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Properties

Label 8954.2.a.bu
Level $8954$
Weight $2$
Character orbit 8954.a
Self dual yes
Analytic conductor $71.498$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $1$

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [8954,2,Mod(1,8954)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("8954.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(8954, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 8954 = 2 \cdot 11^{2} \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8954.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [24,-24,8,24,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(71.4980499699\)
Analytic rank: \(0\)
Dimension: \(24\)
Twist minimal: no (minimal twist has level 814)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 24 q - 24 q^{2} + 8 q^{3} + 24 q^{4} + 6 q^{5} - 8 q^{6} - 3 q^{7} - 24 q^{8} + 36 q^{9} - 6 q^{10} + 8 q^{12} - 7 q^{13} + 3 q^{14} + 10 q^{15} + 24 q^{16} - 20 q^{17} - 36 q^{18} + 3 q^{19} + 6 q^{20}+ \cdots - 63 q^{98}+O(q^{100}) \) 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.

Copy content comment:embeddings in the coefficient field
 
Copy content gp:mfembed(f)
 
Label   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1.1 −1.00000 −3.11535 1.00000 −1.11545 3.11535 2.89747 −1.00000 6.70541 1.11545
1.2 −1.00000 −2.98629 1.00000 −0.478866 2.98629 1.48395 −1.00000 5.91792 0.478866
1.3 −1.00000 −2.91522 1.00000 0.226297 2.91522 −3.31572 −1.00000 5.49851 −0.226297
1.4 −1.00000 −2.37491 1.00000 −4.01131 2.37491 −4.85068 −1.00000 2.64019 4.01131
1.5 −1.00000 −2.19241 1.00000 4.32104 2.19241 2.07942 −1.00000 1.80668 −4.32104
1.6 −1.00000 −1.72157 1.00000 0.872616 1.72157 1.30360 −1.00000 −0.0362095 −0.872616
1.7 −1.00000 −1.01276 1.00000 4.27488 1.01276 −1.47893 −1.00000 −1.97431 −4.27488
1.8 −1.00000 −0.751120 1.00000 −0.996693 0.751120 0.452697 −1.00000 −2.43582 0.996693
1.9 −1.00000 −0.668486 1.00000 0.0279769 0.668486 5.18207 −1.00000 −2.55313 −0.0279769
1.10 −1.00000 −0.472517 1.00000 −2.89241 0.472517 0.0281863 −1.00000 −2.77673 2.89241
1.11 −1.00000 −0.156157 1.00000 2.47620 0.156157 −2.89830 −1.00000 −2.97562 −2.47620
1.12 −1.00000 0.416283 1.00000 −2.54925 −0.416283 −1.97882 −1.00000 −2.82671 2.54925
1.13 −1.00000 0.921450 1.00000 2.91854 −0.921450 −5.02258 −1.00000 −2.15093 −2.91854
1.14 −1.00000 0.982048 1.00000 4.17331 −0.982048 5.04153 −1.00000 −2.03558 −4.17331
1.15 −1.00000 1.13392 1.00000 −3.79713 −1.13392 2.93249 −1.00000 −1.71422 3.79713
1.16 −1.00000 1.21834 1.00000 0.762060 −1.21834 −3.90756 −1.00000 −1.51564 −0.762060
1.17 −1.00000 2.00807 1.00000 −2.39225 −2.00807 −2.46045 −1.00000 1.03233 2.39225
1.18 −1.00000 2.32337 1.00000 −0.523734 −2.32337 0.177553 −1.00000 2.39805 0.523734
1.19 −1.00000 2.33100 1.00000 2.73265 −2.33100 3.48514 −1.00000 2.43354 −2.73265
1.20 −1.00000 2.67472 1.00000 3.26295 −2.67472 −1.98719 −1.00000 4.15412 −3.26295
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.24
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \( +1 \)
\(11\) \( +1 \)
\(37\) \( -1 \)

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 8954.2.a.bu 24
11.b odd 2 1 8954.2.a.bv 24
11.c even 5 2 814.2.h.d ✓ 48
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
814.2.h.d ✓ 48 11.c even 5 2
8954.2.a.bu 24 1.a even 1 1 trivial
8954.2.a.bv 24 11.b odd 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(8954))\):

\( T_{3}^{24} - 8 T_{3}^{23} - 22 T_{3}^{22} + 325 T_{3}^{21} - 131 T_{3}^{20} - 5336 T_{3}^{19} + \cdots - 12421 \) Copy content Toggle raw display
\( T_{5}^{24} - 6 T_{5}^{23} - 72 T_{5}^{22} + 460 T_{5}^{21} + 2174 T_{5}^{20} - 15046 T_{5}^{19} + \cdots - 103444 \) Copy content Toggle raw display
\( T_{7}^{24} + 3 T_{7}^{23} - 111 T_{7}^{22} - 336 T_{7}^{21} + 5138 T_{7}^{20} + 15614 T_{7}^{19} + \cdots - 2330624 \) Copy content Toggle raw display
\( T_{17}^{24} + 20 T_{17}^{23} - 59 T_{17}^{22} - 3562 T_{17}^{21} - 10640 T_{17}^{20} + \cdots - 2871247389696 \) Copy content Toggle raw display