Properties

Label 6018.2.a.bc
Level 6018
Weight 2
Character orbit 6018.a
Self dual yes
Analytic conductor 48.054
Analytic rank 0
Dimension 14
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6018 = 2 \cdot 3 \cdot 17 \cdot 59 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6018.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(48.0539719364\)
Analytic rank: \(0\)
Dimension: \(14\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

Coefficients of the \(q\)-expansion are expressed in terms of a basis \(1,\beta_1,\ldots,\beta_{13}\) for the coefficient ring described below. We also show the integral \(q\)-expansion of the trace form.

\(f(q)\) \(=\) \( q + q^{2} - q^{3} + q^{4} + \beta_{1} q^{5} - q^{6} -\beta_{6} q^{7} + q^{8} + q^{9} +O(q^{10})\) \( q + q^{2} - q^{3} + q^{4} + \beta_{1} q^{5} - q^{6} -\beta_{6} q^{7} + q^{8} + q^{9} + \beta_{1} q^{10} -\beta_{2} q^{11} - q^{12} + ( 1 - \beta_{9} ) q^{13} -\beta_{6} q^{14} -\beta_{1} q^{15} + q^{16} + q^{17} + q^{18} + ( 1 + \beta_{7} + \beta_{10} ) q^{19} + \beta_{1} q^{20} + \beta_{6} q^{21} -\beta_{2} q^{22} + ( -\beta_{4} - \beta_{6} ) q^{23} - q^{24} + ( 2 - \beta_{2} - \beta_{3} + \beta_{4} ) q^{25} + ( 1 - \beta_{9} ) q^{26} - q^{27} -\beta_{6} q^{28} + ( \beta_{1} + \beta_{2} - \beta_{4} + \beta_{5} - \beta_{6} ) q^{29} -\beta_{1} q^{30} + ( -\beta_{7} + \beta_{8} ) q^{31} + q^{32} + \beta_{2} q^{33} + q^{34} + ( 1 - \beta_{1} - \beta_{2} + \beta_{4} - \beta_{5} + \beta_{6} - \beta_{7} - \beta_{11} - \beta_{13} ) q^{35} + q^{36} + ( 1 + \beta_{1} + \beta_{3} ) q^{37} + ( 1 + \beta_{7} + \beta_{10} ) q^{38} + ( -1 + \beta_{9} ) q^{39} + \beta_{1} q^{40} + ( -2 + 2 \beta_{1} + \beta_{2} + \beta_{3} + \beta_{7} - \beta_{10} ) q^{41} + \beta_{6} q^{42} + ( 1 - \beta_{8} + \beta_{11} + \beta_{13} ) q^{43} -\beta_{2} q^{44} + \beta_{1} q^{45} + ( -\beta_{4} - \beta_{6} ) q^{46} + ( -1 + \beta_{1} + \beta_{3} - \beta_{5} - \beta_{10} + \beta_{13} ) q^{47} - q^{48} + ( 3 - \beta_{1} + \beta_{2} - \beta_{8} + \beta_{11} + \beta_{12} ) q^{49} + ( 2 - \beta_{2} - \beta_{3} + \beta_{4} ) q^{50} - q^{51} + ( 1 - \beta_{9} ) q^{52} + ( 2 + \beta_{2} - \beta_{3} + \beta_{5} + \beta_{7} + 2 \beta_{9} + \beta_{11} - \beta_{13} ) q^{53} - q^{54} + ( 1 + \beta_{1} - \beta_{2} - \beta_{3} + \beta_{4} - \beta_{11} - \beta_{12} ) q^{55} -\beta_{6} q^{56} + ( -1 - \beta_{7} - \beta_{10} ) q^{57} + ( \beta_{1} + \beta_{2} - \beta_{4} + \beta_{5} - \beta_{6} ) q^{58} + q^{59} -\beta_{1} q^{60} + ( 2 + \beta_{4} - \beta_{5} - 2 \beta_{7} - \beta_{10} + \beta_{13} ) q^{61} + ( -\beta_{7} + \beta_{8} ) q^{62} -\beta_{6} q^{63} + q^{64} + ( 2 \beta_{1} + \beta_{5} - \beta_{8} - \beta_{11} ) q^{65} + \beta_{2} q^{66} + ( \beta_{2} - \beta_{4} - \beta_{6} + \beta_{7} - \beta_{12} ) q^{67} + q^{68} + ( \beta_{4} + \beta_{6} ) q^{69} + ( 1 - \beta_{1} - \beta_{2} + \beta_{4} - \beta_{5} + \beta_{6} - \beta_{7} - \beta_{11} - \beta_{13} ) q^{70} + ( -1 - \beta_{2} - \beta_{5} - \beta_{7} - \beta_{10} - \beta_{12} ) q^{71} + q^{72} + ( 2 - \beta_{2} + \beta_{3} + \beta_{4} - \beta_{5} + \beta_{6} - \beta_{11} - \beta_{13} ) q^{73} + ( 1 + \beta_{1} + \beta_{3} ) q^{74} + ( -2 + \beta_{2} + \beta_{3} - \beta_{4} ) q^{75} + ( 1 + \beta_{7} + \beta_{10} ) q^{76} + ( \beta_{2} - \beta_{3} - \beta_{4} - \beta_{6} - \beta_{7} - \beta_{10} + \beta_{11} + 2 \beta_{13} ) q^{77} + ( -1 + \beta_{9} ) q^{78} + ( \beta_{2} - \beta_{3} - \beta_{4} + \beta_{5} + \beta_{7} + \beta_{9} + \beta_{11} ) q^{79} + \beta_{1} q^{80} + q^{81} + ( -2 + 2 \beta_{1} + \beta_{2} + \beta_{3} + \beta_{7} - \beta_{10} ) q^{82} + ( 3 - \beta_{1} - \beta_{7} + \beta_{10} - \beta_{11} + \beta_{12} ) q^{83} + \beta_{6} q^{84} + \beta_{1} q^{85} + ( 1 - \beta_{8} + \beta_{11} + \beta_{13} ) q^{86} + ( -\beta_{1} - \beta_{2} + \beta_{4} - \beta_{5} + \beta_{6} ) q^{87} -\beta_{2} q^{88} + ( 3 - \beta_{1} - \beta_{3} + \beta_{6} + \beta_{8} + \beta_{10} - \beta_{13} ) q^{89} + \beta_{1} q^{90} + ( 2 - \beta_{1} + \beta_{2} + 2 \beta_{5} - \beta_{6} + 2 \beta_{7} + 2 \beta_{8} + \beta_{10} + 2 \beta_{12} - \beta_{13} ) q^{91} + ( -\beta_{4} - \beta_{6} ) q^{92} + ( \beta_{7} - \beta_{8} ) q^{93} + ( -1 + \beta_{1} + \beta_{3} - \beta_{5} - \beta_{10} + \beta_{13} ) q^{94} + ( 2 + \beta_{3} + \beta_{5} + 2 \beta_{6} - \beta_{7} - \beta_{8} + 2 \beta_{10} + \beta_{11} + \beta_{12} - \beta_{13} ) q^{95} - q^{96} + ( 2 - 2 \beta_{1} + \beta_{2} + \beta_{5} + \beta_{6} + 2 \beta_{8} + \beta_{10} + \beta_{12} - \beta_{13} ) q^{97} + ( 3 - \beta_{1} + \beta_{2} - \beta_{8} + \beta_{11} + \beta_{12} ) q^{98} -\beta_{2} q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14q + 14q^{2} - 14q^{3} + 14q^{4} + 2q^{5} - 14q^{6} + q^{7} + 14q^{8} + 14q^{9} + O(q^{10}) \) \( 14q + 14q^{2} - 14q^{3} + 14q^{4} + 2q^{5} - 14q^{6} + q^{7} + 14q^{8} + 14q^{9} + 2q^{10} + 3q^{11} - 14q^{12} + 16q^{13} + q^{14} - 2q^{15} + 14q^{16} + 14q^{17} + 14q^{18} + 13q^{19} + 2q^{20} - q^{21} + 3q^{22} + 4q^{23} - 14q^{24} + 32q^{25} + 16q^{26} - 14q^{27} + q^{28} - 2q^{30} - 13q^{31} + 14q^{32} - 3q^{33} + 14q^{34} + 14q^{36} + 12q^{37} + 13q^{38} - 16q^{39} + 2q^{40} - 18q^{41} - q^{42} + 29q^{43} + 3q^{44} + 2q^{45} + 4q^{46} - 14q^{48} + 49q^{49} + 32q^{50} - 14q^{51} + 16q^{52} + 24q^{53} - 14q^{54} + 15q^{55} + q^{56} - 13q^{57} + 14q^{59} - 2q^{60} + 29q^{61} - 13q^{62} + q^{63} + 14q^{64} + 6q^{65} - 3q^{66} + 4q^{67} + 14q^{68} - 4q^{69} - 10q^{71} + 14q^{72} + 18q^{73} + 12q^{74} - 32q^{75} + 13q^{76} + 20q^{77} - 16q^{78} + 7q^{79} + 2q^{80} + 14q^{81} - 18q^{82} + 28q^{83} - q^{84} + 2q^{85} + 29q^{86} + 3q^{88} + 23q^{89} + 2q^{90} + 9q^{91} + 4q^{92} + 13q^{93} + 5q^{95} - 14q^{96} - 7q^{97} + 49q^{98} + 3q^{99} + O(q^{100}) \)

