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Properties

Label 1143.4.a.i
Level $1143$
Weight $4$
Character orbit 1143.a
Self dual yes
Analytic conductor $67.439$
Analytic rank $1$
Dimension $22$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1143,4,Mod(1,1143)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1143, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1143.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1143 = 3^{2} \cdot 127 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1143.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(67.4391831366\)
Analytic rank: \(1\)
Dimension: \(22\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 22 q + 118 q^{4} - 10 q^{7}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 22 q + 118 q^{4} - 10 q^{7} - 104 q^{10} - 262 q^{13} - 146 q^{16} - 240 q^{19} - 184 q^{22} + 138 q^{25} - 798 q^{28} - 1118 q^{31} - 1452 q^{34} - 2006 q^{37} - 2884 q^{40} - 1708 q^{43} - 2396 q^{46} - 1248 q^{49} - 2420 q^{52} - 2072 q^{55} - 2816 q^{58} - 1490 q^{61} - 602 q^{64} - 348 q^{67} - 2200 q^{70} - 3148 q^{73} - 5282 q^{76} - 366 q^{79} - 3888 q^{82} - 720 q^{85} - 2276 q^{88} - 1308 q^{91} - 5706 q^{94} - 6192 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Display 100 coefficients 10 coefficients

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.

comment: embeddings in the coefficient field
 
gp: mfembed(f)
 
Label   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1.1 −5.25086 0 19.5715 13.3955 0 −10.8593 −60.7603 0 −70.3378
1.2 −4.87970 0 15.8114 15.7099 0 0.998775 −38.1175 0 −76.6593
1.3 −4.70950 0 14.1794 −7.47056 0 −21.6829 −29.1019 0 35.1826
1.4 −4.20782 0 9.70573 −1.05782 0 15.4111 −7.17738 0 4.45112
1.5 −3.98059 0 7.84513 1.44609 0 10.9403 0.616467 0 −5.75631
1.6 −3.75854 0 6.12666 −12.4556 0 −13.7776 7.04103 0 46.8148
1.7 −3.00223 0 1.01339 5.35146 0 −5.28056 20.9754 0 −16.0663
1.8 −2.49888 0 −1.75560 4.48484 0 17.4755 24.3781 0 −11.2071
1.9 −2.26145 0 −2.88584 −16.7261 0 −26.3883 24.6178 0 37.8251
1.10 −2.13260 0 −3.45202 −10.0689 0 31.2092 24.4226 0 21.4730
1.11 −0.916634 0 −7.15978 19.3314 0 −3.04631 13.8960 0 −17.7199
1.12 0.916634 0 −7.15978 −19.3314 0 −3.04631 −13.8960 0 −17.7199
1.13 2.13260 0 −3.45202 10.0689 0 31.2092 −24.4226 0 21.4730
1.14 2.26145 0 −2.88584 16.7261 0 −26.3883 −24.6178 0 37.8251
1.15 2.49888 0 −1.75560 −4.48484 0 17.4755 −24.3781 0 −11.2071
1.16 3.00223 0 1.01339 −5.35146 0 −5.28056 −20.9754 0 −16.0663
1.17 3.75854 0 6.12666 12.4556 0 −13.7776 −7.04103 0 46.8148
1.18 3.98059 0 7.84513 −1.44609 0 10.9403 −0.616467 0 −5.75631
1.19 4.20782 0 9.70573 1.05782 0 15.4111 7.17738 0 4.45112
1.20 4.70950 0 14.1794 7.47056 0 −21.6829 29.1019 0 35.1826
See all 22 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.22
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(3\) \(1\)
\(127\) \(-1\)

Inner twists

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

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 1143.4.a.i ✓ 22
3.b odd 2 1 inner 1143.4.a.i ✓ 22
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1143.4.a.i ✓ 22 1.a even 1 1 trivial
1143.4.a.i ✓ 22 3.b odd 2 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{22} - 147 T_{2}^{20} + 9429 T_{2}^{18} - 346863 T_{2}^{16} + 8089911 T_{2}^{14} + \cdots - 63475779136 \) acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(1143))\). Copy content Toggle raw display