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Properties

Label 1629.4.a.f
Level $1629$
Weight $4$
Character orbit 1629.a
Self dual yes
Analytic conductor $96.114$
Analytic rank $1$
Dimension $25$
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] = [1629,4,Mod(1,1629)] 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("1629.1"); S:= CuspForms(chi, 4); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1629, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 4, names="a")
 
Level: \( N \) \(=\) \( 1629 = 3^{2} \cdot 181 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1629.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [25] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(96.1141113994\)
Analytic rank: \(1\)
Dimension: \(25\)
Twist minimal: no (minimal twist has level 181)
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.

\(\operatorname{Tr}(f)(q) = \) \( 25 q - 7 q^{2} + 125 q^{4} - 26 q^{5} + 31 q^{7} - 87 q^{8} + 49 q^{10} - 339 q^{11} + 28 q^{13} - 257 q^{14} + 605 q^{16} - 242 q^{17} + 248 q^{19} - 306 q^{20} + 200 q^{22} - 367 q^{23} + 785 q^{25} - 364 q^{26}+ \cdots + 5022 q^{98}+O(q^{100}) \) 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 −5.34718 0 20.5923 −15.0230 0 3.26574 −67.3333 0 80.3309
1.2 −5.27014 0 19.7744 17.0735 0 29.7127 −62.0525 0 −89.9794
1.3 −5.02198 0 17.2203 −6.54851 0 −30.7112 −46.3039 0 32.8865
1.4 −4.85992 0 15.6188 0.157129 0 −1.60559 −37.0269 0 −0.763634
1.5 −4.82610 0 15.2912 1.77680 0 2.96396 −35.1882 0 −8.57499
1.6 −4.13372 0 9.08768 −7.01840 0 21.3765 −4.49616 0 29.0121
1.7 −3.59304 0 4.90992 5.97197 0 11.1345 11.1028 0 −21.4575
1.8 −3.31947 0 3.01886 −20.1700 0 15.7597 16.5347 0 66.9537
1.9 −2.21916 0 −3.07535 −10.6225 0 −13.0028 24.5779 0 23.5729
1.10 −1.75078 0 −4.93476 16.8452 0 16.5089 22.6460 0 −29.4923
1.11 −1.62427 0 −5.36176 −9.74180 0 6.98620 21.7030 0 15.8233
1.12 −0.863777 0 −7.25389 9.78803 0 −22.5059 13.1760 0 −8.45468
1.13 −0.503023 0 −7.74697 3.03913 0 35.4676 7.92109 0 −1.52875
1.14 0.739807 0 −7.45269 −20.2090 0 −14.4643 −11.4320 0 −14.9508
1.15 0.839976 0 −7.29444 8.74367 0 −31.1625 −12.8470 0 7.34448
1.16 1.04213 0 −6.91396 14.2170 0 −12.1784 −15.5423 0 14.8160
1.17 1.45128 0 −5.89377 −13.7766 0 6.19849 −20.1638 0 −19.9937
1.18 1.49508 0 −5.76474 13.0303 0 2.13573 −20.5794 0 19.4813
1.19 3.54983 0 4.60127 −20.9148 0 34.8436 −12.0649 0 −74.2439
1.20 4.07076 0 8.57108 −4.57188 0 −10.8014 2.32474 0 −18.6110
See all 25 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.25
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(3\) \( -1 \)
\(181\) \( +1 \)

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 1629.4.a.f 25
3.b odd 2 1 181.4.a.c ✓ 25
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
181.4.a.c ✓ 25 3.b odd 2 1
1629.4.a.f 25 1.a even 1 1 trivial

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{25} + 7 T_{2}^{24} - 138 T_{2}^{23} - 1014 T_{2}^{22} + 8085 T_{2}^{21} + 63408 T_{2}^{20} + \cdots + 18978701312 \) acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(1629))\). Copy content Toggle raw display