Properties

Label 6017.2.a.f
Level $6017$
Weight $2$
Character orbit 6017.a
Self dual yes
Analytic conductor $48.046$
Analytic rank $0$
Dimension $121$
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: \(0\)
Dimension: \(121\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 121 q + 2 q^{2} + 18 q^{3} + 138 q^{4} + 13 q^{5} + 10 q^{6} + 56 q^{7} + 12 q^{8} + 143 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 121 q + 2 q^{2} + 18 q^{3} + 138 q^{4} + 13 q^{5} + 10 q^{6} + 56 q^{7} + 12 q^{8} + 143 q^{9} + 20 q^{10} - 121 q^{11} + 40 q^{12} + 31 q^{13} + 7 q^{14} + 53 q^{15} + 164 q^{16} - 23 q^{17} + 14 q^{18} + 62 q^{19} + 53 q^{20} + 19 q^{21} - 2 q^{22} + 34 q^{23} + 34 q^{24} + 172 q^{25} + 34 q^{26} + 87 q^{27} + 91 q^{28} - 30 q^{29} + 2 q^{30} + 102 q^{31} + 31 q^{32} - 18 q^{33} + 30 q^{34} + 20 q^{35} + 164 q^{36} + 58 q^{37} + 35 q^{38} + 42 q^{39} + 52 q^{40} - 12 q^{41} + 56 q^{42} + 96 q^{43} - 138 q^{44} + 72 q^{45} + 48 q^{46} + 136 q^{47} + 99 q^{48} + 199 q^{49} - 7 q^{50} + 22 q^{51} + 81 q^{52} + 24 q^{53} + 37 q^{54} - 13 q^{55} + 28 q^{56} + 25 q^{57} + 76 q^{58} + 58 q^{59} + 81 q^{60} + 14 q^{61} - 2 q^{62} + 152 q^{63} + 236 q^{64} - 29 q^{65} - 10 q^{66} + 112 q^{67} - 61 q^{68} + 41 q^{69} + 105 q^{70} + 56 q^{71} + 71 q^{72} + 113 q^{73} - 23 q^{74} + 111 q^{75} + 144 q^{76} - 56 q^{77} + 59 q^{78} + 80 q^{79} + 100 q^{80} + 177 q^{81} + 123 q^{82} + 6 q^{83} + 79 q^{84} + 26 q^{85} + 14 q^{86} + 180 q^{87} - 12 q^{88} + 26 q^{89} + 75 q^{90} + 72 q^{91} + 58 q^{92} + 139 q^{93} + 37 q^{94} + 39 q^{95} + 66 q^{96} + 136 q^{97} + 7 q^{98} - 143 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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 −2.76609 1.72204 5.65124 1.59310 −4.76331 4.82706 −10.0996 −0.0345853 −4.40666
1.2 −2.74533 −1.76027 5.53683 −2.91942 4.83253 1.39362 −9.70977 0.0985659 8.01478
1.3 −2.73908 1.22981 5.50258 −1.73351 −3.36855 −3.95971 −9.59385 −1.48757 4.74824
1.4 −2.69280 3.13292 5.25118 0.629801 −8.43634 −1.84618 −8.75479 6.81521 −1.69593
1.5 −2.68922 1.49908 5.23192 −2.86648 −4.03136 3.78429 −8.69136 −0.752759 7.70861
1.6 −2.66480 −1.17356 5.10118 4.42559 3.12731 1.20677 −8.26404 −1.62275 −11.7933
1.7 −2.61029 −0.993650 4.81359 −3.58363 2.59371 2.54427 −7.34428 −2.01266 9.35430
1.8 −2.58820 0.659368 4.69880 0.894285 −1.70658 −1.01597 −6.98504 −2.56523 −2.31459
1.9 −2.57735 −3.20978 4.64274 2.33292 8.27272 1.38140 −6.81126 7.30267 −6.01276
1.10 −2.54623 −1.76925 4.48328 −0.663879 4.50492 −3.59601 −6.32301 0.130248 1.69039
1.11 −2.47328 −1.34586 4.11710 2.94670 3.32869 −2.85130 −5.23618 −1.18866 −7.28801
1.12 −2.37440 −0.379878 3.63775 −1.52566 0.901981 2.31296 −3.88867 −2.85569 3.62251
1.13 −2.32206 0.535084 3.39196 −0.511363 −1.24250 3.83500 −3.23221 −2.71368 1.18742
1.14 −2.30378 2.53807 3.30742 3.98214 −5.84717 −4.26603 −3.01201 3.44182 −9.17400
1.15 −2.29477 3.40179 3.26597 3.88142 −7.80633 2.49357 −2.90510 8.57220 −8.90697
1.16 −2.27604 3.24984 3.18035 −3.77187 −7.39676 3.04189 −2.68652 7.56146 8.58492
1.17 −2.26471 2.40007 3.12892 2.90605 −5.43547 2.22739 −2.55669 2.76034 −6.58136
1.18 −2.25579 −2.77556 3.08857 0.288075 6.26106 1.78637 −2.45557 4.70373 −0.649836
1.19 −2.22670 0.200688 2.95817 3.39958 −0.446870 −0.867591 −2.13356 −2.95972 −7.56983
1.20 −2.10704 −1.55624 2.43961 −0.464512 3.27907 −0.781558 −0.926282 −0.578102 0.978744
See next 80 embeddings (of 121 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.121
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.f 121
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
6017.2.a.f 121 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(6017))\):

\( T_{2}^{121} - 2 T_{2}^{120} - 188 T_{2}^{119} + 372 T_{2}^{118} + 17194 T_{2}^{117} - 33647 T_{2}^{116} - 1019456 T_{2}^{115} + 1972170 T_{2}^{114} + 44060514 T_{2}^{113} - 84226056 T_{2}^{112} + \cdots + 1821051786576 \) Copy content Toggle raw display
\( T_{3}^{121} - 18 T_{3}^{120} - 91 T_{3}^{119} + 3517 T_{3}^{118} - 4348 T_{3}^{117} - 324004 T_{3}^{116} + 1280446 T_{3}^{115} + 18521561 T_{3}^{114} - 113294975 T_{3}^{113} - 721690198 T_{3}^{112} + \cdots - 12\!\cdots\!24 \) Copy content Toggle raw display