Properties

Label 6017.2.a.e
Level 6017
Weight 2
Character orbit 6017.a
Self dual Yes
Analytic conductor 48.046
Analytic rank 0
Dimension 119
CM No

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Newspace parameters

Level: \( N \) = \( 6017 = 11 \cdot 547 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6017.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.0459868962\)
Analytic rank: \(0\)
Dimension: \(119\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \(119q \) \(\mathstrut +\mathstrut 15q^{2} \) \(\mathstrut +\mathstrut 15q^{3} \) \(\mathstrut +\mathstrut 133q^{4} \) \(\mathstrut +\mathstrut 6q^{5} \) \(\mathstrut +\mathstrut 16q^{6} \) \(\mathstrut +\mathstrut 72q^{7} \) \(\mathstrut +\mathstrut 39q^{8} \) \(\mathstrut +\mathstrut 128q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(119q \) \(\mathstrut +\mathstrut 15q^{2} \) \(\mathstrut +\mathstrut 15q^{3} \) \(\mathstrut +\mathstrut 133q^{4} \) \(\mathstrut +\mathstrut 6q^{5} \) \(\mathstrut +\mathstrut 16q^{6} \) \(\mathstrut +\mathstrut 72q^{7} \) \(\mathstrut +\mathstrut 39q^{8} \) \(\mathstrut +\mathstrut 128q^{9} \) \(\mathstrut +\mathstrut 22q^{10} \) \(\mathstrut +\mathstrut 119q^{11} \) \(\mathstrut +\mathstrut 40q^{12} \) \(\mathstrut +\mathstrut 67q^{13} \) \(\mathstrut +\mathstrut 3q^{14} \) \(\mathstrut +\mathstrut 22q^{15} \) \(\mathstrut +\mathstrut 145q^{16} \) \(\mathstrut +\mathstrut 57q^{17} \) \(\mathstrut +\mathstrut 53q^{18} \) \(\mathstrut +\mathstrut 68q^{19} \) \(\mathstrut +\mathstrut 25q^{20} \) \(\mathstrut +\mathstrut 21q^{21} \) \(\mathstrut +\mathstrut 15q^{22} \) \(\mathstrut +\mathstrut 21q^{23} \) \(\mathstrut +\mathstrut 34q^{24} \) \(\mathstrut +\mathstrut 137q^{25} \) \(\mathstrut +\mathstrut 10q^{26} \) \(\mathstrut +\mathstrut 54q^{27} \) \(\mathstrut +\mathstrut 149q^{28} \) \(\mathstrut +\mathstrut 46q^{29} \) \(\mathstrut +\mathstrut 10q^{30} \) \(\mathstrut +\mathstrut 87q^{31} \) \(\mathstrut +\mathstrut 58q^{32} \) \(\mathstrut +\mathstrut 15q^{33} \) \(\mathstrut +\mathstrut 16q^{34} \) \(\mathstrut +\mathstrut 40q^{35} \) \(\mathstrut +\mathstrut 137q^{36} \) \(\mathstrut +\mathstrut 39q^{37} \) \(\mathstrut +\mathstrut 27q^{38} \) \(\mathstrut +\mathstrut 72q^{39} \) \(\mathstrut +\mathstrut 46q^{40} \) \(\mathstrut +\mathstrut 50q^{41} \) \(\mathstrut -\mathstrut 4q^{42} \) \(\mathstrut +\mathstrut 122q^{43} \) \(\mathstrut +\mathstrut 133q^{44} \) \(\mathstrut +\mathstrut 12q^{45} \) \(\mathstrut +\mathstrut 22q^{46} \) \(\mathstrut +\mathstrut 92q^{47} \) \(\mathstrut +\mathstrut 9q^{48} \) \(\mathstrut +\mathstrut 161q^{49} \) \(\mathstrut +\mathstrut 2q^{50} \) \(\mathstrut -\mathstrut 12q^{51} \) \(\mathstrut +\mathstrut 177q^{52} \) \(\mathstrut +\mathstrut 12q^{53} \) \(\mathstrut +\mathstrut 19q^{54} \) \(\mathstrut +\mathstrut 6q^{55} \) \(\mathstrut -\mathstrut 16q^{56} \) \(\mathstrut +\mathstrut 43q^{57} \) \(\mathstrut +\mathstrut 56q^{58} \) \(\mathstrut +\mathstrut 39q^{59} \) \(\mathstrut +\mathstrut 27q^{60} \) \(\mathstrut +\mathstrut 114q^{61} \) \(\mathstrut +\mathstrut 66q^{62} \) \(\mathstrut +\mathstrut 196q^{63} \) \(\mathstrut +\mathstrut 161q^{64} \) \(\mathstrut +\mathstrut 7q^{65} \) \(\mathstrut +\mathstrut 16q^{66} \) \(\mathstrut +\mathstrut 59q^{67} \) \(\mathstrut +\mathstrut 139q^{68} \) \(\mathstrut -\mathstrut 24q^{69} \) \(\mathstrut +\mathstrut 9q^{70} \) \(\mathstrut +\mathstrut 11q^{71} \) \(\mathstrut +\mathstrut 92q^{72} \) \(\mathstrut +\mathstrut 123q^{73} \) \(\mathstrut +\mathstrut q^{74} \) \(\mathstrut +\mathstrut 19q^{75} \) \(\mathstrut +\mathstrut 92q^{76} \) \(\mathstrut +\mathstrut 72q^{77} \) \(\mathstrut -\mathstrut 101q^{78} \) \(\mathstrut +\mathstrut 78q^{79} \) \(\mathstrut -\mathstrut 34q^{80} \) \(\mathstrut +\mathstrut 139q^{81} \) \(\mathstrut +\mathstrut 73q^{82} \) \(\mathstrut +\mathstrut 108q^{83} \) \(\mathstrut -\mathstrut 31q^{84} \) \(\mathstrut +\mathstrut 30q^{85} \) \(\mathstrut -\mathstrut 18q^{86} \) \(\mathstrut +\mathstrut 164q^{87} \) \(\mathstrut +\mathstrut 39q^{88} \) \(\mathstrut +\mathstrut 15q^{89} \) \(\mathstrut -\mathstrut 41q^{90} \) \(\mathstrut +\mathstrut 60q^{91} \) \(\mathstrut -\mathstrut 26q^{92} \) \(\mathstrut -\mathstrut 2q^{93} \) \(\mathstrut +\mathstrut 45q^{94} \) \(\mathstrut +\mathstrut 75q^{95} \) \(\mathstrut +\mathstrut 42q^{96} \) \(\mathstrut +\mathstrut 73q^{97} \) \(\mathstrut +\mathstrut 32q^{98} \) \(\mathstrut +\mathstrut 128q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1.1 −2.72929 2.06420 5.44901 −2.31705 −5.63378 0.650725 −9.41333 1.26091 6.32390
1.2 −2.72367 −2.85757 5.41840 −2.70389 7.78308 4.38831 −9.31062 5.16569 7.36452
1.3 −2.68163 0.369101 5.19115 2.09046 −0.989794 1.10498 −8.55750 −2.86376 −5.60585
1.4 −2.67204 2.89488 5.13980 2.14144 −7.73524 4.84141 −8.38968 5.38033 −5.72201
1.5 −2.64305 −0.959171 4.98572 −4.09680 2.53514 −1.46535 −7.89140 −2.07999 10.8280
1.6 −2.64280 −2.08644 4.98439 2.06491 5.51405 1.23299 −7.88714 1.35325 −5.45715
1.7 −2.59415 −0.508113 4.72962 4.04973 1.31812 4.63801 −7.08105 −2.74182 −10.5056
1.8 −2.46359 −1.49738 4.06928 −0.810928 3.68894 4.87400 −5.09785 −0.757845 1.99779
1.9 −2.40399 −2.26995 3.77918 −1.51011 5.45695 −2.08665 −4.27714 2.15269 3.63028
1.10 −2.39877 0.712166 3.75408 0.976168 −1.70832 −3.65167 −4.20764 −2.49282 −2.34160
1.11 −2.37466 0.769590 3.63899 −2.34020 −1.82751 −2.65740 −3.89204 −2.40773 5.55717
1.12 −2.35458 −1.66572 3.54404 1.38814 3.92207 −2.86994 −3.63557 −0.225374 −3.26849
1.13 −2.35115 2.19609 3.52790 0.407257 −5.16332 −2.35563 −3.59233 1.82279 −0.957522
1.14 −2.33754 1.15439 3.46412 −4.35932 −2.69844 3.66625 −3.42244 −1.66738 10.1901
1.15 −2.30862 2.25355 3.32972 2.61387 −5.20258 1.15866 −3.06981 2.07847 −6.03443
1.16 −2.22427 3.08840 2.94737 −2.11023 −6.86944 3.85755 −2.10721 6.53822 4.69372
1.17 −2.14072 −2.03723 2.58269 3.12940 4.36115 −2.52931 −1.24739 1.15032 −6.69918
1.18 −1.98872 0.557360 1.95500 0.637327 −1.10843 2.66044 0.0894893 −2.68935 −1.26746
1.19 −1.97087 1.79688 1.88432 −3.99793 −3.54141 −0.876225 0.227993 0.228774 7.87939
1.20 −1.94884 3.22760 1.79797 1.61357 −6.29006 −0.583291 0.393727 7.41737 −3.14458
See next 80 embeddings (of 119 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.119
Significant digits:
Format:

Inner twists

This newform does not have CM; other inner twists have not been computed.

Atkin-Lehner signs

\( p \) Sign
\(11\) \(-1\)
\(547\) \(1\)

Hecke kernels

This newform can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(6017))\):

\(T_{2}^{119} - \cdots\)
\(T_{3}^{119} - \cdots\)