# Stored data for newform 63.7.m.d, downloaded from the LMFDB on 20 April 2024.
{"label": "63.7.m.d", "space_label": "63.7.m", "level": 63, "weight": 7, "hecke_orbit": 4, "hecke_orbit_code": 13511623633272895, "dim": 8, "is_polredabs": true, "trace_hash": 1274014356223609089, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[2, [20358144, 1281408, 992080, -12248, 37712, 442, 227, -5, 1]]], "qexp_display": "q+(1+\\beta _{1}-\\beta _{2})q^{2}+(1-43\\beta _{2}+4\\beta _{3}+\\cdots)q^{4}+\\cdots", "char_order": 6, "char_parity": -1, "char_degree": 2, "char_conductor": 7, "char_orbit_label": "m", "char_is_real": false, "Nk2": 3087, "analytic_conductor": 14.493407268050612, "hecke_ring_index": 84, "level_radical": 21, "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": false, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.167", "prec": 17}, "analytic_rank_proved": true, "char_values": [63, 6, [29, 10], [6, 1]], "hecke_ring_generator_nbound": 7, "inner_twist_count": 2, "level_primes": [3, 7], "conrey_indexes": [10, 19], "field_disc": 209173825936033529481, "field_disc_factorization": [[3, 4], [3359, 2], [478411, 2]], "field_poly": [21068100, -601290, 985651, 36821, 39800, 473, 212, -1, 1], "hecke_ring_index_factorization": [[2, 2], [3, 1], [7, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.101", "prec": 17}, {"__RealLiteral__": 0, "data": "7.530", "prec": 17}, {"__RealLiteral__": 0, "data": "3.417", "prec": 17}, {"__RealLiteral__": 0, "data": "243.828", "prec": 24}, {"__RealLiteral__": 0, "data": "320.559", "prec": 24}, {"__RealLiteral__": 0, "data": "13246.851", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "6.2.3.c6", "trace_display": [5, 0, 294, -656], "traces": [0, 8, 5, 0, -173, 294, 0, -656, -3326, 0, -3411, 314, 0, 0, 5360, 0, -12721, 5532, 0, -18234, 0, 0, 86106, -3928, 0, -17038, -12366, 0, 85037, 8300, 0, -89508, 186207, 0, 0, 25860, 0, 64706, 77136, 0, 221823, 0, 0, 45740, -92529, 0, -111504, -483276, 0, -310684, -967216, 0, -1673988, 540974, 0, 0, 241885, 0, 539799, 181770, 0, 418224, 0, 0, 2378626, 414204, 0, -1158902, 821250, 0, 1087917, -1442344, 0, -378666, 432940, 0, 0, -1065994, 0, 611452, 2094945, 0, -1561266, 0, 0, -275112, -816224, 0, -366441, 989196, 0, 304446, -678720, 0, -716148, 591792, 0, 0, -3509629, 0, -318746, -1670628, 0, 4997958, 0, 0, -4341090, 4064210, 0, 864326, 8572551, 0, -7943282, 6139040, 0, 2926872, -6432753, 0, 0, -2459604, 0, -505046, -18654276, 0, 3803145, 0, 0, -3423056, 10737599, 0, 9596796, 7970226, 0, 555570, 2748148, 0, 6145902, -1007680, 0, 0, -8882901, 0, 8798784, -15818868, 0, 8200710, 0, 0, -10093652, 10379444, 0, -652870, 34454814, 0, -13508055, -138492, 0, -17027568, 2600101, 0, 0, -16800784, 0, -4844324, -47327994, 0, -21979773, 0, 0, -22491652, 8783034, 