Properties

Label 6.17.b.a
Level 6
Weight 17
Character orbit 6.b
Analytic conductor 9.739
Analytic rank 0
Dimension 6
CM No
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 6 = 2 \cdot 3 \)
Weight: \( k \) = \( 17 \)
Character orbit: \([\chi]\) = 6.b (of order \(2\) and degree \(1\))

Newform invariants

Self dual: No
Analytic conductor: \(9.7394726314\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: \(\mathbb{Q}[x]/(x^{6} + \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{27}\cdot 3^{13} \)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

$q$-expansion

Coefficients of the \(q\)-expansion are expressed in terms of a basis \(1,\beta_1,\ldots,\beta_{5}\) for the coefficient ring described below. We also show the integral \(q\)-expansion of the trace form.

\(f(q)\) \(=\) \( q -\beta_{1} q^{2} + ( 1001 + \beta_{1} - \beta_{2} ) q^{3} -32768 q^{4} + ( 206 \beta_{1} - 32 \beta_{2} - \beta_{4} ) q^{5} + ( 26624 - 1001 \beta_{1} + \beta_{2} + \beta_{3} + \beta_{4} + 2 \beta_{5} ) q^{6} + ( -27982 - 114 \beta_{1} + 617 \beta_{2} - 3 \beta_{3} - 8 \beta_{4} + 7 \beta_{5} ) q^{7} + 32768 \beta_{1} q^{8} + ( -1702623 - 63618 \beta_{1} - 1107 \beta_{2} + 33 \beta_{3} - 48 \beta_{4} - 42 \beta_{5} ) q^{9} +O(q^{10})\) \( q -\beta_{1} q^{2} + ( 1001 + \beta_{1} - \beta_{2} ) q^{3} -32768 q^{4} + ( 206 \beta_{1} - 32 \beta_{2} - \beta_{4} ) q^{5} + ( 26624 - 1001 \beta_{1} + \beta_{2} + \beta_{3} + \beta_{4} + 2 \beta_{5} ) q^{6} + ( -27982 - 114 \beta_{1} + 617 \beta_{2} - 3 \beta_{3} - 8 \beta_{4} + 7 \beta_{5} ) q^{7} + 32768 \beta_{1} q^{8} + ( -1702623 - 63618 \beta_{1} - 1107 \beta_{2} + 33 \beta_{3} - 48 \beta_{4} - 42 \beta_{5} ) q^{9} + ( 6549504 + 696 \beta_{1} - 3730 \beta_{2} + 78 \beta_{3} + 46 \beta_{4} - 20 \beta_{5} ) q^{10} + ( 476804 \beta_{1} + 13198 \beta_{2} - 271 \beta_{4} - 405 \beta_{5} ) q^{11} + ( -32800768 - 32768 \beta_{1} + 32768 \beta_{2} ) q^{12} + ( 293858690 - 7680 \beta_{1} + 42490 \beta_{2} + 1290 \beta_{3} - 610 \beta_{4} + 1040 \beta_{5} ) q^{13} + ( 30966 \beta_{1} - 15008 \beta_{2} - 2656 \beta_{4} - 1296 \beta_{5} ) q^{14} + ( -1346703072 + 5029764 \beta_{1} - 28749 \beta_{2} + 1221 \beta_{3} - 5340 \beta_{4} + 255 \beta_{5} ) q^{15} + 1073741824 q^{16} + ( -9218096 \beta_{1} - 17128 \beta_{2} + 3292 \beta_{4} + 2268 \beta_{5} ) q^{17} + ( -2091528192 + 1713495 \beta_{1} - 75654 \beta_{2} + 1626 \beta_{3} + 19770 \beta_{4} - 7548 \beta_{5} ) q^{18} + ( 10051163282 - 24690 \beta_{1} + 125002 \beta_{2} - 14586 \beta_{3} - 1069 \beta_{4} - 3793 \beta_{5} ) q^{19} + ( -6750208 \beta_{1} + 1048576 \beta_{2} + 32768 \beta_{4} ) q^{20} + ( -25961776958 - 18464014 \beta_{1} - 601604 \beta_{2} - 26892 \beta_{3} + 5913 \beta_{4} + 42444 \beta_{5} ) q^{21} + ( 15705550848 + 778296 \beta_{1} - 4233010 \beta_{2} - 12882 \beta_{3} + 56206 \beta_{4} - 60500 \beta_{5} ) q^{22} + ( -85262936 \beta_{1} - 9322588 \beta_{2} - 31898 \beta_{4} + 153738 \beta_{5} ) q^{23} + ( -872415232 + 32800768 \beta_{1} - 32768 \beta_{2} - 32768 \beta_{3} - 32768 \beta_{4} - 65536 \beta_{5} ) q^{24} + ( -12620406911 - 2416464 \beta_{1} + 13126650 \beta_{2} + 14058 \beta_{3} - 173274 \beta_{4} + 177960 \beta_{5} ) q^{25} + ( -298219810 \beta_{1} + 22912640 \beta_{2} + 234880 \beta_{4} - 285120 \beta_{5} ) q^{26} + ( 55031829993 + 1220115645 \beta_{1} + 3928743 \beta_{2} + 198198 \beta_{3} - 89271 \beta_{4} + 98397 \beta_{5} ) q^{27} + ( 916914176 + 3735552 \beta_{1} - 20217856 \beta_{2} + 98304 \beta_{3} + 262144 \beta_{4} - 229376 \beta_{5} ) q^{28} + ( -1862261686 \beta_{1} - 13298672 \beta_{2} - 1225867 \beta_{4} - 480168 \beta_{5} ) q^{29} + ( 164613255168 + 1346951976 \beta_{1} - 1924458 \beta_{2} + 266166 \beta_{3} + 476118 \beta_{4} - 552420 \beta_{5} ) q^{30} + ( -474367275022 - 6072210 \beta_{1} + 33303255 \beta_{2} + 548955 \beta_{3} - 459870 \beta_{4} + 642855 \beta_{5} ) q^{31} -1073741824 \beta_{1} q^{32} + ( 547048232736 + 5884994442 \beta_{1} + 16483323 \beta_{2} - 654657 \beta_{3} - 2432688 \beta_{4} + 755214 \beta_{5} ) q^{33} + ( -302159609856 - 5593440 \beta_{1} + 30323368 \beta_{2} - 66264 \beta_{3} - 396376 \beta_{4} + 374288 \beta_{5} ) q^{34} + ( -11181344144 \beta_{1} + 15326948 \beta_{2} + 4635634 \beta_{4} + 2463210 \beta_{5} ) q^{35} + ( 55791550464 + 2084634624 \beta_{1} + 36274176 \beta_{2} - 1081344 \beta_{3} + 1572864 \beta_{4} + 1376256 \beta_{5} ) q^{36} + ( 413972680322 + 43375584 \beta_{1} - 237391378 \beta_{2} - 3107874 \beta_{3} + 3246250 \beta_{4} - 4282208 \beta_{5} ) q^{37} + ( -10007906554 \beta_{1} - 226697824 \beta_{2} - 4440224 \beta_{4} + 1566864 \beta_{5} ) q^{38} + ( -1459846144430 + 29747993450 \beta_{1} - 316741460 \beta_{2} + 737910 \beta_{3} + 13203810 \beta_{4} - 4472820 \beta_{5} ) q^{39} + ( -214614147072 - 22806528 \beta_{1} + 122224640 \beta_{2} - 2555904 \beta_{3} - 1507328 \beta_{4} + 655360 \beta_{5} ) q^{40} + ( -50513852092 \beta_{1} + 491723296 \beta_{2} + 5330210 \beta_{4} - 5947344 \beta_{5} ) q^{41} + ( -608819621888 + 25964061158 \beta_{1} + 3183722 \beta_{2} + 1952522 \beta_{3} - 15473494 \beta_{4} + 6599428 \beta_{5} ) q^{42} + ( 7692513531794 - 9049842 \beta_{1} + 50823534 \beta_{2} + 2739402 \beta_{3} - 776865 \beta_{4} + 1689999 \beta_{5} ) q^{43} + ( -15623913472 \beta_{1} - 432472064 \beta_{2} + 8880128 \beta_{4} + 13271040 \beta_{5} ) q^{44} + ( -7749458797248 + 64822254390 \beta_{1} + 1233167166 \beta_{2} - 56826 \beta_{3} - 15937119 \beta_{4} - 6616980 \beta_{5} ) q^{45} + ( -2851934232576 - 201641520 \beta_{1} + 1104159988 \beta_{2} + 15402036 \beta_{3} - 15136396 \beta_{4} + 20270408 \beta_{5} ) q^{46} + ( -23281637760 \beta_{1} - 53459400 \beta_{2} - 52499220 \beta_{4} - 30120660 \beta_{5} ) q^{47} + ( 1074815565824 + 1073741824 \beta_{1} - 1073741824 \beta_{2} ) q^{48} + ( 7025918968515 + 305550480 \beta_{1} - 1640508634 \beta_{2} + 29390262 \beta_{3} + 20425498 \beta_{4} - 10628744 \beta_{5} ) q^{49} + ( 12446244767 \beta_{1} + 926864256 \beta_{2} - 34764672 \beta_{4} - 37765440 \beta_{5} ) q^{50} + ( -509278165632 - 48069431784 \beta_{1} - 35111916 \beta_{2} + 7682004 \beta_{3} + 29280816 \beta_{4} + 7683264 \beta_{5} ) q^{51} + ( -9629161553920 + 251658240 \beta_{1} - 1392312320 \beta_{2} - 42270720 \beta_{3} + 19988480 \beta_{4} - 34078720 \beta_{5} ) q^{52} + ( 93951277766 \beta_{1} + 668927008 \beta_{2} + 149985083 \beta_{4} + 76492512 \beta_{5} ) q^{53} + ( 40003713054720 - 55615593537 \beta_{1} + 3054575043 \beta_{2} + 553059 \beta_{3} + 48569859 \beta_{4} - 39952458 \beta_{5} ) q^{54} + ( -25926969826368 - 1183475232 \beta_{1} + 6361677990 \beta_{2} - 101610666 \beta_{3} - 79695342 \beta_{4} + 45825120 \beta_{5} ) q^{55} + ( -1014693888 \beta_{1} + 491782144 \beta_{2} + 87031808 \beta_{4} + 42467328 \beta_{5} ) q^{56} + ( 4508782130722 - 280643651242 \beta_{1} - 10369942049 \beta_{2} - 29637333 \beta_{3} - 118322370 \beta_{4} + 77675274 \beta_{5} ) q^{57} + ( -61107352350720 + 1552328040 \beta_{1} - 