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Properties

Label 3179.2.a.bi
Level $3179$
Weight $2$
Character orbit 3179.a
Self dual yes
Analytic conductor $25.384$
Analytic rank $0$
Dimension $28$
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] = [3179,2,Mod(1,3179)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3179, 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("3179.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 3179 = 11 \cdot 17^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3179.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: \(25.3844428026\)
Analytic rank: \(0\)
Dimension: \(28\)
Twist minimal: no (minimal twist has level 187)
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.

\(\operatorname{Tr}(f)(q) = \) \( 28 q + 8 q^{3} + 24 q^{4} + 16 q^{5} + 16 q^{6} + 12 q^{7} + 20 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 28 q + 8 q^{3} + 24 q^{4} + 16 q^{5} + 16 q^{6} + 12 q^{7} + 20 q^{9} + 24 q^{10} - 28 q^{11} + 24 q^{12} + 16 q^{14} - 16 q^{15} + 16 q^{16} + 32 q^{20} + 8 q^{23} - 8 q^{24} + 20 q^{25} - 24 q^{26} + 32 q^{27} + 32 q^{28} + 36 q^{29} + 40 q^{30} + 56 q^{31} + 40 q^{32} - 8 q^{33} + 16 q^{35} + 40 q^{36} + 64 q^{37} - 8 q^{38} + 32 q^{39} + 72 q^{40} + 28 q^{41} + 24 q^{42} + 16 q^{43} - 24 q^{44} + 24 q^{45} - 36 q^{47} + 56 q^{48} + 16 q^{49} + 56 q^{50} - 20 q^{53} + 64 q^{54} - 16 q^{55} + 48 q^{56} + 32 q^{57} - 16 q^{58} - 28 q^{59} + 8 q^{60} + 104 q^{61} - 8 q^{62} + 28 q^{63} + 32 q^{65} - 16 q^{66} - 12 q^{67} - 32 q^{69} + 40 q^{71} + 40 q^{72} + 76 q^{73} + 24 q^{74} - 16 q^{75} - 16 q^{76} - 12 q^{77} - 24 q^{78} + 24 q^{79} + 8 q^{80} + 12 q^{81} + 56 q^{82} + 32 q^{83} - 40 q^{84} - 16 q^{86} - 8 q^{87} - 52 q^{89} + 16 q^{90} + 80 q^{91} - 56 q^{92} + 24 q^{97} - 24 q^{98} - 20 q^{99}+O(q^{100}) \) 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 −2.57447 −0.262331 4.62792 −1.26895 0.675364 −0.195142 −6.76552 −2.93118 3.26688
1.2 −2.42395 2.89926 3.87553 −2.22550 −7.02766 −1.23132 −4.54618 5.40573 5.39450
1.3 −2.40039 1.98044 3.76185 1.54647 −4.75381 3.54271 −4.22913 0.922127 −3.71212
1.4 −2.31697 −0.164442 3.36837 0.0254514 0.381007 −3.93176 −3.17047 −2.97296 −0.0589703
1.5 −2.07580 −1.79573 2.30896 −1.45571 3.72759 4.42094 −0.641346 0.224658 3.02177
1.6 −1.86094 −3.04898 1.46310 4.00111 5.67397 2.90599 0.999144 6.29627 −7.44583
1.7 −1.58514 −2.48730 0.512654 0.985381 3.94270 −2.21700 2.35764 3.18665 −1.56196
1.8 −1.48538 1.25787 0.206341 0.557132 −1.86841 −3.17779 2.66426 −1.41777 −0.827551
1.9 −1.27330 0.253917 −0.378700 2.03961 −0.323314 −2.19108 3.02881 −2.93553 −2.59704
1.10 −1.18051 2.90707 −0.606407 −1.56905 −3.43181 0.377318 3.07688 5.45105 1.85228
1.11 −1.06445 −2.41033 −0.866938 −1.04101 2.56569 1.06429 3.05172 2.80969 1.10810
1.12 −0.365948 0.910193 −1.86608 4.13843 −0.333083 4.25066 1.41478 −2.17155 −1.51445
1.13 −0.185341 −1.44802 −1.96565 −2.00436 0.268379 0.596525 0.734999 −0.903233 0.371491
1.14 0.0977087 −2.00936 −1.99045 4.15379 −0.196332 −1.90685 −0.389902 1.03754 0.405861
1.15 0.132166 0.341095 −1.98253 −1.32478 0.0450811 3.97147 −0.526354 −2.88365 −0.175090
1.16 0.546622 1.99091 −1.70120 2.03051 1.08827 3.18620 −2.02316 0.963711 1.10992
1.17 0.558491 2.55533 −1.68809 −2.99225 1.42713 −0.944321 −2.05976 3.52969 −1.67114
1.18 0.811826 0.325394 −1.34094 −1.65316 0.264163 −4.66644 −2.71226 −2.89412 −1.34208
1.19 0.993655 1.33642 −1.01265 −3.92751 1.32794 1.61937 −2.99353 −1.21398 −3.90259
1.20 1.05589 −0.418655 −0.885097 1.19765 −0.442053 −3.31423 −3.04634 −2.82473 1.26458
See all 28 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.28
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(11\) \(1\)
\(17\) \(-1\)

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 3179.2.a.bi 28
17.b even 2 1 3179.2.a.bh 28
17.e odd 16 2 187.2.h.a ✓ 56
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
187.2.h.a ✓ 56 17.e odd 16 2
3179.2.a.bh 28 17.b even 2 1
3179.2.a.bi 28 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(3179))\):

\( T_{2}^{28} - 40 T_{2}^{26} + 704 T_{2}^{24} - 8 T_{2}^{23} - 7184 T_{2}^{22} + 248 T_{2}^{21} + \cdots - 32 \) Copy content Toggle raw display
\( T_{3}^{28} - 8 T_{3}^{27} - 20 T_{3}^{26} + 304 T_{3}^{25} - 102 T_{3}^{24} - 4888 T_{3}^{23} + \cdots + 34 \) Copy content Toggle raw display
\( T_{5}^{28} - 16 T_{5}^{27} + 48 T_{5}^{26} + 512 T_{5}^{25} - 3388 T_{5}^{24} - 3096 T_{5}^{23} + \cdots + 101128 \) Copy content Toggle raw display