Properties

Label 6017.2.a.d
Level $6017$
Weight $2$
Character orbit 6017.a
Self dual yes
Analytic conductor $48.046$
Analytic rank $1$
Dimension $107$
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: \(1\)
Dimension: \(107\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 107 q - 3 q^{2} - 18 q^{3} + 91 q^{4} - 15 q^{5} - 54 q^{7} - 3 q^{8} + 95 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 107 q - 3 q^{2} - 18 q^{3} + 91 q^{4} - 15 q^{5} - 54 q^{7} - 3 q^{8} + 95 q^{9} - 14 q^{10} - 107 q^{11} - 50 q^{12} - 24 q^{13} - 17 q^{14} - 47 q^{15} + 63 q^{16} + 25 q^{17} - 37 q^{18} - 55 q^{19} - 31 q^{20} + 15 q^{21} + 3 q^{22} - 38 q^{23} + 4 q^{24} + 62 q^{25} - 16 q^{26} - 57 q^{27} - 101 q^{28} + 27 q^{29} - 14 q^{30} - 112 q^{31} - 4 q^{32} + 18 q^{33} - 66 q^{34} + 8 q^{35} + 35 q^{36} - 60 q^{37} - 45 q^{38} - 58 q^{39} - 50 q^{40} - 14 q^{41} - 36 q^{42} - 78 q^{43} - 91 q^{44} - 68 q^{45} - 18 q^{46} - 109 q^{47} - 99 q^{48} + 61 q^{49} - 32 q^{50} - 10 q^{51} - 111 q^{52} - 30 q^{53} - 3 q^{54} + 15 q^{55} - 44 q^{56} + q^{57} - 98 q^{58} - 48 q^{59} - 119 q^{60} - 30 q^{61} + 32 q^{62} - 126 q^{63} + 3 q^{64} + 43 q^{65} - 77 q^{67} + 53 q^{68} - 51 q^{69} - 87 q^{70} - 40 q^{71} - 82 q^{72} - 83 q^{73} + 11 q^{74} - 69 q^{75} - 108 q^{76} + 54 q^{77} - 53 q^{78} - 66 q^{79} - 96 q^{80} + 51 q^{81} - 133 q^{82} - 32 q^{83} + 27 q^{84} - 66 q^{85} - 46 q^{86} - 136 q^{87} + 3 q^{88} - 56 q^{89} + 9 q^{90} - 86 q^{91} - 94 q^{92} - 33 q^{93} - 93 q^{94} - 25 q^{95} - 4 q^{96} - 109 q^{97} - 38 q^{98} - 95 q^{99}+O(q^{100}) \) 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 −2.75999 −3.06184 5.61754 −2.40388 8.45065 −3.94507 −9.98436 6.37487 6.63467
1.2 −2.74218 −0.127111 5.51953 0.930528 0.348561 −1.52234 −9.65117 −2.98384 −2.55167
1.3 −2.62131 1.98857 4.87127 −3.39892 −5.21266 −2.62575 −7.52650 0.954412 8.90963
1.4 −2.60586 −1.61281 4.79053 1.44359 4.20277 4.40298 −7.27174 −0.398838 −3.76179
1.5 −2.59133 1.08669 4.71497 2.54775 −2.81596 −0.206322 −7.03537 −1.81911 −6.60204
1.6 −2.52748 −3.01490 4.38814 1.64213 7.62008 3.19622 −6.03597 6.08959 −4.15044
1.7 −2.41913 2.57679 3.85218 −1.00520 −6.23359 1.76420 −4.48067 3.63986 2.43171
1.8 −2.41316 −1.13111 3.82334 3.33661 2.72954 −4.21510 −4.40000 −1.72060 −8.05177
1.9 −2.40409 −1.43849 3.77967 −1.50400 3.45826 0.877876 −4.27850 −0.930757 3.61576
1.10 −2.38163 −3.08400 3.67215 2.12353 7.34495 −4.46240 −3.98245 6.51107 −5.05746
1.11 −2.34564 1.00441 3.50205 3.21165 −2.35600 2.32596 −3.52327 −1.99115 −7.53339
1.12 −2.29221 −1.10986 3.25421 −2.25000 2.54402 −3.87042 −2.87492 −1.76822 5.15746
1.13 −2.27956 2.53160 3.19638 −2.07837 −5.77093 −1.61665 −2.72721 3.40901 4.73776
1.14 −2.25361 −2.32484 3.07875 −3.74526 5.23928 −1.13542 −2.43109 2.40489 8.44036
1.15 −2.23665 0.286457 3.00262 −1.07868 −0.640706 −2.04238 −2.24251 −2.91794 2.41263
1.16 −2.18792 2.65305 2.78699 0.440982 −5.80465 2.17034 −1.72186 4.03866 −0.964832
1.17 −2.16456 1.81828 2.68531 1.50320 −3.93577 −2.76616 −1.48340 0.306139 −3.25377
1.18 −2.10238 0.723159 2.42000 −4.03444 −1.52035 0.772372 −0.882990 −2.47704 8.48191
1.19 −2.03276 −2.20432 2.13212 2.54068 4.48086 2.78766 −0.268560 1.85904 −5.16459
1.20 −1.94021 −0.488619 1.76440 −3.27450 0.948022 −5.11134 0.457109 −2.76125 6.35321
See next 80 embeddings (of 107 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.107
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.d 107
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
6017.2.a.d 107 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(6017))\):

\( T_{2}^{107} + 3 T_{2}^{106} - 148 T_{2}^{105} - 448 T_{2}^{104} + 10594 T_{2}^{103} + 32379 T_{2}^{102} - 488643 T_{2}^{101} - 1509048 T_{2}^{100} + 16324926 T_{2}^{99} + 50982788 T_{2}^{98} - 421009081 T_{2}^{97} + \cdots - 19904 \) Copy content Toggle raw display
\( T_{3}^{107} + 18 T_{3}^{106} - 46 T_{3}^{105} - 2717 T_{3}^{104} - 7408 T_{3}^{103} + 187989 T_{3}^{102} + 1025495 T_{3}^{101} - 7677676 T_{3}^{100} - 64496240 T_{3}^{99} + 190707793 T_{3}^{98} + \cdots - 2485795611644 \) Copy content Toggle raw display