Basis of coefficient ring in terms of a root \(\nu\) of \(x^{14} - 2 x^{13} - 49 x^{12} + 79 x^{11} + 956 x^{10} - 1179 x^{9} - 9396 x^{8} + 8315 x^{7} + 48570 x^{6} - 28124 x^{5} - 125592 x^{4} + 40576 x^{3} + 138096 x^{2} - 22032 x - 43744\):

\(\beta_{0}\)\(=\)\( 1 \)
\(\beta_{1}\)\(=\)\( \nu \)
\(\beta_{2}\)\(=\)\((\)\(16618726754 \nu^{13} - 2880670567959 \nu^{12} - 19196372187770 \nu^{11} + 218934418638321 \nu^{10} + 664075790819685 \nu^{9} - 5146738100625936 \nu^{8} - 8545314250127135 \nu^{7} + 50968867163271240 \nu^{6} + 48833287977907775 \nu^{5} - 217396661630863236 \nu^{4} - 114630360428554364 \nu^{3} + 335998399721244300 \nu^{2} + 82447262577467504 \nu - 121204003017027824\)\()/ 7894197520302920 \)
\(\beta_{3}\)\(=\)\((\)\(186379188393 \nu^{13} - 14081190935493 \nu^{12} + 28753457488965 \nu^{11} + 579978221320162 \nu^{10} - 1128332602443005 \nu^{9} - 9178698567078167 \nu^{8} + 14347689427204105 \nu^{7} + 69366955830930035 \nu^{6} - 77170871949262535 \nu^{5} - 252075259966176062 \nu^{4} + 175862488069791692 \nu^{3} + 386591439015569500 \nu^{2} - 160331873586642872 \nu - 147416272648448328\)\()/ 7894197520302920 \)
\(\beta_{4}\)\(=\)\((\)\(202997915147 \nu^{13} - 16961861503452 \nu^{12} + 9557085301195 \nu^{11} + 798912639958483 \nu^{10} - 464256811623320 \nu^{9} - 14325436667704103 \nu^{8} + 5802375177076970 \nu^{7} + 120335822994201275 \nu^{6} - 28337583971354760 \nu^{5} - 469471921597039298 \nu^{4} + 61232127641237328 \nu^{3} + 730484036257116720 \nu^{2} - 77884611009175368 \nu - 323879658307596592\)\()/ 7894197520302920 \)
\(\beta_{5}\)\(=\)\((\)\(-236276976171 \nu^{13} + 2329023024781 \nu^{12} + 3942662986183 \nu^{11} - 87670549177272 \nu^{10} + 50692387805607 \nu^{9} + 1220653172685771 \nu^{8} - 1404708310869837 \nu^{7} - 7517982884554071 \nu^{6} + 9313167069656711 \nu^{5} + 17549153084715332 \nu^{4} - 20706135037061272 \nu^{3} - 1669417898377500 \nu^{2} + 7626075980681936 \nu - 13207959668528272\)\()/ 3157679008121168 \)
\(\beta_{6}\)\(=\)\((\)\(443751573941 \nu^{13} - 3008483462819 \nu^{12} - 15414700154749 \nu^{11} + 114215106567488 \nu^{10} + 218559476116059 \nu^{9} - 1599349359996641 \nu^{8} - 1794366343522957 \nu^{7} + 9814685899795205 \nu^{6} + 9382257151775639 \nu^{5} - 22696271950686584 \nu^{4} - 25513830497582096 \nu^{3} + 2824971170499412 \nu^{2} + 19999582304517216 \nu + 13827833046029584\)\()/ 3157679008121168 \)
\(\beta_{7}\)\(=\)\((\)\(2226419771871 \nu^{13} - 14073288977621 \nu^{12} - 88902889968565 \nu^{11} + 621826637080384 \nu^{10} + 1279836923435835 \nu^{9} - 10443761348377309 \nu^{8} - 7309843756060875 \nu^{7} + 82123225867424865 \nu^{6} + 4465199891261865 \nu^{5} - 295403685028325434 \nu^{4} + 86934350501483764 \nu^{3} + 380724393788637740 \nu^{2} - 151910773512655624 \nu - 79394039693874016\)\()/ 15788395040605840 \)
