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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Newspace parameters

Level: \( N \) \(=\) \( 1134 = 2 \cdot 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1134.a (trivial)

Newform invariants

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

\(f(q)\) \(=\) \( q + q^{2} + q^{4} + 3q^{5} + q^{7} + q^{8} + O(q^{10}) \) \( q + q^{2} + q^{4} + 3q^{5} + q^{7} + q^{8} + 3q^{10} + 6q^{11} + 2q^{13} + q^{14} + q^{16} - 6q^{17} - 7q^{19} + 3q^{20} + 6q^{22} - 3q^{23} + 4q^{25} + 2q^{26} + q^{28} - 6q^{29} + 2q^{31} + q^{32} - 6q^{34} + 3q^{35} + 2q^{37} - 7q^{38} + 3q^{40} + 2q^{43} + 6q^{44} - 3q^{46} + q^{49} + 4q^{50} + 2q^{52} - 6q^{53} + 18q^{55} + q^{56} - 6q^{58} + 5q^{61} + 2q^{62} + q^{64} + 6q^{65} + 8q^{67} - 6q^{68} + 3q^{70} - 3q^{71} + 2q^{73} + 2q^{74} - 7q^{76} + 6q^{77} + 5q^{79} + 3q^{80} - 12q^{83} - 18q^{85} + 2q^{86} + 6q^{88} + 2q^{91} - 3q^{92} - 21q^{95} + 2q^{97} + q^{98} + O(q^{100}) \)

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.

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 \(S_{2}^{\mathrm{new}}(\Gamma_0(1134))\):

\( T_{5} - 3 \)
\( T_{11} - 6 \)
\( T_{13} - 2 \)

Hecke characteristic polynomials

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