Properties

Label 1134.2.a.h
Level $1134$
Weight $2$
Character orbit 1134.a
Self dual yes
Analytic conductor $9.055$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1134,2,Mod(1,1134)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1134, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1134.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1134 = 2 \cdot 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1134.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: \(9.05503558921\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 126)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \( q + q^{2} + q^{4} + 3 q^{5} + q^{7} + q^{8}+O(q^{10}) \) Copy content Toggle raw display \( q + q^{2} + q^{4} + 3 q^{5} + q^{7} + q^{8} + 3 q^{10} + 6 q^{11} + 2 q^{13} + q^{14} + q^{16} - 6 q^{17} - 7 q^{19} + 3 q^{20} + 6 q^{22} - 3 q^{23} + 4 q^{25} + 2 q^{26} + q^{28} - 6 q^{29} + 2 q^{31} + q^{32} - 6 q^{34} + 3 q^{35} + 2 q^{37} - 7 q^{38} + 3 q^{40} + 2 q^{43} + 6 q^{44} - 3 q^{46} + q^{49} + 4 q^{50} + 2 q^{52} - 6 q^{53} + 18 q^{55} + q^{56} - 6 q^{58} + 5 q^{61} + 2 q^{62} + q^{64} + 6 q^{65} + 8 q^{67} - 6 q^{68} + 3 q^{70} - 3 q^{71} + 2 q^{73} + 2 q^{74} - 7 q^{76} + 6 q^{77} + 5 q^{79} + 3 q^{80} - 12 q^{83} - 18 q^{85} + 2 q^{86} + 6 q^{88} + 2 q^{91} - 3 q^{92} - 21 q^{95} + 2 q^{97} + q^{98}+O(q^{100}) \) 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.

comment: embeddings in the coefficient field
 
gp: mfembed(f)
 
Label   \(\iota_m(\nu)\) \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1.1
0
1.00000 0 1.00000 3.00000 0 1.00000 1.00000 0 3.00000
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \( -1 \)
\(3\) \( -1 \)
\(7\) \( -1 \)

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 1134.2.a.h 1
3.b odd 2 1 1134.2.a.a 1
4.b odd 2 1 9072.2.a.w 1
7.b odd 2 1 7938.2.a.u 1
9.c even 3 2 378.2.f.a 2
9.d odd 6 2 126.2.f.a 2
12.b even 2 1 9072.2.a.c 1
21.c even 2 1 7938.2.a.l 1
36.f odd 6 2 3024.2.r.a 2
36.h even 6 2 1008.2.r.d 2
63.g even 3 2 2646.2.h.e 2
63.h even 3 2 2646.2.e.f 2
63.i even 6 2 882.2.e.d 2
63.j odd 6 2 882.2.e.b 2
63.k odd 6 2 2646.2.h.a 2
63.l odd 6 2 2646.2.f.c 2
63.n odd 6 2 882.2.h.j 2
63.o even 6 2 882.2.f.h 2
63.s even 6 2 882.2.h.f 2
63.t odd 6 2 2646.2.e.j 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
126.2.f.a 2 9.d odd 6 2
378.2.f.a 2 9.c even 3 2
882.2.e.b 2 63.j odd 6 2
882.2.e.d 2 63.i even 6 2
882.2.f.h 2 63.o even 6 2
882.2.h.f 2 63.s even 6 2
882.2.h.j 2 63.n odd 6 2
1008.2.r.d 2 36.h even 6 2
1134.2.a.a 1 3.b odd 2 1
1134.2.a.h 1 1.a even 1 1 trivial
2646.2.e.f 2 63.h even 3 2
2646.2.e.j 2 63.t odd 6 2
2646.2.f.c 2 63.l odd 6 2
2646.2.h.a 2 63.k odd 6 2
2646.2.h.e 2 63.g even 3 2
3024.2.r.a 2 36.f odd 6 2
7938.2.a.l 1 21.c even 2 1
7938.2.a.u 1 7.b odd 2 1
9072.2.a.c 1 12.b even 2 1
9072.2.a.w 1 4.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 \(S_{2}^{\mathrm{new}}(\Gamma_0(1134))\):

\( T_{5} - 3 \) Copy content Toggle raw display
\( T_{11} - 6 \) Copy content Toggle raw display
\( T_{13} - 2 \) Copy content Toggle raw display

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T - 1 \) Copy content Toggle raw display
$3$ \( T \) Copy content Toggle raw display
$5$ \( T - 3 \) Copy content Toggle raw display
$7$ \( T - 1 \) Copy content Toggle raw display
$11$ \( T - 6 \) Copy content Toggle raw display
$13$ \( T - 2 \) Copy content Toggle raw display
$17$ \( T + 6 \) Copy content Toggle raw display
$19$ \( T + 7 \) Copy content Toggle raw display
$23$ \( T + 3 \) Copy content Toggle raw display
$29$ \( T + 6 \) Copy content Toggle raw display
$31$ \( T - 2 \) Copy content Toggle raw display
$37$ \( T - 2 \) Copy content Toggle raw display
$41$ \( T \) Copy content Toggle raw display
$43$ \( T - 2 \) Copy content Toggle raw display
$47$ \( T \) Copy content Toggle raw display
$53$ \( T + 6 \) Copy content Toggle raw display
$59$ \( T \) Copy content Toggle raw display
$61$ \( T - 5 \) Copy content Toggle raw display
$67$ \( T - 8 \) Copy content Toggle raw display
$71$ \( T + 3 \) Copy content Toggle raw display
$73$ \( T - 2 \) Copy content Toggle raw display
$79$ \( T - 5 \) Copy content Toggle raw display
$83$ \( T + 12 \) Copy content Toggle raw display
$89$ \( T \) Copy content Toggle raw display
$97$ \( T - 2 \) Copy content Toggle raw display
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