Properties

Label 6017.2.a.c
Level 6017
Weight 2
Character orbit 6017.a
Self dual Yes
Analytic conductor 48.046
Analytic rank 1
Dimension 106
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: \(1\)
Dimension: \(106\)
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.

\(\operatorname{Tr}(f)(q) = \) \(106q \) \(\mathstrut -\mathstrut 13q^{2} \) \(\mathstrut -\mathstrut 15q^{3} \) \(\mathstrut +\mathstrut 93q^{4} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut -\mathstrut 22q^{6} \) \(\mathstrut -\mathstrut 66q^{7} \) \(\mathstrut -\mathstrut 39q^{8} \) \(\mathstrut +\mathstrut 97q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(106q \) \(\mathstrut -\mathstrut 13q^{2} \) \(\mathstrut -\mathstrut 15q^{3} \) \(\mathstrut +\mathstrut 93q^{4} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut -\mathstrut 22q^{6} \) \(\mathstrut -\mathstrut 66q^{7} \) \(\mathstrut -\mathstrut 39q^{8} \) \(\mathstrut +\mathstrut 97q^{9} \) \(\mathstrut -\mathstrut 30q^{10} \) \(\mathstrut +\mathstrut 106q^{11} \) \(\mathstrut -\mathstrut 26q^{12} \) \(\mathstrut -\mathstrut 72q^{13} \) \(\mathstrut +\mathstrut 3q^{14} \) \(\mathstrut -\mathstrut 46q^{15} \) \(\mathstrut +\mathstrut 75q^{16} \) \(\mathstrut -\mathstrut 65q^{17} \) \(\mathstrut -\mathstrut 37q^{18} \) \(\mathstrut -\mathstrut 63q^{19} \) \(\mathstrut -\mathstrut 25q^{20} \) \(\mathstrut -\mathstrut 27q^{21} \) \(\mathstrut -\mathstrut 13q^{22} \) \(\mathstrut -\mathstrut 23q^{23} \) \(\mathstrut -\mathstrut 56q^{24} \) \(\mathstrut +\mathstrut 74q^{25} \) \(\mathstrut +\mathstrut 2q^{26} \) \(\mathstrut -\mathstrut 54q^{27} \) \(\mathstrut -\mathstrut 115q^{28} \) \(\mathstrut -\mathstrut 45q^{29} \) \(\mathstrut -\mathstrut 14q^{30} \) \(\mathstrut -\mathstrut 89q^{31} \) \(\mathstrut -\mathstrut 96q^{32} \) \(\mathstrut -\mathstrut 15q^{33} \) \(\mathstrut -\mathstrut 26q^{34} \) \(\mathstrut -\mathstrut 52q^{35} \) \(\mathstrut +\mathstrut 91q^{36} \) \(\mathstrut -\mathstrut 35q^{37} \) \(\mathstrut +\mathstrut 7q^{38} \) \(\mathstrut -\mathstrut 34q^{39} \) \(\mathstrut -\mathstrut 74q^{40} \) \(\mathstrut -\mathstrut 32q^{41} \) \(\mathstrut -\mathstrut 94q^{43} \) \(\mathstrut +\mathstrut 93q^{44} \) \(\mathstrut -\mathstrut 46q^{45} \) \(\mathstrut -\mathstrut 20q^{46} \) \(\mathstrut -\mathstrut 105q^{47} \) \(\mathstrut -\mathstrut 57q^{48} \) \(\mathstrut +\mathstrut 80q^{49} \) \(\mathstrut -\mathstrut 60q^{50} \) \(\mathstrut -\mathstrut 36q^{51} \) \(\mathstrut -\mathstrut 137q^{52} \) \(\mathstrut -\mathstrut 61q^{54} \) \(\mathstrut -\mathstrut 12q^{55} \) \(\mathstrut +\mathstrut 32q^{56} \) \(\mathstrut -\mathstrut 71q^{57} \) \(\mathstrut -\mathstrut 28q^{58} \) \(\mathstrut -\mathstrut 15q^{59} \) \(\mathstrut -\mathstrut 21q^{60} \) \(\mathstrut -\mathstrut 80q^{61} \) \(\mathstrut -\mathstrut 84q^{62} \) \(\mathstrut -\mathstrut 182q^{63} \) \(\mathstrut +\mathstrut 55q^{64} \) \(\mathstrut -\mathstrut 73q^{65} \) \(\mathstrut -\mathstrut 22q^{66} \) \(\mathstrut -\mathstrut 58q^{67} \) \(\mathstrut -\mathstrut 145q^{68} \) \(\mathstrut -\mathstrut 8q^{69} \) \(\mathstrut -\mathstrut 39q^{70} \) \(\mathstrut -\mathstrut 11q^{71} \) \(\mathstrut -\mathstrut 100q^{72} \) \(\mathstrut -\mathstrut 155q^{73} \) \(\mathstrut -\mathstrut 15q^{74} \) \(\mathstrut -\mathstrut 15q^{75} \) \(\mathstrut -\mathstrut 132q^{76} \) \(\mathstrut -\mathstrut 66q^{77} \) \(\mathstrut -\mathstrut 45q^{78} \) \(\mathstrut -\mathstrut 50q^{79} \) \(\mathstrut -\mathstrut 28q^{80} \) \(\mathstrut +\mathstrut 114q^{81} \) \(\mathstrut -\mathstrut 57q^{82} \) \(\mathstrut -\mathstrut 96q^{83} \) \(\mathstrut -\mathstrut 27q^{84} \) \(\mathstrut -\mathstrut 74q^{85} \) \(\mathstrut +\mathstrut 54q^{86} \) \(\mathstrut -\mathstrut 182q^{87} \) \(\mathstrut -\mathstrut 39q^{88} \) \(\mathstrut +\mathstrut 9q^{89} \) \(\mathstrut -\mathstrut 53q^{90} \) \(\mathstrut +\mathstrut 6q^{91} \) \(\mathstrut -\mathstrut 18q^{92} \) \(\mathstrut -\mathstrut 26q^{93} \) \(\mathstrut -\mathstrut 33q^{94} \) \(\mathstrut -\mathstrut 49q^{95} \) \(\mathstrut -\mathstrut 56q^{96} \) \(\mathstrut -\mathstrut 102q^{97} \) \(\mathstrut -\mathstrut 76q^{98} \) \(\mathstrut +\mathstrut 97q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −2.78235 −0.369906 5.74149 −3.02150 1.02921 −3.23246 −10.4101 −2.86317 8.40687
1.2 −2.76753 −2.67959 5.65924 2.34491 7.41585 −2.59530 −10.1271 4.18020 −6.48960
1.3 −2.73187 −0.157601 5.46313 2.56928 0.430546 −5.24072 −9.46082 −2.97516 −7.01894
1.4 −2.70820 2.96568 5.33437 −1.26109 −8.03167 1.85077 −9.03015 5.79526 3.41529
1.5 −2.66450 0.632884 5.09957 −0.0737087 −1.68632 1.42532 −8.25880 −2.59946 0.196397
1.6 −2.61585 1.81779 4.84270 3.74717 −4.75507 0.406260 −7.43608 0.304348 −9.80206
1.7 −2.58511 −2.87890 4.68281 −1.51557 7.44229 0.161489 −6.93538 5.28808 3.91792
1.8 −2.57284 2.82606 4.61950 1.34186 −7.27099 −3.61511 −6.73954 4.98661 −3.45239
1.9 −2.47702 3.19961 4.13562 −3.89998 −7.92550 −4.57915 −5.28996 7.23752 9.66032
1.10 −2.43520 −0.763891 3.93019 1.56797 1.86023 2.19104 −4.70040 −2.41647 −3.81832
1.11 −2.42329 −0.918445 3.87233 −2.10804 2.22566 −2.69568 −4.53719 −2.15646 5.10839
1.12 −2.39408 −0.179689 3.73161 −1.83517 0.430189 0.373924 −4.14560 −2.96771 4.39353
1.13 −2.37596 1.38475 3.64518 0.740241 −3.29011 −0.0236528 −3.90889 −1.08246 −1.75878
1.14 −2.32740 −3.07559 3.41677 −1.26158 7.15812 0.599145 −3.29739 6.45928 2.93620
1.15 −2.32398 −3.12042 3.40089 3.91464 7.25180 −0.989043 −3.25564 6.73703 −9.09756
1.16 −2.18387 1.05356 2.76930 1.41364 −2.30083 4.87614 −1.68005 −1.89002 −3.08721
1.17 −2.16812 −0.750565 2.70073 −2.22726 1.62731 3.66777 −1.51925 −2.43665 4.82897
1.18 −2.11348 −1.48934 2.46682 2.94089 3.14770 2.33045 −0.986611 −0.781868 −6.21552
1.19 −2.01004 −2.26087 2.04024 −3.50443 4.54443 2.31355 −0.0808885 2.11154 7.04404
1.20 −1.99930 −0.450091 1.99721 2.88473 0.899867 −0.362986 0.00557515 −2.79742 −5.76745
See next 80 embeddings (of 106 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.106
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 \(S_{2}^{\mathrm{new}}(\Gamma_0(6017))\):

\(T_{2}^{106} + \cdots\)
\(T_{3}^{106} + \cdots\)