# Stored data for newform 99.6.e.a, downloaded from the LMFDB on 18 May 2024.
{"label": "99.6.e.a", "space_label": "99.6.e", "level": 99, "weight": 6, "hecke_orbit": 1, "hecke_orbit_code": 274978570339, "dim": 46, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[2, [4643328708227642691608484249600, -21549607618221104265251153510400, 109548994266776111382047584419840, 8870626488800664637934539898880, 97730665391752482626254485323776, -4937799014518237400731112964096, 48252887571064526009276911583232, -4049632219732730342373345722368, 15404300307902724715818544791552, -1826555819862311352075224088576, 3482607934530073084133522538496, -385744310495893048215340449792, 542550443495559184614604013568, -51391603701216575666462916608, 62811957307869359405251608576, -4765661151782189059808157696, 5437477395139048192791572480, -327293109177104115383310336, 365271314795175174982990848, -17406714999620077710098432, 19185415535601101115744768, -740645678255582714488704, 804937614692085574427328, -25427238567512285463840, 27197825564859338804400, -708585583780584276576, 749536397866455681564, -16011632611319769774, 16915353569003541579, -292910993616086829, 314489338170433632, -4327037658094451, 4810232165191356, -51210947244822, 60488744359859, -480696214917, 619213708764, -3485892614, 5103090180, -18843939, 32886829, -68757, 159744, -142, 528, 0, 1]]], "char_order": 3, "char_parity": 1, "char_degree": 2, "char_conductor": 9, "char_orbit_label": "e", "char_is_real": false, "Nk2": 3564, "analytic_conductor": 15.877998161485083, "level_radical": 33, "self_twist_type": 0, "is_self_dual": false, "is_self_twist": false, "is_cm": false, "is_rm": false, "analytic_rank_proved": true, "char_values": [99, 3, [56, 46], [2, 3]], "inner_twist_count": 2, "level_primes": [3, 11], "conrey_indexes": [34, 67], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 23, "sato_tate_group": "5.2.3.c3", "trace_display": [0, 15, -36, 167], "traces": [46, 0, 15, -320, -36, 273, 167, 426, -63, -1200, 2783, -1419, 1871, -1329, 3090, -3584, 534, 5391, -7282, -1917, -8319, 0, -8292, 351, -10049, 19140, 19953, 7586, -5970, -15150, 9542, -3831, 3630, 2982, 6480, 28881, -32014, 1221, -17544, 40635, 12030, -55365, 25943, -77440, 70578, -154008, 9756, -65463, -6990, 101805, -42117, 144446, 107838, -2322, -8712, -16602, -100233, 95367, -20310, -215301, 100247, -30594, 28323, -169154, 20931, 26862, 84956, 168471, -30243, 212292, 72186, 144522, -346888, 86619, 103413, 340334, -20207, -386061, 123113, -30246, -73683, -399966, 30672, -38850, 268335, -211260, 180009, 25773, 65028, 460017, -656042, -196731, 232206, 230262, -325926, -517071, 357002, -428928, 7623, -626456, -149979, 378069, 131552, 224169, 119271, 672750, 279162, 537732, -294850, -72600, 479160, 433166, -175701, -990558, 13671, -614598, -479538, -279300, -333786, 704835, -336743, 75363, -607047, 619613, 1526394, -134721, -419338, -103419, 1487565, 837558, 284184, -549219, 831580, -888402, -769473, -995886, 31572, 1436619, 241643, -500955, -1264449, 704031, 452782, -2626209, -2347410, 115086, 2322261, 371489, 316935, -2954730, 637613, -739428, -1516284, -321618, 9420, 6129426, 1453439, 1058079, -657072, 2526816, -2405214, -3214782, -774034, 623142, 536514, 1664589, 682200, -4595643, 358374, 1907106, -2467179, -3786142, 664017, 6609933, 914765, 433664, -2213283, 594840, 836184, -755037, -6482314, 1004811, 5473557, 3669678, 963927, -2770125, 32307, 1427322, -339633, -1592190, -818358, 6206469, 1855178, -3497136, -4347123, 1194123, 403392, 118701, -5496052, 680433, 4507581, 1629459, 1178346, -6659121, 2044629, -3595338, 179487, -10969036, -440561, 11609808, 3711365, -2485311, -5230188, 2934354, -1324926, 499959, -3456758, -197994, 6492075, 231957, -2515995, -5065497, 2730143, 9588714, -692199, -8238324, 1010058, 8772714, 4971086, 678537, -152097, 6218607, -3279918, -1870074, -15556734, -2909097, 1607844, 9781338, 844263, -8749956, 7256231, 0, 4338765, -16157422, 1531617, 4150005, 3376351, -3794346, -7895799, 8462409, 1903080, -3656304, -2006664, -2625345, 12361191, 8926384, -343884, -8681859, 8334946, -711078, -2456235, -18629220, -1147350, -59895, 8174898, 4938111, -4873689, 15131510, -5148834, 4981014, -9254026, 7571433, 8460474, 10109535, 1215929, -18892635, 5718923, -355818, 