0, 13960606, -4731168, 0, 20601304, -32608238, 0, 5173866, 5948648, 0, 0, 33663306, 0, 12473280, 5222832, 0, 28183500, 0, 0, 23622444, 20715116, 0, -11228368, 44516241, 0, -30012554, -8590456, 0, -25240488, 28251874, 0, 0, -37150030, 0, 12423108, 14760330, 0, 76610712, 0, 0, 4853576, 23486841, 0, -6498363, 15144024, 0, 10984758, -63179660, 0, -59799303, 27367416, 0, 0, -62278779, 0, 75605718, -24690666, 0, 40251162, 0, 0, -29321118, 13719248, 0, -40377864, 83764035, 0, -41530734, 4149608, 0, -75150930, -35387358, 0, 0, -44620866, 0, -41087538, 47501835, 0, -29025927, 0, 0, 30845040, -48269273, 0, -47354689, -81282432, 0, 17554834, -56336256, 0, -15422715, 52089020, 0, 0, -21225702, 0, -4166296, 69808794, 0, 34592370, 0, 0, 164071056, 71549312, 0, 31468834, 75593016, 0, -29609160, -76419952, 0, 89518314, -80950308, 0, 0, -9271200, 0, -50491948, -64767255, 0, -177265512, 0, 0, -99372660, -56572474, 0, 96907998, 3775968, 0, -8308178, 218758486, 0, 170354610, 26653032, 0, 0, 166216278, 0, -9906771, -5099160, 0, 164280276, 0, 0, -94076014, -20146522, 0, 18720114, -143674113, 0, 8619744, 132079584, 0, 113492526, -114663836, 0, 0, 51873156, 0, -19212490, -203019615, 0, -227531700, 0, 0, -169824928, -63966205, 0, 50303322, -107529150, 0, 128293096, 320611724, 0, -179392860, 28985036, 0, 0, 197460176, 0, -43535145, -92476452, 0, -135202176, 0, 0, -42302556, 36190136, 0, 33717002, -154712484, 0, 169764792, -138455448, 0, 161861616, -20157248, 0, 0, -25875058, 0, 21857758, -21685314, 0, -7320960, 0, 0, -152599204, -71576946, 0, 8301828, 109058388, 0, -190529058, 34302322, 0, 320128431, -155721136, 0, 0, 129812263, 0, -188126958, 283620822, 0, -157361574, 0, 0, 640855580, -130511656, 0, -28143894, -538665732, 0, 257693934, -207289472, 0, -130289748, 225851682, 0, 0, 267703806, 0, -34724046, 1007800632, 0, -115377750, 0, 0, 92061868, -225477356, 0, -285310215, -217477104, 0, 287082120, 1599222, 0, 49513914, -23621608, 0, 0, -63783861, 0, -134541284, 387165264, 0, -52870662, 0, 0, 17255088, -375831778, 0, -10811556, -1007104221, 0, -466829155, -74410600, 0, -248951340, -179358894, 0, 0, -220364436, 0, 82653596, -81109848, 0, 90671616, 0, 0, 170869828, -330728369, 0, -356837238, 512473884, 0, -181779100, 645938352, 0, 78766749, 59485336, 0, 0, -40078080, 0, -100837896, 397606452, 0, -310062750, 0, 0, -73572712, -18028482, 0, 107928116, 182628348, 0, 353961660, -157727068, 0, 69716268, 373494078, 0, 0, -28866532, 0, 240056186, 341645751, 0, 716046057, 0, 0, 604488336, 111064736, 0, -203289847, 498682338, 0, 168878376, -368996990, 0, -883419966, 43611060, 0, 0, 370920862, 0, 47309448, 269162988, 0, 282177354, 0, 0, 492344652, -158453004, 0, 284931076, -807308751, 0, -45473382, -1525687752, 0, 363111714, -143053780, 0, 0, 178423016, 0, 