# Stored data for newform 10.6.a.b, downloaded from the LMFDB on 24 April 2024.
{"label": "10.6.a.b", "space_label": "10.6.a", "level": 10, "weight": 6, "hecke_orbit": 2, "hecke_orbit_code": 4503599728033802, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 567743362650038994, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[3, [-24, 1]]], "qexp_display": "q-4q^{2}+24q^{3}+2^{4}q^{4}+5^{2}q^{5}-96q^{6}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 360, "fricke_eigenval": -1, "atkin_lehner_string": "+-", "analytic_conductor": 1.6038381981298064, "hecke_ring_index": 1, "level_radical": 10, "field_poly_is_cyclotomic": false, "field_poly_root_of_unity": 0, "field_poly_is_real_cyclotomic": false, "hecke_ring_index_proved": true, "self_twist_type": 0, "is_self_dual": true, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": 0, "analytic_rank_proved": true, "char_values": [10, 1, [7], [1]], "hecke_ring_generator_nbound": 1, "inner_twist_count": 1, "level_primes": [2, 5], "conrey_indexes": [1], "field_disc": 1, "field_disc_factorization": [], "field_poly": [0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.004", "prec": 17}, {"__RealLiteral__": 0, "data": "0.993", "prec": 17}, {"__RealLiteral__": 0, "data": "0.063", "prec": 17}, {"__RealLiteral__": 0, "data": "1.983", "prec": 17}, {"__RealLiteral__": 0, "data": "0.235", "prec": 17}, {"__RealLiteral__": 0, "data": "4.915", "prec": 17}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "5.2.3.c1", "atkin_lehner_eigenvals": [[2, 1], [5, -1]], "trace_display": [-4, 24, 25, -172], "traces": [0, 1, -4, 24, 16, 25, -96, -172, -64, 333, -100, 132, 384, -946, 688, 600, 256, -222, -1332, 500, 400, -4128, -528, 3564, -1536, 625, 3784, 2160, -2752, 2190, -2400, 2312, -1024, 3168, 888, -4300, 5328, -11242, -2000, -22704, -1600, 1242, 16512, 20624, 2112, 8325, -14256, 6588, 6144, 12777, -2500, -5328, -15136, -21066, -8640, 3300, 11008, 12000, -8760, 7980, 9600, 16622, -9248, -57276, 4096, -23650, -12672, 1808, -3552, 85536, 17200, -24528, -21312, 20474, 44968, 15000, 8000, -22704, 90816, -46240, 6400, -29079, -4968, -51576, -66048, -5550, -82496, 52560, -8448, -110310, -33300, 162712, 57024, 55488, -26352, 12500, -24576, -78382, -51108, 43956, 10000, 141942, 21312, -436, 60544, -103200, 84264, 232968, 34560, -174850, -13200, -269808, -44032, 182994, -48000, 89100, 35040, -315018, -31920, 38184, -38400, -143627, -66488, 29808, 36992, 15625, 229104, -122452, -16384, 494976, 94600, -241908, 50688, -86000, -7232, 54000, 14208, 277098, -342144, -193540, -68800, 158112, 98112, -124872, 85248, 54750, -81896, 306648, -179872, 140550, -60000, 433952, -32000, -73926, 90816, 57800, -363264, -555922, 184960, -505584, -25600, -613008, 116316, -66616, 19872, 79200, 206304, -205692, 264192, 523623, 22200, 166500, 329984, 433854, -210240, -107500, 33792, 191520, 441240, -489180, 133200, 719462, -650848, 398928, -228096, -281050, -221952, -29304, 105408, -371520, -50000, -185928, 98304, -591406, 313528, -567600, 204432, 449478, -175824, 157160, -40000, 43392, -567768, -376680, -85248, 31050, 1744, 1186812, -242176, 66000, 412800, 253052, -337056, -588672, -931872, 515600, -138240, -397664, 699400, 491376, 52800, 210012, 1079232, 1073444, 176128, 208125, -731976, -626832, 192000, -116650, -356400, -544896, -140160, -743046, 1260072, 164700, 127680, -1109760, -152736, 978720, 153600, -1132798, 574508, -1222776, 265952, 319425, -119232, -473000, -147968, -1237824, -62500, 905652, -916416, 470448, 489808, -133200, 65536, 1939938, -1979904, 1933624, -378400, 729270, 967632, -805476, -202752, -526650, 344000, -2647440, 28928, -858690, -216000, -383608, -56832, 3905088, -1108392, 82500, 1368576, 2010758, 774160, 769896, 275200, 202602, -632448, -221536, -392448, 300000, 499488, -213624, -340992, -1370573, -219000, -1881168, 327584, -322506, -1226592, 199500, 719488, 285120, -562200, -3371544, 240000, -3547328, -1735808, 