8392700518 \beta_{2} + 55283514 \beta_{3} + 108248026 \beta_{4} - 89820188 \beta_{5} ) q^{58} + ( 289011050620 \beta_{1} - 15383889490 \beta_{2} - 216922859 \beta_{4} + 156339963 \beta_{5} ) q^{59} + ( 44128766263296 - 164815306752 \beta_{1} + 942047232 \beta_{2} - 40009728 \beta_{3} + 174981120 \beta_{4} - 8355840 \beta_{5} ) q^{60} + ( 51006083649794 - 355148640 \beta_{1} + 1941881574 \beta_{2} + 22505238 \beta_{3} - 26439438 \beta_{4} + 33941184 \beta_{5} ) q^{61} + ( 472359197782 \beta_{1} + 10564358880 \beta_{2} + 55088160 \beta_{4} - 162991440 \beta_{5} ) q^{62} + ( -133608719319054 - 1014891870378 \beta_{1} + 22769472411 \beta_{2} - 32456949 \beta_{3} - 15832752 \beta_{4} + 51671049 \beta_{5} ) q^{63} -35184372088832 q^{64} + ( 1694030761900 \beta_{1} + 22182666800 \beta_{2} + 14445550 \beta_{4} - 402229800 \beta_{5} ) q^{65} + ( 192929054502912 - 544794463320 \beta_{1} - 11843990922 \beta_{2} + 126587286 \beta_{3} - 326699082 \beta_{4} - 125823780 \beta_{5} ) q^{66} + ( 329974428334802 + 707023854 \beta_{1} - 3555574404 \beta_{2} + 456435144 \beta_{3} + 28766697 \beta_{4} + 123378351 \beta_{5} ) q^{67} + ( 302058569728 \beta_{1} + 561250304 \beta_{2} - 107872256 \beta_{4} - 74317824 \beta_{5} ) q^{68} + ( -390963758782272 - 1488047313684 \beta_{1} - 10199529966 \beta_{2} + 345092154 \beta_{3} + 135809376 \beta_{4} - 388251636 \beta_{5} ) q^{69} + ( -366287217893376 - 6812835024 \beta_{1} + 36888213580 \beta_{2} - 154669812 \beta_{3} - 479265844 \beta_{4} + 427709240 \beta_{5} ) q^{70} + ( 1767143431336 \beta_{1} - 24458101348 \beta_{2} - 708006158 \beta_{4} + 33368598 \beta_{5} ) q^{71} + ( 68535195795456 - 56147804160 \beta_{1} + 2479030272 \beta_{2} - 53280768 \beta_{3} - 647823360 \beta_{4} + 247332864 \beta_{5} ) q^{72} + ( 644034564125570 + 4405946400 \beta_{1} - 24321030192 \beta_{2} - 651057264 \beta_{3} + 345713184 \beta_{4} - 562732272 \beta_{5} ) q^{73} + ( -402115607010 \beta_{1} - 62421484160 \beta_{2} - 167907712 \beta_{4} + 1056452544 \beta_{5} ) q^{74} + ( -562710577633687 + 1194017236681 \beta_{1} + 291455717 \beta_{2} - 437350914 \beta_{3} + 791734338 \beta_{4} + 518119740 \beta_{5} ) q^{75} + ( -329356518424576 + 809041920 \beta_{1} - 4096065536 \beta_{2} + 477954048 \beta_{3} + 35028992 \beta_{4} + 124289024 \beta_{5} ) q^{76} + ( -6371448271412 \beta_{1} + 119712525632 \beta_{2} + 3030127702 \beta_{4} - 421267392 \beta_{5} ) q^{77} + ( 972907082076160 + 1455297378830 \beta_{1} + 24387876770 \beta_{2} - 434411230 \beta_{3} + 1106636450 \beta_{4} + 1515532420 \beta_{5} ) q^{78} + ( 305967747350258 + 6536177070 \beta_{1} - 35852897417 \beta_{2} - 598973829 \beta_{3} + 495392354 \beta_{4} - 695050297 \beta_{5} ) q^{79} + ( 221190815744 \beta_{1} - 34359738368 \beta_{2} - 1073741824 \beta_{4} ) q^{80} + ( -117226000244223 + 6005573356572 \beta_{1} - 56534481684 \beta_{2} - 993912876 \beta_{3} + 459953694 \beta_{4} - 3143425860 \beta_{5} ) q^{81} + ( -1652170564558848 + 4949506704 \beta_{1} - 27435385564 \beta_{2} - 915333276 \beta_{3} + 397123492 \beta_{4} - 702234584 \beta_{5} ) q^{82} + ( -5000622624228 \beta_{1} - 87426015318 \beta_{2} + 694106667 \beta_{4} + 2030322753 \beta_{5} ) q^{83} + ( 850715507359744 + 605028810752 \beta_{1} + 19713359872 \beta_{2} + 881197056 \beta_{3} - 193757184 \beta_{4} - 1390804992 \beta_{5} ) q^{84} + ( 478828727831808 + 15218232192 \beta_{1} - 81977927160 \beta_{2} + 1026307656 \beta_{3} + 1038144792 \beta_{4} - 696042240 \beta_{5} ) q^{85} + ( -7701380595770 \beta_{1} + 46549307040 \beta_{2} + 614930016 \beta_{4} - 497621232 \beta_{5} ) q^{86} + ( -500013483434400 + 8910504307452 \beta_{1} - 3848936127 \beta_{2} + 2942219703 \beta_{3} - 5100693684 \beta_{4} + 6353850525 \beta_{5} ) q^{87} + ( -514639490187264 - 25503203328 \beta_{1} + 138707271680 \beta_{2} + 422117376 \beta_{3} - 1841758208 \beta_{4} + 1982464000 \beta_{5} ) q^{88} + ( -3041402130140 \beta_{1} + 13451507960 \beta_{2} - 7129018394 \beta_{4} - 4473705492 \beta_{5} ) q^{89} + ( 2131634152009728 + 7770329465688 \beta_{1} - 114226258482 \beta_{2} - 697830354 \beta_{3} + 42639246 \beta_{4} - 3982485780 \beta_{5} ) q^{90} + ( -304046855600540 - 118635362820 \beta_{1} + 645376429230 \beta_{2} + 2190280950 \beta_{3} - 8578253580 \beta_{4} + 9308347230 \beta_{5} ) q^{91} + ( 2793895886848 \beta_{1} + 305482563584 \beta_{2} + 1045233664 \beta_{4} - 5037686784 \beta_{5} ) q^{92} + ( -1859472576273662 + 13124304515498 \beta_{1} + 450109812982 \beta_{2} - 221351130 \beta_{3} + 6397549695 \beta_{4} - 1222017840 \beta_{5} ) q^{93} + ( -763312823255040 + 80395138080 \beta_{1} - 435462061560 \beta_{2} + 1564803720 \beta_{3} + 5667995400 \beta_{4} - 5146394160 \beta_{5} ) q^{94} + ( -22638617244968 \beta_{1} - 604445635204 \beta_{2} - 9033572822 \beta_{4} + 5840209350 \beta_{5} ) q^{95} + ( 28587302322176 - 1074815565824 \beta_{1} + 1073741824 \beta_{2} + 1073741824 \beta_{3} + 1073741824 \beta_{4} + 2147483648 \beta_{5} ) q^{96} + ( 5182915520940866 + 142683795312 \beta_{1} - 774156625802 \beta_{2} + 666424902 \beta_{3} + 10159965146 \beta_{4} - 9937823512 \beta_{5} ) q^{97} + ( -7099193368291 \beta_{1} + 382532526208 \beta_{2} + 13039707008 \beta_{4} + 643298112 \beta_{5} ) q^{98} + ( -4799036141790912 + 4525004215260 \beta_{1} - 677337535152 \beta_{2} - 7186615254 \beta_{3} - 15703295049 \beta_{4} - 4700752641 \beta_{5} ) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q + 6006q^{3} - 196608q^{4} + 159744q^{6} - 167892q^{7} - 10215738q^{9} + O(q^{10}) \) \( 6q + 6006q^{3} - 196608q^{4} + 159744q^{6} - 167892q^{7} - 10215738q^{9} + 39297024q^{10} - 196804608q^{12} + 1763152140q^{13} - 8080218432q^{15} + 6442450944q^{16} - 12549169152q^{18} + 60306979692q^{19} - 155770661748q^{21} + 94233305088q^{22} - 5234491392q^{24} - 75722441466q^{25} + 330190979958q^{27} + 5501485056q^{28} + 987679531008q^{30} - 2846203650132q^{31} + 3282289396416q^{33} - 1812957659136q^{34} + 334749302784q^{36} + 2483836081932q^{37} - 8759076866580q^{39} - 1287684882432q^{40} - 3652917731328q^{42} + 46155081190764q^{43} - 46496752783488q^{45} - 17111605395456q^{46} + 6448893394944q^{48} + 42155513811090q^{49} - 3055668993792q^{51} - 57774969323520q^{52} + 240022278328320q^{54} - 155561818958208q^{55} + 27052692784332q^{57} - 366644114104320q^{58} + 264772597579776q^{60} + 306036501898764q^{61} - 801652315914324q^{63} - 211106232532992q^{64} + 1157574327017472q^{66} + 1979846570008812q^{67} - 2345782552693632q^{69} - 2197723307360256q^{70} + 411211174772736q^{72} + 3864207384753420q^{73} - 3376263465802122q^{75} - 1976139110547456q^{76} + 5837442492456960q^{78} + 1835806484101548q^{79} - 703356001465338q^{81} - 9913023387353088q^{82} + 5104293044158464q^{84} + 2872972366990848q^{85} - 3000080900606400q^{87} - 3087836941123584q^{88} + 12789804912058368q^{90} - 1824281133603240q^{91} - 11156835457641972q^{93} - 4579876939530240q^{94} + 171523813933056q^{96} + 31097493125645196q^{97} - 28794216850745472q^{99} + O(q^{100}) \)