217390486, -108236271, 0, -5680494, 0, 0, -546704048, 667197552, 0, 245953158, 603534252, 0, -929678254, 942117604, 0, 488873130, -14054506, 0, 0, -392941035, 0, -483792396, -1025820570, 0, -513771804, 0, 0, -1649640744, 358978472, 0, 178531186, -141407280, 0, 1027774140, 147597152, 0, -214916964, 4836689, 0, 0, 435399078, 0, 413333142, -1896570732, 0, -685266633, 0, 0, -58095324, 585534375, 0, 193698134, 862442988, 0, -94809708, 1413321780, 0, 495707184, -124256776, 0, 0, -480581090, 0, -297203063, -1203426900, 0, -163770408, 0, 0, -1257041976, -396459780, 0, 480719716, -885896334, 0, 860305677, -916953208, 0, 1109473494, -163713663, 0, 0, -123203208, 0, -208488244, -630094341, 0, 633758292, 0, 0, -1608331076, 441153707, 0, 36217725, 1310095326, 0, -1358331474, 1182743522, 0, -451649151, -297581080, 0, 0, -428951712, 0, 211746924, -127423236, 0, 801420030, 0, 0, 1194125936, 1193846990, 0, -356274870, 2435170770, 0, -494916288, -25069048, 0, 158494518, -985836290, 0, 0, -486644556, 0, 761364648, -2420337816, 0, 910995408, 0, 0, 957642440, 1078432555, 0, 1348973887, 1563504018, 0, -58316970, 339335436, 0, -640778409, 293028038, 0, 0, -14307049, 0, 1226588234, 1125224424, 0, 1298699790, 0, 0, 3438082668, 149868240, 0, 474397272, 886861368, 0, -1627689856, -3017475868, 0, -1330814178, 1759527575, 0, 0, -1281925296, 0, -1006942312, 425678484, 0, -635722146, 0, 0, -3150558048, -587902494, 0, -2037284652, 494920968, 0, -547686930, 357240962, 0, -3969224370, 183806420, 0, 0, -2235524088, 0, 121385376, 762356640, 0, 534321942, 0, 0, 1618044288, 259156348, 0, -1133789834, -971027154, 0, -528512685, -2086387720, 0, 1056270780, -910055024, 0, 0, -1231285348, 0, 948832184, 687473952, 0, -646888248, 0, 0, 1524708536, -238990796, 0, -304392906, 2060243016, 0, 286495252, 14289312, 0, 295944066, 1654416600, 0, 0, 724247040, 0, 129714781, 1996641564, 0, 1295642946, 0, 0, -484580028, -509026500, 0, 67539840, -645125568, 0, 3934996631, -2960569584, 0, -566226096, 445569642, 0, 0, -1739530792, 0, 338198904, -1353351846, 0, 1012467972, 0, 0, -796001760, 1098041154, 0, -747205116, 435357780, 0, 76387416, 1608725676, 0, -835894692, -153560980, 0, 0, 3193011573, 0, 831008394, 16935792, 0, 1682266338, 0, 0, -677499732, 2006565434, 0, 242792728, -3547494264, 0, -3301771521, 2307303908, 0, -855481842, 20968611, 0, 0, 1056439608, 0, -304275696, -1044465174, 0, -3622945896, 0, 0, 663453100, -2853431750, 0, -1561174880, -1824942846, 0, 4022396294, -2019767282, 0, 685769436, 680061040, 0, 0, 2020398132, 0, 188262261, 2905174248, 0, 1894651116, 0, 0, 5184044100, -861137584, 0, 1202350704, -1876446090, 0, -2210932356, -997481948, 0, 1211292498, 171902024, 0, 0, -1566714894, 0, -2549845916, -2957915667, 0, -1818255465, 0, 0, -4211894644, 211431168, 0, 2547246975, -1126172676, 