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Properties

Label 1127.2.c.a
Level $1127$
Weight $2$
Character orbit 1127.c
Analytic conductor $8.999$
Analytic rank $0$
Dimension $24$
Inner twists $4$

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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] = [1127,2,Mod(1126,1127)] 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("1127.1126"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1127, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 1127 = 7^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1127.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [24,-8] 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: no
Analytic conductor: \(8.99914030780\)
Analytic rank: \(0\)
Dimension: \(24\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 24 q - 8 q^{2} + 8 q^{4} - 24 q^{8} + 24 q^{9} + 8 q^{16} + 8 q^{18} + 120 q^{25} + 16 q^{29} - 56 q^{32} + 56 q^{36} - 32 q^{39} - 16 q^{46} - 88 q^{50} - 16 q^{58} + 24 q^{64} - 16 q^{71} - 88 q^{72}+ \cdots + 80 q^{95}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1126.1 −2.56754 1.17876i 4.59228 4.00852 − 3.02652i 0 −6.65579 1.61052 −10.2921
1126.2 −2.56754 1.17876i 4.59228 −4.00852 − 3.02652i 0 −6.65579 1.61052 10.2921
1126.3 −2.56754 − 1.17876i 4.59228 −4.00852 3.02652i 0 −6.65579 1.61052 10.2921
1126.4 −2.56754 − 1.17876i 4.59228 4.00852 3.02652i 0 −6.65579 1.61052 −10.2921
1126.5 −1.60043 − 1.27469i 0.561391 3.24948 2.04006i 0 2.30240 1.37517 −5.20057
1126.6 −1.60043 1.27469i 0.561391 −3.24948 − 2.04006i 0 2.30240 1.37517 5.20057
1126.7 −1.60043 − 1.27469i 0.561391 −3.24948 2.04006i 0 2.30240 1.37517 5.20057
1126.8 −1.60043 1.27469i 0.561391 3.24948 − 2.04006i 0 2.30240 1.37517 −5.20057
1126.9 −0.545336 1.68337i −1.70261 −1.18444 − 0.918002i 0 2.01917 0.166269 0.645920
1126.10 −0.545336 − 1.68337i −1.70261 1.18444 0.918002i 0 2.01917 0.166269 −0.645920
1126.11 −0.545336 1.68337i −1.70261 1.18444 − 0.918002i 0 2.01917 0.166269 −0.645920
1126.12 −0.545336 − 1.68337i −1.70261 −1.18444 0.918002i 0 2.01917 0.166269 0.645920
1126.13 −0.218114 2.36321i −1.95243 3.26337 − 0.515449i 0 0.862080 −2.58475 −0.711788
1126.14 −0.218114 − 2.36321i −1.95243 −3.26337 0.515449i 0 0.862080 −2.58475 0.711788
1126.15 −0.218114 2.36321i −1.95243 −3.26337 − 0.515449i 0 0.862080 −2.58475 0.711788
1126.16 −0.218114 − 2.36321i −1.95243 3.26337 0.515449i 0 0.862080 −2.58475 −0.711788
1126.17 1.14577 0.356686i −0.687209 −3.71421 0.408681i 0 −3.07893 2.87277 −4.25563
1126.18 1.14577 − 0.356686i −0.687209 3.71421 − 0.408681i 0 −3.07893 2.87277 4.25563
1126.19 1.14577 0.356686i −0.687209 3.71421 0.408681i 0 −3.07893 2.87277 4.25563
1126.20 1.14577 − 0.356686i −0.687209 −3.71421 − 0.408681i 0 −3.07893 2.87277 −4.25563
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1126.24
Significant digits:
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Inner twists

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

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 1127.2.c.a ✓ 24
7.b odd 2 1 inner 1127.2.c.a ✓ 24
23.b odd 2 1 inner 1127.2.c.a ✓ 24
161.c even 2 1 inner 1127.2.c.a ✓ 24
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1127.2.c.a ✓ 24 1.a even 1 1 trivial
1127.2.c.a ✓ 24 7.b odd 2 1 inner
1127.2.c.a ✓ 24 23.b odd 2 1 inner
1127.2.c.a ✓ 24 161.c even 2 1 inner