Basis of coefficient ring in terms of a root \(\nu\) of \(x^{6} + 55116 x^{4} + 758395257 x^{2} + 123254139008\):

\(\beta_{0}\)\(=\)\( 1 \)
\(\beta_{1}\)\(=\)\((\)\( 16 \nu^{5} + 4853824 \nu^{3} + 121597790224 \nu \)\()/ 8558504955 \)
\(\beta_{2}\)\(=\)\((\)\( -199889 \nu^{5} + 15267252 \nu^{4} - 9288096866 \nu^{3} + 523452257328 \nu^{2} - 111237611022911 \nu + 1876454917224888 \)\()/ 316664683335 \)
\(\beta_{3}\)\(=\)\((\)\(-8998261 \nu^{5} - 4512031524 \nu^{4} - 418952112154 \nu^{3} - 119109271737456 \nu^{2} - 4665639931139659 \nu + 99298786896212904\)\()/ 316664683335 \)
\(\beta_{4}\)\(=\)\((\)\( 3331582 \nu^{5} - 162850688 \nu^{4} + 154831546348 \nu^{3} - 5583490744832 \nu^{2} + 1489912321552978 \nu - 20015519117065472 \)\()/ 105554894445 \)
\(\beta_{5}\)\(=\)\((\)\( 176186 \nu^{5} + 5765256 \nu^{4} + 8202127844 \nu^{3} + 197667285984 \nu^{2} + 90816664739414 \nu + 708591367343664 \)\()/ 2214438345 \)
\(1\)\(=\)\(\beta_0\)
\(\nu\)\(=\)\((\)\(2 \beta_{5} - 20 \beta_{4} - 748 \beta_{2} - 19 \beta_{1}\)\()/62208\)
\(\nu^{2}\)\(=\)\((\)\(254 \beta_{5} - 213 \beta_{4} + 123 \beta_{3} + 15819 \beta_{2} - 2900 \beta_{1} - 253974528\)\()/13824\)
\(\nu^{3}\)\(=\)\((\)\(-57202 \beta_{5} + 550708 \beta_{4} + 20711564 \beta_{2} + 130082147 \beta_{1}\)\()/62208\)
\(\nu^{4}\)\(=\)\((\)\(-1734674 \beta_{5} + 1383243 \beta_{4} - 1054293 \beta_{3} - 101963589 \beta_{2} + 18662540 \beta_{1} + 1752172349184\)\()/3456\)
\(\nu^{5}\)\(=\)\((\)\(2153303750 \beta_{5} - 15067743932 \beta_{4} - 598446208324 \beta_{2} - 6042375801577 \beta_{1}\)\()/62208\)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/6\mathbb{Z}\right)^\times\).