0, -944970532, 154646868, 0, -2260744515, -965501364, 0, 0, 3662278046, 0, 732557688, -730127562, 0, -1225977444, 0, 0, -6148368852, 1887708312, 0, -1067708602, 6764013207, 0, 2328744192, 3769318784, 0, 1364469930, -676710263, 0, 0, 118517196, 0, -182503246, -123422016, 0, -2459303136, 0, 0, 745260692, -2163401732, 0, 5771452623, -2711894736, 0, 994892796, -604461036, 0, 6176305008, 1833317556, 0, 0, 1314893194, 0, -1181499408, 567616218, 0, -1265099472, 0, 0, 672159108, -145080112, 0, -2346432210, 2252731998, 0, -2182876794, -955215976, 0, 1652339592, -4307200380, 0, 0, -5597718232, 0, -2414916304, -290909538, 0, 788712765, 0, 0, -6087588872, -4190506920, 0, 78210237, -4572027282, 0, -1228988130, 10656371530, 0, 7925635140, 370039496, 0, 0, 2970592767, 0, 1143378915, -225811308, 0, 2617463484, 0, 0, 8407259640, 671403472, 0, -190432012, -5571544491, 0, 2119364508, 3784383840, 0, 2680658094, -4986841388, 0, 0], "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, 7, 4, -1, 6, 0]], "char_orbit_index": 13, "prim_orbit_index": 4, "minimal_twist": "21.7.f.a", "char_is_minimal": true, "conrey_index": 10, "id": null, "nf_label": null, "fricke_eigenval": null, "atkin_lehner_string": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "atkin_lehner_eigenvals": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0], [1, 1, -1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [1, 0, -43, 4, 0, -1, 1, -1], [26, -2, 25, 5, -1, 0, -2, -1], [0, 0, 0, 0, 0, 0, 0, 0], [-75, -19, -12, 6, 6, -1, 5, 4], [-392, -42, -4, 46, -9, -13, -12, -8], [0, 0, 0, 0, 0, 0, 0, 0], [-593, 60, 299, -32, -14, -1, -1, 9], [12, 1, 44, -105, -3, -11, 9, -13], [0, 0, 0, 0, 0, 0, 0, 0], [303, 3, -567, 2, 18, -19, 39, -40], [-249, -122, 1844, -31, 25, 30, -25, 13], [0, 0, 0, 0, 0, 0, 0, 0], [-3015, -626, 3035, 20, 5, -40, -55, 35], [896, 182, -436, -82, -30, -42, -42, 6], [0, 0, 0, 0, 0, 0, 0, 0], [-1425, 166, -1594, -251, -125, -88, -118, -125], [1482, -366, -2922, -354, 39, -27, 42, -30], [0, 0, 0, 0, 0, 0, 0, 0], [10930, -220, -44, 264, 37, -7, -132, -88], [-944, 344, 1008, 64, 144, -128, -48, -16], [0, 0, 0, 0, 0, 0, 0, 0], [-60, 43, -3927, 1021, -129, 103, -189, 17], [-358, -1221, -804, 2678, -341, -210, -367, -341], [0, 0, 0, 0, 0, 0, 0, 0], [5681, 2932, 8285, -2154, 261, 194, 71, 225], [1040, 1537, -145, -1392, 48, -97, -435, -290], [0, 0, 0, 0, 0, 0, 0, 0], [-14670, -1086, 7313, 530, 62, 70, 70, -18], [-465, 116, 45905, -4330, -348, 581, -813, 349], [0, 0, 0, 0, 0, 0, 0, 0], [8976, -464, -17884, -248, 358, -142, 68, 148], [19652, -1261, -32617, -804, 344, -47, 127, -50], [0, 0, 0, 0, 0, 0, 0, 0], [16431, -1368, -16544, -113, -79, 226, 260, -147], [14333, -5074, -7018, 2639, -390, -501, -501, 93], [0, 0, 0, 0, 0, 0, 0, 0], [18317, 586, 18335, -1200, 