3406608, 128000, 415550, 295704, 1443008, -363264, -10464, -231200, 171312, 1453056, -1026886, 2223688, -1431900, -739840, 752958, 2022336, 289080, 102400, 5591232, 2452032, -111000, -465264, -591250, 266464, -4196400, -79488, -1133136, -316800, 1994132, -825216, -3743586, 822768, 45200, -1056768, -987022, -2094492, 4391856, -88800, 305184, -666000, 693160, -1319936, 2138400, -1735416, 2206008, 840960, 2741870, 430000, -2043360, -135168, -2389566, -766080, -613200, -1764960, 916416, 1956720, -279480, -532800, -2226099, -2877848, -3447048, 2603392, 511850, -1595712, -2476372, 912384, 413586, 1124200, 3623352, 887808, 2745254, 117216, 375000, -421632, -2071740, 1486080, -1189060, 200000, -2938848, 743712, 3257604, -393216, -567600, 2365624, 6867792, -1254112, 1983510, 2270400, -791208, -817728, -5805792, -1797912, -1156000, 703296, 4974158, -628640, -2064000, 160000, -1342638, -173568, -2187152, 2271072, -726975, 1506720, -1483944, 340992, -1094230, -124200, 6650352, -6976, -1372560, -4747248, -1289400, 968704, -4644960, -264000, -954060, -1651200, -1593898, -1012208, 2193804, 1348224, -138750, 2354688, -2858984, 3727488, -2996928, -2062400, -2646648, 552960, 3723554, 1590656, 1314000, -2797600, 1782000, -1965504, -2583400, -211200, 4254741, -840048, 7562064, -4316928, -2757750, -4293776, 3373200, -704512, 4307730, -832500, 163944, 2927904, 10414848, 2507328, 4067800, -768000, -2243542, 466600, -479520, 1425600, 1656702, 2179584, -2891596, 560640, 1387200, 2972184, -6526992, -5040288, -310976, -658800, -13342128, -510720, 2722368, 4439040, 312500, 610944, -7014978, -3914880, -5962320, -614400, 10634932, 4531192, -14712192, -2298032, -1959550, 4891104, 2991908, -1063808, -1598784, -1277700, -1204188, 476928, -486180, 1892000, 1098900, 591872, 4218816, 4951296, 9205460, 250000, -4936608, -3622608, -3359556, 3665664, 3548550, -1881792, 12566952, -1959232, -2537010, 532800, -3521528, -262144, 1080000, -7759752, -10900, 7919616, 869616, -7734496, 10412496, 1513600, -9315798, -2917080, -5028016, -3870528, -2580000, 3221904, -513264, 811008, 6265753, 2106600, 2657340, -1376000, -1174932, 10589760, 5824200, -115712, -11740320, 3434760, 1686564, 864000, 134222, 1534432, 17267088, 227328, -4371250, -15620352, 605648, 4433568, 5535126, -330000, 1095000, -5474304, 7953280, -8043032, -6745200, -3096640, -7062402, -3079584, -19510304, -1100800, -703296, -810408, -10302936, 2529792, 4574850, 886144, 5001588, 1569792, 1047690, -1200000, 14076452, -1997952, -4462272, 854496, 2227500, 1363968, 1626818, 5482292, -14193744, 876000, 8871072, 7524672, -2780712, -1310336, -7875450, 1290024, 6960888, 4906368, 1156000, -798000, 10787472, -2877952, -11363886, -1140480, 954600, 2248800, 3771840, 13486176, 14868840, -960000, -1236118, 14189312, 602064, 6943232, -3590675, -13626432, -12449812, -512000, -9040320, -1662200, -6232248, -1182816, -8734906, -5772032, 745200, 1453056, 12549498, 41856, -14665780, 924800, 7698240, -685248, 18973320, -5812224, 390625, 4107544, 1584000, -8894752, 2495724, 5727600, -196288, 2959360, 6073248, -3011832, -3061300, -8089344, -12087042, -1156320, -8167824, -409600, -11159598, -22364928, -2251576, -9808128, 12374400, 444000, 8053188, 1861056, 1053360, 2365000, -9543936, -1065856, -416466, 16785600, -6047700, 317952, 6817842, 4532544, 13172100, 1267200, -1694938, -7976528, 5040288, 3300864, -2150000, 14974344, 7805160, -3291072, 25762656, -180800, 2194104, 4227072, -8916046, 3948088, 1350000, 8377968, -14289402, -17567424, 13481704, 355200, -15043968, -1220736, -5333136, 2664000, 6927450, -2772640, -2799600, 5279744, 19928436, -8553600, 698252, 6941664, -7560432, -8824032, -4838500, -3363840, -275724, -10967480, -17833104, -1720000, 17987982, 8173440, -5621000, 540672, 3952800, 9558264, -24414024, 3064320, -13946410, 2452800, -15397920, 7059840, 8239968, -3665664, -3121800, -7826880, 23489280, 1117920, 6222720, 2131200, 74992, 8904396, -27187152, 