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Properties

Label 841.4.a.i
Level $841$
Weight $4$
Character orbit 841.a
Self dual yes
Analytic conductor $49.621$
Analytic rank $0$
Dimension $21$
CM no
Inner twists $1$

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Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [841,4,Mod(1,841)] 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("841.1"); S:= CuspForms(chi, 4); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(841, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 4, names="a")
 
Level: \( N \) \(=\) \( 841 = 29^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 841.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [21,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(49.6206063148\)
Analytic rank: \(0\)
Dimension: \(21\)
Twist minimal: no (minimal twist has level 29)
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.

\(\operatorname{Tr}(f)(q) = \) \( 21 q + 6 q^{2} - q^{3} + 90 q^{4} + 35 q^{5} + 26 q^{6} + 37 q^{7} + 51 q^{8} + 188 q^{9} + 37 q^{10} - 7 q^{11} - 68 q^{12} + 97 q^{13} - 68 q^{14} - 330 q^{15} + 310 q^{16} + 70 q^{17} + 305 q^{18} - 73 q^{19}+ \cdots + 8702 q^{99}+O(q^{100}) \) 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.

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 −5.03979 −4.10050 17.3995 5.61831 20.6656 23.4793 −47.3712 −10.1859 −28.3151
1.2 −4.99811 −7.28662 16.9811 18.4749 36.4193 −6.85185 −44.8884 26.0948 −92.3397
1.3 −4.40657 −3.38892 11.4179 3.00636 14.9335 −3.63540 −15.0611 −15.5152 −13.2478
1.4 −4.19503 3.68104 9.59829 −16.8481 −15.4421 −1.11840 −6.70489 −13.4499 70.6782
1.5 −3.43388 9.14452 3.79157 −5.89225 −31.4012 28.3262 14.4513 56.6222 20.2333
1.6 −3.12804 5.26604 1.78461 −10.0822 −16.4724 −5.39859 19.4420 0.731188 31.5376
1.7 −1.62919 5.65337 −5.34573 13.9077 −9.21044 −14.2629 21.7428 4.96064 −22.6583
1.8 −1.18795 −7.34487 −6.58876 1.74990 8.72537 −21.5895 17.3308 26.9471 −2.07880
1.9 −0.765028 −4.91525 −7.41473 −3.09630 3.76030 21.6038 11.7927 −2.84031 2.36876
1.10 −0.720053 1.28637 −7.48152 3.38147 −0.926251 −21.7530 11.1475 −25.3453 −2.43483
1.11 0.550953 −9.96498 −7.69645 10.3008 −5.49024 17.6817 −8.64801 72.3008 5.67526
1.12 0.604452 5.07443 −7.63464 20.2395 3.06725 8.14730 −9.45039 −1.25014 12.2338
1.13 2.17873 0.884165 −3.25312 −14.1746 1.92636 17.3640 −24.5176 −26.2183 −30.8826
1.14 2.35527 −0.395486 −2.45270 −11.6438 −0.931476 7.76573 −24.6189 −26.8436 −27.4242
1.15 2.89852 −4.45749 0.401406 −3.28305 −12.9201 −34.7925 −22.0247 −7.13078 −9.51599
1.16 2.93292 7.94540 0.602047 −15.2999 23.3033 10.4958 −21.6976 36.1294 −44.8733
1.17 4.05460 6.11792 8.43978 16.9978 24.8057 11.2951 1.78313 10.4290 68.9192
1.18 4.70700 0.626516 14.1559 19.7268 2.94901 26.8676 28.9757 −26.6075 92.8541
1.19 4.86780 −8.27656 15.6955 12.6139 −40.2886 26.7207 37.4602 41.5014 61.4021
1.20 5.13312 −5.88101 18.3489 −8.16248 −30.1879 −36.1470 53.1222 7.58626 −41.8990
See all 21 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.21
Significant digits:
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Atkin-Lehner signs

\( p \) Sign
\(29\) \( +1 \)

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 841.4.a.i 21
29.b even 2 1 841.4.a.h 21
29.e even 14 2 29.4.d.a ✓ 42
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
29.4.d.a ✓ 42 29.e even 14 2
841.4.a.h 21 29.b even 2 1
841.4.a.i 21 1.a even 1 1 trivial

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{21} - 6 T_{2}^{20} - 111 T_{2}^{19} + 689 T_{2}^{18} + 5057 T_{2}^{17} - 32968 T_{2}^{16} + \cdots - 192851968 \) acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(841))\). Copy content Toggle raw display