1339425, -32821080, 1133535, 13878759, 7024235, 2027427, -10435905, 1157970, 5526762, -7345530, -10751888, -10144764, 14248587, 12007751, 5751873, -21744873, 8546505, -11139210, 911493, -17266200, 2188524, 19238298, 8937550, 989166, -12758790, 12610055, -9531360, 1515519, -16894054, 458953, 6283074, 5522622, -5231280, -11499768, 7601387, -420150, -8795988, -6048700, 3476544, 25478163, 722370, 6037908, -8942895, 9952875, 9332004, 3552363, -17270068, 7150953, 7160703, 9214527, 493803, -1785597, 8350889, 4878306, -875133, -14088942, -729789, 12276453, 3098846, -7804668, -12208239, 7761954, 2309164, 7145226, -32074676, -5381961, 601518, 9725331, -1925547, -22454595, 11640482, -17663448, -4221018, -927102, 5738433, 36849558, 9250329, -11400114, 14721879, -1326519, -5437152, -2493063, -13186236, 184764, 219615, 8532397, 511026, -18152829, 5081123, 12022842, 1385667, 6451884, -10949652, 15144348, 7692440, -360822, 5090814, 4355802, -1221288, 16812522, -23004166, -1005978, 9601968, 1983117, -8021238, -25787322, 392040, -3793596, -27558675, -6496480, -7692675, 10569957, 10378524, 12883920, 2271366, 4048482, 9496644, -1893771, -20368570, -13586238, 13724037, -8373371, 4517181, -15235698, -464069, 18781020, -22840947, 16007574, -1936847, 3261447, -258730, 2351967, -3793863, 441896, 37645704, -1449747, 186390, 12914265, -7012173, -147741, -14079822, -8168322, 1877084, 13109766, -14286222, -881970, 10207095, 9883845, -2879327, 34642725, 5448630, -17022891, -7282218, -16513578, 6705026, 4348854, -4405446, -5403397, 162615, -39021972, 17640008, 9833670, -13509675, 48560652, 4287894, -14961915, 11826939, -13224849, 23712702, -10365700, -3825774, -25356357, 2911260, -8589450, 19910379, -23877483, -2655660, -6067017, -13937242, -35601864, -25908147, 16991226, 11543586, -9749091, 270407, 9480966, 27286599, -25947123, 11750238, 44077338, -12727304, -1024899, 27587145, -32997825, -3139103, 2491242, 2525762, -48487554, -15854013, 103779726, -28369782, -3194043, -9676160, 36623157, 20939739, -4685120, -34063386, -14961753, -10983394, -12149172, -4189485, -27815505, 6340482, 1206375, 9485085, 22089414, 5361147, 37280120, 43399848, 595017, 11413055, -38632770, 55623537, -31324638, -2885928, -27017451, 4625316, -9317484, -46833750, -36819247, 26190270, 34404582, -14648987, 935688, -18328977, 4429230, 7328040, 2773260, -1180476, -40448487, 29649483, -40588083, 42366054, 36769482, 32279336, 12740532, -27950568, -7310433, 12991632, 4007157, -2435027, -80540970, -3903156, 63300826, -15321948, -47345796, 1411839, 16106538, 46628820, -34077621, -1691580, 99684783, -2347306, 41057073, -71500179, -18788022, -30947157, 19845858, 2251628, 8619336, -8699517, 24636810, -6566967, -60425703, -5885942, -56314968, 53890740, -29909722, -43557684, 102428955, 9856006, -19071939, -15906297, -77530320, 18173487, 26668173, 5253780, -11015664, 44150589, 36740262, -5956248, -44837613, 13064276, -17477966, 51370224, -34711848, 43097652, 77209443, 329798, -19882083, -40389168, -7021224, -13931658, 28539330, 6524199, 75671736, -44382213, 94086330, -45045330, -102750075, -1130504, 73960311, 74010351, -49669216, -57309324, 4671810, 18795744, 36879237, -98540847, -61595946, -76072341, 92546559, 37332848, 61048752, -18216468, 71788538, -527076, -119337486, 2947418, 6134502, 73027395, -70608918, -5551500, 11837430, 4895696, -5366850, -99673689, 2008842, 37069899, -29075439, -12536743, 101448498, -19499292, 48405210, 28688430, -142211598, -34485599, -1703838, 4645674, -79114213, 12898734, 112012092, 40593686, 28045776, -124693443, -110739096, 59554362, 56980773, -8414862, 23078814, 25580781, 203634378, -49581324, -212094171, 11647103, -2233968, 56418561, -80071791, -87825288, 26667009, -4915020, -35318163, 17607777, -41743117, -45307434, 44699061, -12202542, -41083350, 2807316, 214176138, 65399556, -36849219, 39331802, 9292827, 66652284, -38248149, -12101562, 166247217, 43175046, 2263449, -23542050, -134318103, -12129887, 109125951, -31461862, -55220322, 46302921, 144779052, -2939061, 30329874, -40866623, -23153742, 67550166, -1850937, 84310050, -46636533, -40798176, -44271306, -109811205, -98514193, 47566311, -30410715, 3265547, -91567398, 8611812, 123814452, -13552440, -31127256, -3256773, 19920654, 106493382, -122806732, -56803530, -14332248, 