11511392, 1368750, 13788192, -7767292, -10413568, -22280427, -2047400, -4578528, 6382848, 24208334, 9905488, 7666200, -3649536, 238656, -1654344, 12684980, -4496800, -11352000, -14493408, 19763244, -3551232, 3513750, -10981016, -17174808, -468864, -40070496, -1500000, -9017608, 1686528, 21735648, 8286960, 10848800, -5944320, -1125562, 4756240, 11290752, -800000, 22574682, 11755392, 30074200, -2974848, -1848150, -13030416, -7549080, 1572864, -632350, 2270400, 46558512, -9462496, -12586746, -27471168, 1445000, 5016448, 46406976, -7934040, 621000, -9081600, -3237696, 3164832, 4730400, 3270912, -13898050, 23223168, 21579248, 7191648, -19331424, 4624000, -31474968, -2813184, -15724412, -19896632, -12639600, 2514560, -30976002, 8256000, -1462536, -640000, -36733230, 5370552, 2702568, 694272, -15325200, 8748608, -20608560, -9084288, 4249290, 2907900, 3423332, -6026880, -9206592, 5935776, -1665400, -1363968, 10312000, 4376920, 54183096, 496800, 31057062, -26601408, -31190356, 27904, 1980000, 5490240, -8284872, 18988992, -18168850, 5157600, 48258192, -3874816, -2836494, 18579840, -5142300, 1056000, 4993920, 3816240, -10274280, 6604800, -15715049, 6375592, 4862448, 4048832, 13090575, -8775216, 24703844, -5392896, -5316864, 555000, -40066488, -9418752, 6285974, 11435936, 4162500, -14909952, 15405018, 11987712, 14352620, 8249600, -5126976, 10586592, 13327764, -2211840, 10846350, -14894216, -32893752, -6362624, -6103680, -5256000, -1710368, 11190400, -26101206, -7128000, -2687500, 7862016, 32484638, 10333600, -7740144, 844800, 15460002, -17018964, -1694776, 3360192, 4788000, -30248256, -2872572, 17267712, 21061744, 11031000, -3838428, 17175104, 3294000, -13492800, -12229500, 2818048, -80917056, -17230920, 5063280, 3330000, 4676652, -655776, -85135872, -11711616, 17986550, -41659392, 39542168, -10029312, 47266686, -16271200, 11317752, 3072000, -6808032, 8974168, 9973200, -1866400, 41608176, 1918080, 8513480, -5702400, 34632192, -6626808, 23203488, -8718336, -7026250, 11566384, -145188, -2242560, -7545870, -5548800, 6388500, -11888736, 4111488, 26107968, -732600, 20161152, -18450022, 1243904, -24645264, 2635200, 6750462, 53368512, 4426488, 2042880, -9288000, -10889472, 6456768, -17756160, -19368404, -1250000, 18070992, -2443776, -39664806, 28059912, -4648200, 15659520, 6937920, 23849280, -47660856, 2457600, -23283807, -42539728, 77578344, -18124768, -14785150, 58848768, -34301452, 9192128, -2664000, 7838200, -5771148, -19564416, 33288880, -11967632, -14190000, 4255232, 7087458, 6395136, -14560920, 5110800, -58225050, 4816752, 45936204, -1907712, 11236950, 1944720, -27195264, -7568000, 73503936, -4395600, -45029848, -2367488, 47859168, -16875264, 3929000, -19805184, -23736442, -36821840, -24282720, -1000000], "weight_parity": 1, "has_non_self_twist": 0, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": false, "level_is_squarefree": true, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "10.6.a.b", "char_is_minimal": true, "conrey_index": 1, "id": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0], [1], [-4], [24], [16], [25], [-96], [-172], [-64], [333], [-100], [132], [384], [-946], [688], [600], [256], [-222], [-1332], [500], [400], [-4128], [-528], [3564], [-1536], [625], [3784], [2160], [-2752], [2190], [-2400], [2312], [-1024], [3168], [888], [-4300], [5328], [-11242], [-2000], [-22704], [-1600], [1242], [16512], [20624], [2112], [8325], [-14256], [6588], [6144], [12777], [-2500], [-5328], [-15136], [-21066], [-8640], [3300], [11008], [12000], [-8760], [7980], [9600], [16622], [-9248], [-57276], [4096], [-23650], [-12672], [1808], [-3552], [85536], [17200], [-24528], [-21312], [20474], [44968], [15000], [8000], [-22704], [90816], [-46240], [6400], [-29079], [-4968], [-51576], [-66048], [-5550], [-82496], [52560], [-8448], [-110310], [-33300], [162712], [57024], [55488], [-26352], [12500], [-24576], [-78382], [-51108], [43956], [10000]]}