\(\beta_{8}\)\(=\)\((\)\(-5727717858944 \nu^{13} + 7373884997349 \nu^{12} + 260235001126690 \nu^{11} - 207291278819761 \nu^{10} - 4646880167421965 \nu^{9} + 1817846619873516 \nu^{8} + 40551053846921025 \nu^{7} - 4934053698709940 \nu^{6} - 174746025060120125 \nu^{5} - 3134468239806414 \nu^{4} + 333908596796940704 \nu^{3} + 48280623164166500 \nu^{2} - 213409310594817704 \nu - 90032763346833376\)\()/ 15788395040605840 \)
\(\beta_{9}\)\(=\)\((\)\(-3246512395886 \nu^{13} + 10334588586211 \nu^{12} + 126833659135550 \nu^{11} - 358168627839709 \nu^{10} - 1863261897938825 \nu^{9} + 4435000064547344 \nu^{8} + 12733747965022935 \nu^{7} - 23909630494110700 \nu^{6} - 41721469365383055 \nu^{5} + 56781193842740004 \nu^{4} + 72685524970824776 \nu^{3} - 60806142225794540 \nu^{2} - 81782923919894696 \nu + 17065631601733976\)\()/ 7894197520302920 \)
\(\beta_{10}\)\(=\)\((\)\(-10198052289283 \nu^{13} + 32343651313568 \nu^{12} + 416444703490635 \nu^{11} - 1121038637019707 \nu^{10} - 6666675407303450 \nu^{9} + 13997174731938057 \nu^{8} + 52688098277426130 \nu^{7} - 76968570525750485 \nu^{6} - 210583446468153260 \nu^{5} + 182706845683949412 \nu^{4} + 389401116803341508 \nu^{3} - 142957183349222400 \nu^{2} - 242528671429568608 \nu - 25869449120688432\)\()/ 15788395040605840 \)
\(\beta_{11}\)\(=\)\((\)\(12229460566967 \nu^{13} - 60219666399172 \nu^{12} - 443909983325205 \nu^{11} + 2249746437989783 \nu^{10} + 6115066006045500 \nu^{9} - 31255545769888503 \nu^{8} - 41404355245907430 \nu^{7} + 199267414681539515 \nu^{6} + 152264418850087960 \nu^{5} - 579220686043196398 \nu^{4} - 295590582482895472 \nu^{3} + 676467191148702720 \nu^{2} + 158405026529980472 \nu - 260037911487082352\)\()/ 15788395040605840 \)
\(\beta_{12}\)\(=\)\((\)\(-17924326795869 \nu^{13} + 23455557245524 \nu^{12} + 879153061774715 \nu^{11} - 953369861904061 \nu^{10} - 16369355249611440 \nu^{9} + 14477216382795401 \nu^{8} + 143065720146530890 \nu^{7} - 103215181842607525 \nu^{6} - 586122971969355440 \nu^{5} + 354134323447064406 \nu^{4} + 966238739011843464 \nu^{3} - 500374230332802640 \nu^{2} - 384292349947742024 \nu + 166761480409701264\)\()/ 15788395040605840 \)
\(\beta_{13}\)\(=\)\((\)\(-21287880786177 \nu^{13} + 51088675909607 \nu^{12} + 889326633697785 \nu^{11} - 1730523496563728 \nu^{10} - 14193063964416095 \nu^{9} + 21117514546830813 \nu^{8} + 106085745505489865 \nu^{7} - 116847168938051585 \nu^{6} - 361806925655129755 \nu^{5} + 320335811846240008 \nu^{4} + 460439267349737952 \nu^{3} - 452152041773406660 \nu^{2} - 163056024996551552 \nu + 182105343465589472\)\()/ 15788395040605840 \)
\(1\)\(=\)\(\beta_0\)
\(\nu\)\(=\)\(\beta_{1}\)