46495810, -10233817, -90145779, -55088760, 2765604, -17417103, 17025698, 102020604, -108131796, 145732368, 44121168, 26349765, -2532651, -19053090, 151181955, -134525376, 94492242, -88191252, -134738342, 32144643, -79117806, -28097470, 68840937, -746691, -15070498, -57045984, -15642801, 307834074, 2577963, -239161392, -14309959, -39951687, 212056650, -66745887, 20559352, 137026962, 4668410, 127976286, -161670069, -108217242, -11145612, -39772440, 4447215, -70083270, -138548475, 40769982, -67559544, 89182917, 12994208, -1261809, 187445226, -102263409, -70231482, 76523265, 2801108, -21999795, -18282858, -90208857, -38344242, -57635724, -49827332, 81512298, -20333997, 142093776, 63264549, -36768900, 21411422, -25687332, 157855737, -66014182, -50085252, 152331426, -38817424, -141229971, 28851696, -141545577, 83985312, 38838732, 4367253, 112782378, -196216938, 184349958, -39906144, -97292628, -1447873, -64455069, 122208927, -133239645, -59742264, -619641, 32395510, 23805711, -14656725, -42886270, -71988420, -114870735, 4657404, -186299166, -143995437, 212687232, -20986724, 29777829, 65948466, 109631409, 216507504, -34776570, 225043296, 158556231, -13358410, 111454710, -3647076, -10480899, -107193423, 124983474, 48627508, 241350462, -179887725, 239246346, 30841704, -55325796, -32946298, 30399183, 24459666, -98167926, -67895856, 161662491, -204163456, -101793780, -164467191, -13989685, 77026158, -187702206, -11139903, 82360828, -106341795, 171903612, -42661362, -185536620, 7597177, -20739669, 62198739, -80632084, -136594590, 11474937, -4890094, -32788149, 73593672, -188485755, -52511742, 18115353, 88346351, -182736720, -37517931, 312733866, -28188864, -15771261, 7506740, 125265210, 29561214, 4514541, 167004324, 201027690, 36763884, 127887675, 94689138, -92550245, -14896673, -361624095, 19765801, -207741930, 2624031, 203015904, 80221485, 55725330, 70158470, -5488548, 100506141, -1829883, 132749616, -85216635, -40928716, -205363977, 77194236, -105251577, 67231749, -315425232, 105157531, 32553780, -22065318, 163394696, 20184249, -27204054, 11358939, -129071265, 70264779, -124138275, -265228980, -154315431, -306969690, -24197943, -56955582, -108637992, 5770437, -60399111, 39881822, -88420260, -125855730, 328460472, -55317348, 256164507, -3711312, 111000666, 192129219, 85277759, 334540524, 126502074, -46034992, 42873105, 45280200, 11556012, -11152632, 14092386, 156516668, -225373416, -179712387, -75724824, -54015852, 57724539, 121010187, 82298475, 35899290, -4292928, 64937070, 143117001, -435797098, 42643317, -20642442, 42230427, 16976595, -341829606, 149804505, 230049462, -231878268, -51124920, 70693107, 384684351, 153871402, -205099416, 309992493, -25734684, -146140746, 288277965, -435630054, 145424043, 5184729, -94969212, 69238308, -383678295, 210560541, 168786486, -48442302, -105535924, -63847218, 266625588, 245175392, -3118533, 86714883, -1723260, -109506612, 12987459, -209032112, 34271355, 69660291, 149813864, -27061344, -208707774, 3934194, -380630826, -241672842, 109665684, -39184233, 213262443, 266776416, 71451204, -48605709, -137991110, -83826168, -26840583, -453109402, -90562251, 82089465, -75204039, 37478841, -283904829, 170803004, -3509118, -74312964, -240324234], "weight_parity": 1, "has_non_self_twist": 1, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": false, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 9, 3, 1, 3, 0]], "char_orbit_index": 5, "prim_orbit_index": 3, "minimal_twist": "99.6.e.a", "char_is_minimal": true, "conrey_index": 34, "id": null, "is_polredabs": null, "nf_label": null, "trace_hash": null, "qexp_display": null, "fricke_eigenval": null, "atkin_lehner_string": null, "hecke_ring_index": null, "projective_image": null, "projective_image_type": null, "field_poly_is_cyclotomic": null, "field_poly_root_of_unity": null, "artin_degree": null, "artin_image": null, "field_poly_is_real_cyclotomic": null, "artin_field_label": null, "projective_field_label": null, "hecke_ring_index_proved": null, "trace_zratio": null, "hecke_ring_generator_nbound": null, "field_disc": null, "field_disc_factorization": null, "field_poly": null, "hecke_ring_index_factorization": null, "trace_moments": null, "atkin_lehner_eigenvals": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null}