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Properties

Label 1127.4.a.n
Level $1127$
Weight $4$
Character orbit 1127.a
Self dual yes
Analytic conductor $66.495$
Analytic rank $1$
Dimension $26$
Inner twists $2$

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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] = [1127,4,Mod(1,1127)] 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("1127.1"); S:= CuspForms(chi, 4); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1127, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 4, names="a")
 
Level: \( N \) \(=\) \( 1127 = 7^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1127.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [26,-12,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(66.4951525765\)
Analytic rank: \(1\)
Dimension: \(26\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 26 q - 12 q^{2} + 72 q^{4} - 144 q^{8} + 122 q^{9} - 84 q^{11} - 160 q^{15} + 32 q^{16} - 312 q^{18} - 184 q^{22} + 598 q^{23} - 334 q^{25} - 1020 q^{29} - 360 q^{30} - 524 q^{32} + 500 q^{36} - 1920 q^{37}+ \cdots - 8076 q^{99}+O(q^{100}) \) 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 −5.13289 −9.54624 18.3465 1.03959 48.9998 0 −53.1076 64.1306 −5.33608
1.2 −5.13289 9.54624 18.3465 −1.03959 −48.9998 0 −53.1076 64.1306 5.33608
1.3 −4.91107 −1.24297 16.1186 −11.0627 6.10432 0 −39.8713 −25.4550 54.3300
1.4 −4.91107 1.24297 16.1186 11.0627 −6.10432 0 −39.8713 −25.4550 −54.3300
1.5 −4.10509 −5.45081 8.85173 −13.9087 22.3760 0 −3.49643 2.71130 57.0964
1.6 −4.10509 5.45081 8.85173 13.9087 −22.3760 0 −3.49643 2.71130 −57.0964
1.7 −3.19888 −2.46196 2.23284 17.0470 7.87551 0 18.4485 −20.9388 −54.5314
1.8 −3.19888 2.46196 2.23284 −17.0470 −7.87551 0 18.4485 −20.9388 54.5314
1.9 −2.35795 −1.36439 −2.44008 5.33949 3.21717 0 24.6172 −25.1384 −12.5902
1.10 −2.35795 1.36439 −2.44008 −5.33949 −3.21717 0 24.6172 −25.1384 12.5902
1.11 −1.79130 −8.53285 −4.79125 7.86657 15.2849 0 22.9130 45.8096 −14.0914
1.12 −1.79130 8.53285 −4.79125 −7.86657 −15.2849 0 22.9130 45.8096 14.0914
1.13 −0.0707469 −2.01147 −7.99499 −15.7713 0.142305 0 1.13160 −22.9540 1.11577
1.14 −0.0707469 2.01147 −7.99499 15.7713 −0.142305 0 1.13160 −22.9540 −1.11577
1.15 0.523251 −7.07583 −7.72621 16.5895 −3.70243 0 −8.22875 23.0673 8.68047
1.16 0.523251 7.07583 −7.72621 −16.5895 3.70243 0 −8.22875 23.0673 −8.68047
1.17 0.964887 −5.39827 −7.06899 −10.2293 −5.20872 0 −14.5399 2.14132 −9.87008
1.18 0.964887 5.39827 −7.06899 10.2293 5.20872 0 −14.5399 2.14132 9.87008
1.19 2.37731 −8.64576 −2.34841 −2.43693 −20.5536 0 −24.6014 47.7491 −5.79333
1.20 2.37731 8.64576 −2.34841 2.43693 20.5536 0 −24.6014 47.7491 5.79333
See all 26 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.26
Significant digits:
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Atkin-Lehner signs

\( p \) Sign
\(7\) \( +1 \)
\(23\) \( -1 \)

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
7.b odd 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 1127.4.a.n ✓ 26
7.b odd 2 1 inner 1127.4.a.n ✓ 26
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1127.4.a.n ✓ 26 1.a even 1 1 trivial
1127.4.a.n ✓ 26 7.b odd 2 1 inner

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(1127))\):

\( T_{2}^{13} + 6 T_{2}^{12} - 52 T_{2}^{11} - 328 T_{2}^{10} + 944 T_{2}^{9} + 6414 T_{2}^{8} + \cdots + 6784 \) Copy content Toggle raw display
\( T_{3}^{26} - 412 T_{3}^{24} + 72389 T_{3}^{22} - 7108564 T_{3}^{20} + 430002896 T_{3}^{18} + \cdots - 17\!\cdots\!00 \) Copy content Toggle raw display