↑

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
Inner twists $1$

Related objects

Downloads

Learn more

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: \(0\)
Dimension: \(119\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 119 q + 15 q^{2} + 15 q^{3} + 133 q^{4} + 6 q^{5} + 16 q^{6} + 72 q^{7} + 39 q^{8} + 128 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 119 q + 15 q^{2} + 15 q^{3} + 133 q^{4} + 6 q^{5} + 16 q^{6} + 72 q^{7} + 39 q^{8} + 128 q^{9} + 22 q^{10} + 119 q^{11} + 40 q^{12} + 67 q^{13} + 3 q^{14} + 22 q^{15} + 145 q^{16} + 57 q^{17} + 53 q^{18} + 68 q^{19} + 25 q^{20} + 21 q^{21} + 15 q^{22} + 21 q^{23} + 34 q^{24} + 137 q^{25} + 10 q^{26} + 54 q^{27} + 149 q^{28} + 46 q^{29} + 10 q^{30} + 87 q^{31} + 58 q^{32} + 15 q^{33} + 16 q^{34} + 40 q^{35} + 137 q^{36} + 39 q^{37} + 27 q^{38} + 72 q^{39} + 46 q^{40} + 50 q^{41} - 4 q^{42} + 122 q^{43} + 133 q^{44} + 12 q^{45} + 22 q^{46} + 92 q^{47} + 9 q^{48} + 161 q^{49} + 2 q^{50} - 12 q^{51} + 177 q^{52} + 12 q^{53} + 19 q^{54} + 6 q^{55} - 16 q^{56} + 43 q^{57} + 56 q^{58} + 39 q^{59} + 27 q^{60} + 114 q^{61} + 66 q^{62} + 196 q^{63} + 161 q^{64} + 7 q^{65} + 16 q^{66} + 59 q^{67} + 139 q^{68} - 24 q^{69} + 9 q^{70} + 11 q^{71} + 92 q^{72} + 123 q^{73} + q^{74} + 19 q^{75} + 92 q^{76} + 72 q^{77} - 101 q^{78} + 78 q^{79} - 34 q^{80} + 139 q^{81} + 73 q^{82} + 108 q^{83} - 31 q^{84} + 30 q^{85} - 18 q^{86} + 164 q^{87} + 39 q^{88} + 15 q^{89} - 41 q^{90} + 60 q^{91} - 26 q^{92} - 2 q^{93} + 45 q^{94} + 75 q^{95} + 42 q^{96} + 73 q^{97} + 32 q^{98} + 128 q^{99}+O(q^{100}) \) 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 −2.72929 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:

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.e ✓ 119
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
6017.2.a.e ✓ 119 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(6017))\):

\( T_{2}^{119} - 15 T_{2}^{118} - 73 T_{2}^{117} + 2187 T_{2}^{116} - 1533 T_{2}^{115} - 150680 T_{2}^{114} + \cdots + 3654928 \) Copy content Toggle raw display
\( T_{3}^{119} - 15 T_{3}^{118} - 130 T_{3}^{117} + 3027 T_{3}^{116} + 4093 T_{3}^{115} + \cdots - 14226059242 \) Copy content Toggle raw display