# 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 Inner twists $1$

# Related objects

## 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: $$106$$ Twist minimal: yes 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.

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

## 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: Complex embeddings Normalized embeddings Satake parameters Satake angles

## Atkin-Lehner signs

$$p$$ Sign
$$11$$ $$-1$$
$$547$$ $$-1$$

## 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 6017.2.a.c 106

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
6017.2.a.c 106 1.a even 1 1 trivial

## Hecke kernels

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

 $$T_{2}^{106} + \cdots$$ $$T_{3}^{106} + \cdots$$

## Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database