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Properties

Label 8954.2.a.bt
Level $8954$
Weight $2$
Character orbit 8954.a
Self dual yes
Analytic conductor $71.498$
Analytic rank $0$
Dimension $22$
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 = [22,22,5,22,8] 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: \(22\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 22 q + 22 q^{2} + 5 q^{3} + 22 q^{4} + 8 q^{5} + 5 q^{6} + 7 q^{7} + 22 q^{8} + 35 q^{9} + 8 q^{10} + 5 q^{12} + 9 q^{13} + 7 q^{14} + 16 q^{15} + 22 q^{16} + 19 q^{17} + 35 q^{18} + 8 q^{20} + 15 q^{21}+ \cdots + 57 q^{98}+O(q^{100}) \) 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 −3.29717 1.00000 2.91144 −3.29717 1.69384 1.00000 7.87135 2.91144
1.2 1.00000 −3.21746 1.00000 2.27953 −3.21746 −4.33460 1.00000 7.35206 2.27953
1.3 1.00000 −2.66972 1.00000 −3.48071 −2.66972 −0.431242 1.00000 4.12740 −3.48071
1.4 1.00000 −2.02198 1.00000 0.0157389 −2.02198 3.22765 1.00000 1.08838 0.0157389
1.5 1.00000 −1.83766 1.00000 1.98483 −1.83766 4.57575 1.00000 0.377006 1.98483
1.6 1.00000 −1.82514 1.00000 −2.03367 −1.82514 −3.76851 1.00000 0.331146 −2.03367
1.7 1.00000 −1.46469 1.00000 −1.75258 −1.46469 −0.442923 1.00000 −0.854676 −1.75258
1.8 1.00000 −1.41883 1.00000 3.54426 −1.41883 0.419338 1.00000 −0.986935 3.54426
1.9 1.00000 −0.165775 1.00000 0.132791 −0.165775 2.80160 1.00000 −2.97252 0.132791
1.10 1.00000 0.123112 1.00000 −3.89599 0.123112 1.02869 1.00000 −2.98484 −3.89599
1.11 1.00000 0.400389 1.00000 −2.14096 0.400389 −2.77036 1.00000 −2.83969 −2.14096
1.12 1.00000 0.404047 1.00000 −2.05557 0.404047 −3.96539 1.00000 −2.83675 −2.05557
1.13 1.00000 0.560754 1.00000 2.05464 0.560754 −0.565289 1.00000 −2.68555 2.05464
1.14 1.00000 1.02287 1.00000 −0.190102 1.02287 4.41369 1.00000 −1.95374 −0.190102
1.15 1.00000 1.23733 1.00000 −0.662349 1.23733 −1.70353 1.00000 −1.46901 −0.662349
1.16 1.00000 1.58474 1.00000 3.41427 1.58474 2.48424 1.00000 −0.488593 3.41427
1.17 1.00000 2.63152 1.00000 4.07541 2.63152 0.424247 1.00000 3.92490 4.07541
1.18 1.00000 2.72765 1.00000 −3.12288 2.72765 4.54311 1.00000 4.44010 −3.12288
1.19 1.00000 2.77706 1.00000 1.34110 2.77706 4.59117 1.00000 4.71207 1.34110
1.20 1.00000 2.91016 1.00000 4.00601 2.91016 −4.10874 1.00000 5.46906 4.00601
See all 22 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.22
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.bt 22
11.b odd 2 1 8954.2.a.bs 22
11.c even 5 2 814.2.h.c ✓ 44
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
814.2.h.c ✓ 44 11.c even 5 2
8954.2.a.bs 22 11.b odd 2 1
8954.2.a.bt 22 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(8954))\):

\( T_{3}^{22} - 5 T_{3}^{21} - 38 T_{3}^{20} + 216 T_{3}^{19} + 549 T_{3}^{18} - 3849 T_{3}^{17} + \cdots - 919 \) Copy content Toggle raw display
\( T_{5}^{22} - 8 T_{5}^{21} - 36 T_{5}^{20} + 422 T_{5}^{19} + 224 T_{5}^{18} - 8976 T_{5}^{17} + \cdots - 341 \) Copy content Toggle raw display
\( T_{7}^{22} - 7 T_{7}^{21} - 81 T_{7}^{20} + 642 T_{7}^{19} + 2516 T_{7}^{18} - 24584 T_{7}^{17} + \cdots + 4381696 \) Copy content Toggle raw display
\( T_{17}^{22} - 19 T_{17}^{21} - 31 T_{17}^{20} + 2432 T_{17}^{19} - 6481 T_{17}^{18} - 121346 T_{17}^{17} + \cdots - 564075520 \) Copy content Toggle raw display