Properties

Label 1027.4.a.c
Level $1027$
Weight $4$
Character orbit 1027.a
Self dual yes
Analytic conductor $60.595$
Analytic rank $1$
Dimension $56$
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] = [1027,4,Mod(1,1027)] 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("1027.1"); S:= CuspForms(chi, 4); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1027, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 4, names="a")
 
Level: \( N \) \(=\) \( 1027 = 13 \cdot 79 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1027.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [56,-16] 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: \(60.5949615759\)
Analytic rank: \(1\)
Dimension: \(56\)
Twist minimal: yes
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.

\(\operatorname{Tr}(f)(q) = \) \( 56 q - 16 q^{2} - 17 q^{3} + 208 q^{4} - 35 q^{5} + 29 q^{6} - 37 q^{7} - 156 q^{8} + 415 q^{9} - 67 q^{10} - 114 q^{11} - 196 q^{12} - 728 q^{13} - 183 q^{14} - 17 q^{15} + 680 q^{16} - 383 q^{17} - 342 q^{18}+ \cdots - 11354 q^{99}+O(q^{100}) \) 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 −5.49225 −2.91599 22.1648 10.5969 16.0153 −26.2020 −77.7969 −18.4970 −58.2010
1.2 −5.47646 −5.37895 21.9917 10.5004 29.4576 8.79041 −76.6249 1.93314 −57.5049
1.3 −5.29522 7.52079 20.0394 −0.503863 −39.8243 15.2310 −63.7513 29.5623 2.66807
1.4 −5.12297 0.329121 18.2448 −18.7368 −1.68608 −6.25678 −52.4839 −26.8917 95.9881
1.5 −5.12043 −9.71533 18.2188 −12.2172 49.7467 −17.9634 −52.3248 67.3877 62.5571
1.6 −4.90197 −2.15935 16.0293 −19.1743 10.5851 26.5939 −39.3596 −22.3372 93.9918
1.7 −4.89508 3.68063 15.9618 2.74494 −18.0170 19.7788 −38.9738 −13.4530 −13.4367
1.8 −4.35449 0.956303 10.9616 16.0339 −4.16421 −11.4267 −12.8961 −26.0855 −69.8193
1.9 −4.26566 0.165031 10.1958 4.40634 −0.703966 −4.29535 −9.36672 −26.9728 −18.7959
1.10 −4.17502 8.67851 9.43077 0.286821 −36.2329 −11.7908 −5.97348 48.3165 −1.19748
1.11 −3.97383 8.55784 7.79134 21.3795 −34.0074 −16.0395 0.829176 46.2366 −84.9586
1.12 −3.76267 −9.01119 6.15769 4.93378 33.9061 −3.49935 6.93202 54.2015 −18.5642
1.13 −3.75425 6.45205 6.09437 −8.91793 −24.2226 −20.7363 7.15420 14.6289 33.4801
1.14 −3.74612 −9.78763 6.03338 −1.86864 36.6656 30.7111 7.36717 68.7976 7.00014
1.15 −3.62822 −6.15140 5.16395 −13.4354 22.3186 −32.8913 10.2898 10.8398 48.7464
1.16 −3.05544 −4.05698 1.33571 −8.29457 12.3959 23.0676 20.3623 −10.5409 25.3435
1.17 −2.99932 −3.69853 0.995906 −6.33644 11.0931 −16.1487 21.0075 −13.3209 19.0050
1.18 −2.77924 0.606659 −0.275806 12.9489 −1.68605 24.8334 23.0005 −26.6320 −35.9882
1.19 −2.49899 6.99224 −1.75505 −1.06842 −17.4735 34.8067 24.3778 21.8914 2.66997
1.20 −2.44561 −0.637453 −2.01899 −14.3820 1.55896 −16.9912 24.5025 −26.5937 35.1727
See all 56 embeddings
\(n\): e.g. 2-40 or 80-90
Embeddings: e.g. 1-3 or 1.56
Significant digits:
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Atkin-Lehner signs

\( p \) Sign
\(13\) \( +1 \)
\(79\) \( -1 \)

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 1027.4.a.c ✓ 56
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1027.4.a.c ✓ 56 1.a even 1 1 trivial

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{56} + 16 T_{2}^{55} - 200 T_{2}^{54} - 4428 T_{2}^{53} + 13526 T_{2}^{52} + 568899 T_{2}^{51} + \cdots + 49\!\cdots\!76 \) acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(1027))\). Copy content Toggle raw display