Properties

Label 1134.2.a.f
Level 1134
Weight 2
Character orbit 1134.a
Self dual yes
Analytic conductor 9.055
Analytic rank 1
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: \(1\)
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

\(f(q)\) \(=\) \( q + q^{2} + q^{4} - 2q^{5} - q^{7} + q^{8} + O(q^{10}) \) \( q + q^{2} + q^{4} - 2q^{5} - q^{7} + q^{8} - 2q^{10} - q^{11} - 6q^{13} - q^{14} + q^{16} + 5q^{17} - 7q^{19} - 2q^{20} - q^{22} - 4q^{23} - q^{25} - 6q^{26} - q^{28} + 4q^{29} - 6q^{31} + q^{32} + 5q^{34} + 2q^{35} + 2q^{37} - 7q^{38} - 2q^{40} - 3q^{41} - q^{43} - q^{44} - 4q^{46} + q^{49} - q^{50} - 6q^{52} - 12q^{53} + 2q^{55} - q^{56} + 4q^{58} + 7q^{59} - 12q^{61} - 6q^{62} + q^{64} + 12q^{65} + 13q^{67} + 5q^{68} + 2q^{70} + 8q^{71} + q^{73} + 2q^{74} - 7q^{76} + q^{77} - 6q^{79} - 2q^{80} - 3q^{82} - 16q^{83} - 10q^{85} - q^{86} - q^{88} + 6q^{89} + 6q^{91} - 4q^{92} + 14q^{95} - 5q^{97} + q^{98} + O(q^{100}) \)

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 −2.00000 0 −1.00000 1.00000 0 −2.00000
\(n\): 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.f 1
3.b odd 2 1 1134.2.a.c 1
4.b odd 2 1 9072.2.a.f 1
7.b odd 2 1 7938.2.a.bb 1
9.c even 3 2 378.2.f.b 2
9.d odd 6 2 126.2.f.b 2
12.b even 2 1 9072.2.a.t 1
21.c even 2 1 7938.2.a.e 1
36.f odd 6 2 3024.2.r.c 2
36.h even 6 2 1008.2.r.a 2
63.g even 3 2 2646.2.h.b 2
63.h even 3 2 2646.2.e.i 2
63.i even 6 2 882.2.e.e 2
63.j odd 6 2 882.2.e.a 2
63.k odd 6 2 2646.2.h.c 2
63.l odd 6 2 2646.2.f.b 2
63.n odd 6 2 882.2.h.h 2
63.o even 6 2 882.2.f.f 2
63.s even 6 2 882.2.h.g 2
63.t odd 6 2 2646.2.e.h 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
126.2.f.b 2 9.d odd 6 2
378.2.f.b 2 9.c even 3 2
882.2.e.a 2 63.j odd 6 2
882.2.e.e 2 63.i even 6 2
882.2.f.f 2 63.o even 6 2
882.2.h.g 2 63.s even 6 2
882.2.h.h 2 63.n odd 6 2
1008.2.r.a 2 36.h even 6 2
1134.2.a.c 1 3.b odd 2 1
1134.2.a.f 1 1.a even 1 1 trivial
2646.2.e.h 2 63.t odd 6 2
2646.2.e.i 2 63.h even 3 2
2646.2.f.b 2 63.l odd 6 2
2646.2.h.b 2 63.g even 3 2
2646.2.h.c 2 63.k odd 6 2
3024.2.r.c 2 36.f odd 6 2
7938.2.a.e 1 21.c even 2 1
7938.2.a.bb 1 7.b odd 2 1
9072.2.a.f 1 4.b odd 2 1
9072.2.a.t 1 12.b even 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(1134))\):

\( T_{5} + 2 \)
\( T_{11} + 1 \)
\( T_{13} + 6 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 1 - T \)
$3$ 1
$5$ \( 1 + 2 T + 5 T^{2} \)
$7$ \( 1 + T \)
$11$ \( 1 + T + 11 T^{2} \)
$13$ \( 1 + 6 T + 13 T^{2} \)
$17$ \( 1 - 5 T + 17 T^{2} \)
$19$ \( 1 + 7 T + 19 T^{2} \)
$23$ \( 1 + 4 T + 23 T^{2} \)
$29$ \( 1 - 4 T + 29 T^{2} \)
$31$ \( 1 + 6 T + 31 T^{2} \)
$37$ \( 1 - 2 T + 37 T^{2} \)
$41$ \( 1 + 3 T + 41 T^{2} \)
$43$ \( 1 + T + 43 T^{2} \)
$47$ \( 1 + 47 T^{2} \)
$53$ \( 1 + 12 T + 53 T^{2} \)
$59$ \( 1 - 7 T + 59 T^{2} \)
$61$ \( 1 + 12 T + 61 T^{2} \)
$67$ \( 1 - 13 T + 67 T^{2} \)
$71$ \( 1 - 8 T + 71 T^{2} \)
$73$ \( 1 - T + 73 T^{2} \)
$79$ \( 1 + 6 T + 79 T^{2} \)
$83$ \( 1 + 16 T + 83 T^{2} \)
$89$ \( 1 - 6 T + 89 T^{2} \)
$97$ \( 1 + 5 T + 97 T^{2} \)
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