23, -10, 61, 23], [8866, 1052, -16648, 1272, 872, -652, 1084, -864], [0, 0, 0, 0, 0, 0, 0, 0], [6845, -1459, -221, 1680, -620, -841, -663, -442], [-25623, 7226, 25235, -388, -783, 776, 381, 7], [0, 0, 0, 0, 0, 0, 0, 0], [-344, 64, -27616, -184, -192, 408, -536, 280], [-41226, -1220, -39896, 1302, 1234, 192, 2180, 1234], [0, 0, 0, 0, 0, 0, 0, 0], [-66640, 5525, 55496, 1278, -178, -637, 985, -1008], [-121141, -2511, 412, 2099, -1065, -653, 1236, 824], [0, 0, 0, 0, 0, 0, 0, 0], [-275506, -14552, 138340, 7402, -2096, -1426, -1426, 922], [-864, -511, 137478, 7879, 1533, 353, 669, 1375], [0, 0, 0, 0, 0, 0, 0, 0], [46156, -7433, -90141, -7102, 1582, -1251, 2171, -1840], [137333, 20804, -221837, -3878, 1316, 2359, 1393, -665], [0, 0, 0, 0, 0, 0, 0, 0], [130129, 13414, -130901, -772, -1699, 1544, 617, 155], [27852, -2709, -13548, 571, -3079, 811, 811, 2323], [0, 0, 0, 0, 0, 0, 0, 0], [36236, -17232, 39700, 32440, 2744, 1440, 3328, 2744], [-63657, -6697, 126374, -7121, -1106, 682, -940, 516], [0, 0, 0, 0, 0, 0, 0, 0], [281992, 47654, 1044, -48698, 2207, 3251, 3132, 2088], [111258, -24248, -111212, 46, 2178, -92, 2040, -2086], [0, 0, 0, 0, 0, 0, 0, 0], [-2148, -1045, -289965, -4267, 3135, 1103, 987, 3193], [69942, -156, 68274, 1440, -1398, -540, -1986, -1398], [0, 0, 0, 0, 0, 0, 0, 0], [81733, -6836, 115725, 30590, -413, 3300, -2341, 737], [-188446, 20866, 758, -21624, 3408, 4166, 2274, 1516], [0, 0, 0, 0, 0, 0, 0, 0], [-71634, 27083, 34855, -14317, 2297, 3475, 3475, -373], [723, 588, 113570, 21745, -1764, -135, -1041, -1311], [0, 0, 0, 0, 0, 0, 0, 0], [-178434, -20802, 351000, -23238, -6588, 4152, -5868, 3432], [-131974, 22686, -9761, 5245, -2777, -1416, -3562, 4999], [0, 0, 0, 0, 0, 0, 0, 0], [160501, -5248, -157751, 2750, 7518, -5500, -732, -2018], [353365, -7040, -177485, 3990, 4150, 665, 665, -2545], [0, 0, 0, 0, 0, 0, 0, 0], [-111998, -34314, -123606, 74692, -8836, -5544, -9356, -8836], [97070, 15973, -192851, 15078, -698, -197, 1289, -2184], [0, 0, 0, 0, 0, 0, 0, 0], [-38232, 22438, -326, -22112, -3480, -3806, -978, -652], [-198682, -24517, 200278, 1596, -1539, -3192, -6327, 4731], [0, 0, 0, 0, 0, 0, 0, 0], [9479, 2788, -92535, 16374, -8364, -6691, 1115, -12267], [81340, 2428, 81682, -5582, 534, -384, 1644, 534], [0, 0, 0, 0, 0, 0, 0, 0], [-76547, 76118, 193604, -70667, 2651, -4416, -5894, 5827], [-82320, 18704, -2464, -16240, -1680, -4144, -7392, -4928], [0, 0, 0, 0, 0, 0, 0, 0], [-86578, -101972, 41952, 52686, 8748, -726, -726, -6074], [4680, -1292, 137338, -24524, 3876, -5972, 8556, -3388], [0, 0, 0, 0, 0, 0, 0, 0], [-118308, -33555, 232593, -37586, -8058, 4027, -4023, -8], [-150010, -58739, -531307, 18889, -7291, -16086, -4121, -14371], [0, 0, 0, 0, 0, 0, 0, 0], [-44422, -134638, 47578, 3156, 1088, -6312, -8380, 5224]]}