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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 $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [6017,2,Mod(1,6017)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6017, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("6017.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6017 = 11 \cdot 547 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6017.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
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.

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

Display 100 coefficients 10 coefficients

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.

comment: embeddings in the coefficient field
 
gp: mfembed(f)
 
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:

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 \(S_{2}^{\mathrm{new}}(\Gamma_0(6017))\):

\( T_{2}^{106} + 13 T_{2}^{105} - 68 T_{2}^{104} - 1586 T_{2}^{103} - 44 T_{2}^{102} + 91677 T_{2}^{101} + \cdots - 180152 \) Copy content Toggle raw display
\( T_{3}^{106} + 15 T_{3}^{105} - 95 T_{3}^{104} - 2502 T_{3}^{103} + 290 T_{3}^{102} + 197423 T_{3}^{101} + \cdots + 9726334200 \) Copy content Toggle raw display