\(\nu^{2}\)\(=\)\(\beta_{4} - \beta_{3} - \beta_{2} + 7\)
\(\nu^{3}\)\(=\)\(\beta_{13} - \beta_{12} - \beta_{11} - \beta_{10} - \beta_{8} - \beta_{7} - \beta_{5} + 2 \beta_{4} - 3 \beta_{2} + 11 \beta_{1} + 2\)
\(\nu^{4}\)\(=\)\(3 \beta_{13} - \beta_{12} - \beta_{11} - 2 \beta_{10} - 2 \beta_{9} - 4 \beta_{8} + 2 \beta_{7} - 2 \beta_{6} - \beta_{5} + 16 \beta_{4} - 14 \beta_{3} - 18 \beta_{2} + 7 \beta_{1} + 71\)
\(\nu^{5}\)\(=\)\(19 \beta_{13} - 18 \beta_{12} - 23 \beta_{11} - 19 \beta_{10} - 8 \beta_{9} - 20 \beta_{8} - 19 \beta_{7} + 5 \beta_{6} - 17 \beta_{5} + 45 \beta_{4} - 6 \beta_{3} - 62 \beta_{2} + 140 \beta_{1} + 58\)
\(\nu^{6}\)\(=\)\(71 \beta_{13} - 25 \beta_{12} - 24 \beta_{11} - 46 \beta_{10} - 52 \beta_{9} - 91 \beta_{8} + 44 \beta_{7} - 45 \beta_{6} - 11 \beta_{5} + 243 \beta_{4} - 191 \beta_{3} - 292 \beta_{2} + 193 \beta_{1} + 860\)
\(\nu^{7}\)\(=\)\(310 \beta_{13} - 281 \beta_{12} - 405 \beta_{11} - 292 \beta_{10} - 208 \beta_{9} - 346 \beta_{8} - 272 \beta_{7} + 144 \beta_{6} - 222 \beta_{5} + 819 \beta_{4} - 180 \beta_{3} - 1093 \beta_{2} + 1955 \beta_{1} + 1252\)
\(\nu^{8}\)\(=\)\(1320 \beta_{13} - 501 \beta_{12} - 473 \beta_{11} - 784 \beta_{10} - 1058 \beta_{9} - 1652 \beta_{8} + 768 \beta_{7} - 692 \beta_{6} - 38 \beta_{5} + 3752 \beta_{4} - 2706 \beta_{3} - 4713 \beta_{2} + 3995 \beta_{1} + 11634\)
\(\nu^{9}\)\(=\)\(4995 \beta_{13} - 4282 \beta_{12} - 6505 \beta_{11} - 4184 \beta_{10} - 4174 \beta_{9} - 5947 \beta_{8} - 3500 \beta_{7} + 2936 \beta_{6} - 2530 \beta_{5} + 13971 \beta_{4} - 3942 \beta_{3} - 18446 \beta_{2} + 28994 \beta_{1} + 24063\)
\(\nu^{10}\)\(=\)\(22756 \beta_{13} - 9271 \beta_{12} - 8770 \beta_{11} - 11800 \beta_{10} - 19844 \beta_{9} - 28501 \beta_{8} + 12532 \beta_{7} - 8865 \beta_{6} + 1536 \beta_{5} + 59188 \beta_{4} - 39780 \beta_{3} - 76621 \beta_{2} + 74525 \beta_{1} + 169394\)
\(\nu^{11}\)\(=\)\(81353 \beta_{13} - 65487 \beta_{12} - 100665 \beta_{11} - 57174 \beta_{10} - 77614 \beta_{9} - 103428 \beta_{8} - 41640 \beta_{7} + 52937 \beta_{6} - 24732 \beta_{5} + 232684 \beta_{4} - 76579 \beta_{3} - 307057 \beta_{2} + 446895 \beta_{1} + 437040\)
\(\nu^{12}\)\(=\)\(380736 \beta_{13} - 164714 \beta_{12} - 156937 \beta_{11} - 162943 \beta_{10} - 358722 \beta_{9} - 487858 \beta_{8} + 200505 \beta_{7} - 95762 \beta_{6} + 56233 \beta_{5} + 949565 \beta_{4} - 602482 \beta_{3} - 1255126 \beta_{2} + 1324332 \beta_{1} + 2589789\)
\(\nu^{13}\)\(=\)\(1339890 \beta_{13} - 1013394 \beta_{12} - 1533614 \beta_{11} - 739948 \beta_{10} - 1402056 \beta_{9} - 1815204 \beta_{8} - 447344 \beta_{7} + 907917 \beta_{6} - 167693 \beta_{5} + 3840807 \beta_{4} - 1403512 \beta_{3} - 5093009 \beta_{2} + 7061050 \beta_{1} + 7704906\)

