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Properties

Label 1127.4.a.j
Level $1127$
Weight $4$
Character orbit 1127.a
Self dual yes
Analytic conductor $66.495$
Analytic rank $1$
Dimension $22$
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] = [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 = [22,0,-18] 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: \(22\)
Twist minimal: no (minimal twist has level 161)
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.

\(\operatorname{Tr}(f)(q) = \) \( 22 q - 18 q^{3} + 88 q^{4} - 20 q^{5} - 36 q^{6} + 21 q^{8} + 126 q^{9} - 200 q^{10} + 20 q^{11} - 161 q^{12} - 196 q^{13} + 20 q^{15} + 324 q^{16} - 242 q^{17} + 85 q^{18} - 128 q^{19} - 46 q^{20} + 14 q^{22}+ \cdots + 3570 q^{99}+O(q^{100}) \) 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 −5.59052 −1.49010 23.2539 20.2057 8.33045 0 −85.2773 −24.7796 −112.960
1.2 −4.91881 −2.33095 16.1947 −10.5563 11.4655 0 −40.3083 −21.5667 51.9245
1.3 −4.53648 6.86107 12.5797 −6.87441 −31.1251 0 −20.7755 20.0742 31.1856
1.4 −4.32159 −4.28749 10.6761 9.40357 18.5287 0 −11.5651 −8.61747 −40.6384
1.5 −3.13153 −9.46906 1.80647 13.3465 29.6526 0 19.3952 62.6630 −41.7948
1.6 −2.93780 3.29133 0.630669 −19.2434 −9.66926 0 21.6496 −16.1672 56.5334
1.7 −2.51636 −7.19476 −1.66793 −13.7173 18.1046 0 24.3280 24.7646 34.5178
1.8 −2.23994 9.02095 −2.98266 15.1288 −20.2064 0 24.6005 54.3776 −33.8876
1.9 −2.04002 4.88087 −3.83830 4.41190 −9.95709 0 24.1504 −3.17714 −9.00038
1.10 −0.663185 −0.883358 −7.56019 0.920049 0.585829 0 10.3193 −26.2197 −0.610163
1.11 −0.638296 −5.10460 −7.59258 5.92294 3.25824 0 9.95268 −0.943108 −3.78059
1.12 −0.497217 5.81671 −7.75278 −0.0230495 −2.89216 0 7.83254 6.83407 0.0114606
1.13 1.29339 −1.49696 −6.32713 −13.4112 −1.93616 0 −18.5306 −24.7591 −17.3459
1.14 1.80978 −8.50135 −4.72469 −21.7322 −15.3856 0 −23.0289 45.2729 −39.3306
1.15 2.18290 −6.49712 −3.23493 10.5964 −14.1826 0 −24.5248 15.2126 23.1308
1.16 2.38479 1.66619 −2.31275 14.5518 3.97352 0 −24.5938 −24.2238 34.7030
1.17 3.36360 5.33236 3.31384 −3.38935 17.9360 0 −15.7624 1.43407 −11.4004
1.18 3.82448 7.55542 6.62665 −18.4709 28.8955 0 −5.25234 30.0843 −70.6417
1.19 4.17933 0.180310 9.46680 12.4777 0.753575 0 6.13025 −26.9675 52.1485
1.20 4.48785 −8.90181 12.1408 2.08429 −39.9500 0 18.5832 52.2422 9.35398
See all 22 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.22
Significant digits:
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Atkin-Lehner signs

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

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 1127.4.a.j 22
7.b odd 2 1 1127.4.a.m 22
7.c even 3 2 161.4.e.b ✓ 44
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
161.4.e.b ✓ 44 7.c even 3 2
1127.4.a.j 22 1.a even 1 1 trivial
1127.4.a.m 22 7.b odd 2 1

Hecke kernels

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

\( T_{2}^{22} - 132 T_{2}^{20} - 7 T_{2}^{19} + 7399 T_{2}^{18} + 887 T_{2}^{17} - 230614 T_{2}^{16} + \cdots + 971629440 \) Copy content Toggle raw display
\( T_{3}^{22} + 18 T_{3}^{21} - 198 T_{3}^{20} - 5058 T_{3}^{19} + 8510 T_{3}^{18} + 577480 T_{3}^{17} + \cdots + 340543829847 \) Copy content Toggle raw display