\(n\) \(5\)
\(\chi(n)\) \(-1\)

Embeddings

For each embedding \(\iota_m\) of the coefficient field, the values \(\iota_m(a_n)\) are shown below.

For more information on an embedded modular form you can click on its label.

Label \(\iota_m(\nu)\) \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
5.1
12.8250i
172.725i
158.486i
12.8250i
172.725i
158.486i
181.019i −4654.10 + 4624.51i −32768.0 1539.79i 837125. + 842482.i 5.92137e6 5.93164e6i 274580. 4.30458e7i 278731.
5.2 181.019i 1479.09 6392.11i −32768.0 441421.i −1.15709e6 267744.i 2.81464e6 5.93164e6i −3.86713e7 1.89090e7i −7.99057e7
5.3 181.019i 6178.01 + 2208.83i −32768.0 548425.i 399841. 1.11834e6i −8.81996e6 5.93164e6i 3.32888e7 + 2.72924e7i 9.92755e7
5.4 181.019i −4654.10 4624.51i −32768.0 1539.79i 837125. 842482.i 5.92137e6 5.93164e6i 274580. + 4.30458e7i 278731.
5.5 181.019i 1479.09 + 6392.11i −32768.0 441421.i −1.15709e6 + 267744.i 2.81464e6 5.93164e6i −3.86713e7 + 1.89090e7i −7.99057e7
5.6 181.019i 6178.01 2208.83i −32768.0 548425.i 399841. + 1.11834e6i −8.81996e6 5.93164e6i 3.32888e7 2.72924e7i 9.92755e7
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 5.6
Significant digits:
Format:

Inner twists

Char. orbit Parity Mult. Self Twist Proved
1.a Even 1 trivial yes
3.b Odd 1 yes

Hecke kernels

There are no other newforms in \(S_{17}^{\mathrm{new}}(6, [\chi])\).