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 \(\iota_m(\nu)\) \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1.1
−3.63246
−3.15319
−3.00862
−2.67453
−1.69357
−1.44259
−0.625391
0.800423
1.26062
2.33625
2.45834
3.24808
3.97677
4.14985
1.00000 −1.00000 1.00000 −3.63246 −1.00000 4.65920 1.00000 1.00000 −3.63246
1.2 1.00000 −1.00000 1.00000 −3.15319 −1.00000 −5.11963 1.00000 1.00000 −3.15319
1.3 1.00000 −1.00000 1.00000 −3.00862 −1.00000 −0.900066 1.00000 1.00000 −3.00862
1.4 1.00000 −1.00000 1.00000 −2.67453 −1.00000 −1.12425 1.00000 1.00000 −2.67453
1.5 1.00000 −1.00000 1.00000 −1.69357 −1.00000 3.25998 1.00000 1.00000 −1.69357
1.6 1.00000 −1.00000 1.00000 −1.44259 −1.00000 2.70884 1.00000 1.00000 −1.44259
1.7 1.00000 −1.00000 1.00000 −0.625391 −1.00000 −1.55533 1.00000 1.00000 −0.625391
1.8 1.00000 −1.00000 1.00000 0.800423 −1.00000 −4.52948 1.00000 1.00000 0.800423
1.9 1.00000 −1.00000 1.00000 1.26062 −1.00000 3.87711 1.00000 1.00000 1.26062
1.10 1.00000 −1.00000 1.00000 2.33625 −1.00000 −0.683869 1.00000 1.00000 2.33625
1.11 1.00000 −1.00000 1.00000 2.45834 −1.00000 −3.89101 1.00000 1.00000 2.45834
1.12 1.00000 −1.00000 1.00000 3.24808 −1.00000 4.67729 1.00000 1.00000 3.24808
1.13 1.00000 −1.00000 1.00000 3.97677 −1.00000 1.13692 1.00000 1.00000 3.97677
1.14 1.00000 −1.00000 1.00000 4.14985 −1.00000 −1.51570 1.00000 1.00000 4.14985
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.14
Significant digits:
Format:

Inner twists

This newform does not admit any (nontrivial) inner twists.

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 6018.2.a.bc 14
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
6018.2.a.bc 14 1.a even 1 1 trivial

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(3\) \(1\)
\(17\) \(-1\)
\(59\) \(-1\)

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(6018))\):

\(T_{5}^{14} - \cdots\)
\(T_{7}^{14} - \cdots\)