, 0, 0, 0, 0, 0, 0, 274782553200, 0, 0, 0, 0, 0, 0, 276952218764, 183422853540, 0, 290375783550, 0, 0, 0, -1813969632680, 0, 0, -1429713987872, 0, 0, 0, 0, 102093332958, 0, 0, 0, 0, 0, 0, -1568179479820, 0, 0, 0, 0, 0, 1420044960772, 192216796875, 0, 1265937005390, 0, 0, 0, 0, 1779596750790, 0, 0, 0, 0, 0, 3823741004080, -1698793280194, 0, 368351375150, 0, 0, 0, 0, 0, 0, 1591963176240, 0, 0, 0, 2288475094140, -496021948720, 0, 0, 0, 0, 0, 503413095098, 0, 0, -2222419596840, 0, 0, 0, 2440812956824, 0, 0, 0, 0, 0, 0, 0, -2318376780036, 0, 0, 0, 0, 0, 0, -299506421600, 0, 2089375126000, 0, 0, 0, -2798655503050, 0, 0, 0, 0, 0, 0, 0, 0, 0, -745141889790, 0, 0, 0, -148599636800, 0, 0, -147775020137, 0, 0, 0, 0, 0, 0, -1311036950700, 0, 0, 0, 0, 3539370997762, 0, 0, 0, 0, 0, -8372659931240, 2965590157370, 0, 419023437500, 0, 0, 0, 754808596900, 0, 0, 2034824014130, 0, 0, 0, 0, -1035809261890, 0, 0, 0, 0, 0, -4126545643680, 4608266198954, 0, -3478383589732, 0, 0, 0, -5453281250000, -1899025740549, 0, -592939382485, 0, 0, 0, 0, -2494383207320, 0, 0, 0, 0, 0, 0, 0, 0, -5102925133050, 0, 0, 0, 7342653197836, 0, 0, -813708059936, 0, 0, 0, -10332388508760, 2321114391576, 0, 0, 0, 0, 0, 0, 0, 0, 6990743755910, 0, 0, 0, 13970341537100, 0, 0, 0, 0, 0, 0, 0, -3814697265625, 0, 0, 0, 0, 0, 3546287265056, 3016446414120, 0, 1637397244150, 0, 0, 0, 3248747468080, -8130410200656, 0, 6314968266962, 0, 0, 0, 0, 0, 0, -1935165342555, 0, 0, 0, 17031789618520, 2803265373550, 0, 0, 0, 0, 0, 3085991388568, 0, 0, 555783925140, 0, 0, 0, 4476593263500, -10570013553040, 0, 0, 0, 0, 0, -14265991057860, 1727093827350, 0, -5164391194651, 0, 0, 0, 0, 0, 0, 6956674584340, 0, 0, 0, 0, -8324489276820, 0, 0, 0, 0, 0, -4449966529000, 0, 0, 0, 0, 0, 0, 8528598859204, 0, 0, -4139785422724, 0, 0, 0, 0, 11439447454566, 0, -11886429383208, 0, 0, 0, 0, 13054722022588, 0, 2963228450920, 0, 0, 0, 3226876977790, 0, 0, 14787941406250, 0, 0, 0, -15251194969974, 0, 0, 0, 0, 0, 0, -10272858062800, 11262056752880, 0, -14420632296044, 0, 0, 0, -30065778368720, 0, 0, -2757367097650, 0, 0, 0, 0, -3095989391952, 0, 0, 0, 0, 0, 6148566301140, -1270767580380, 0, 0, 0, 0, 0, -17143306684912, 0, 0, 0, 0, 0, 0, 0, 1115588378430, 0, -3651371678700, 0, 0, 0, -6925574437060, 0, 0, -17723905953856, 0, 0, 0, 0, 0, 0, 19428846489130, 0, 0, 0, 8437136058360, 0, 0, 0, 0, 0, 0, 0, -7186103515625, 0, -1525211092010, 0, 0, 0, 0, 0, 0, 7213209468134, 0, 0, 0, 0, -4879379763000, 0, 0, 0, 0, 0, 0, 10248604043018, 0, 21539160705760, 0, 0, 0, 53800926054040, -13381910340840, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 85638691395214, 692380546910, 0, 17865385934796, 0, 0, 0, -26086616288020, 0, 0, -31750765938000, 0, 0, 0, 0, -9302647140900, 0, 0, 0, 0, 0, -14297139878720, -30707372208200, 0, 0, 0, 0, 0, 51823696791616, 0, 0, -1047137983830, 0, 0, 0, 0, -12973427138450, 0, 0, 0, 0, 0, -69846968767320, 0, 0, 7840897399100, 0, 0, 0, 0, 16623438342012, 0, 0, 0, 0, 0, 0, 3550112401930, 0, 18721916015625, 0, 0, 0, 25968605100300, 0, 0, -28642021848540, 0, 0, 0, 55284949219616, 0, 0, -8897983753950, 0, 0, 0, 0, 40349321897904, 0, 0, 0, 0, 0, -88841601562500, 9559352510200, 0, 27857434110410, 0, 0, 0, -71754847879220, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 15919631762400, 8028056926580, 0, 0, 0, 0, 0, -101851020947980, 5721187735350, 0, -48312537805328, 0, 0, 0, 0, 26439622160671, 0, 36657458193060, 0, 0, 0, -471647783120, 2581671878865, 0, 0, 0, 0, 0, -22224195968400, 0, 0, -52194492718510, 0, 0, 0, -8252579353644, 6102032392060, 0, 0, 0, 0, 0, 0, -51795568951200, 0, -22421191163688, 0, 0, 0, 0, 0, 0, 11591883900180, 0, 0], "weight": 10, "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], [1, 0], [0, 5], [0, 0], [487, -487], [0, 0], [0, 0], [0, 0], [4995, 0], [0, 19683], [0, 0], [42908, -42908], [0, 0], [0, 0], [0, 0], [0, 0], [0, -224369], [0, 0], [-98415, 98415], [0, 0], [0, 0], [0, 0], [214540, 0], [0, -1396040], [0, 0], [1953125, -1953125], [0, 0], [0, 0], [0, 0], [7571426, 0], [0, 0], [0, 0], [3679285, -3679285], [0, 0], [0, 0], [0, 0], [9585621, 0], [0, -22743450], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [37101780, 0], [0, -20896196], [0, 0], [6980200, -6980200], [0, 0], [0, 0], [0, 0], [9765625, 0], [0, 0], [0, 0], [58133290, -58133290], [0, 0], [0, 0], [0, 0], [0, 0], [0, 37857130], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [-96480503, 0], [0, 0], [0, 0], [-262469860, 262469860], [0, 0], [0, 0], [0, 0], [-413067632, 0], [0, 98316585], [0, 0], [113717250, -113717250], [0, 0], [0, 0], [0, 0], [0, 0], [0, 603893176], [0, 0], [-387420489, 387420489], [0, 0], [0, 0], [0, 0], [0, 0], [0, 185508900], [0, 0], [214325460, -214325460], [0, 0], [0, 0], [0, 0], [-679871480, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [844558164, 0], [0, -951171875]]}