Properties

Label 931.2.a.b
Level $931$
Weight $2$
Character orbit 931.a
Self dual yes
Analytic conductor $7.434$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 931 = 7^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 931.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(7.43407242818\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 133)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 3 q^{5} - 4 q^{6} + q^{9} + O(q^{10}) \) \( q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 3 q^{5} - 4 q^{6} + q^{9} - 6 q^{10} + 4 q^{11} - 4 q^{12} + 6 q^{13} + 6 q^{15} - 4 q^{16} + 7 q^{17} + 2 q^{18} - q^{19} - 6 q^{20} + 8 q^{22} + 3 q^{23} + 4 q^{25} + 12 q^{26} + 4 q^{27} + 12 q^{30} - 8 q^{32} - 8 q^{33} + 14 q^{34} + 2 q^{36} - 2 q^{37} - 2 q^{38} - 12 q^{39} + 4 q^{41} + 5 q^{43} + 8 q^{44} - 3 q^{45} + 6 q^{46} - 4 q^{47} + 8 q^{48} + 8 q^{50} - 14 q^{51} + 12 q^{52} + 6 q^{53} + 8 q^{54} - 12 q^{55} + 2 q^{57} - 8 q^{59} + 12 q^{60} + 2 q^{61} - 8 q^{64} - 18 q^{65} - 16 q^{66} + 8 q^{67} + 14 q^{68} - 6 q^{69} - 2 q^{71} - 10 q^{73} - 4 q^{74} - 8 q^{75} - 2 q^{76} - 24 q^{78} + 12 q^{79} + 12 q^{80} - 11 q^{81} + 8 q^{82} + 3 q^{83} - 21 q^{85} + 10 q^{86} + 8 q^{89} - 6 q^{90} + 6 q^{92} - 8 q^{94} + 3 q^{95} + 16 q^{96} - 4 q^{97} + 4 q^{99} + O(q^{100}) \)

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
2.00000 −2.00000 2.00000 −3.00000 −4.00000 0 0 1.00000 −6.00000
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(7\) \(-1\)
\(19\) \(1\)

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 931.2.a.b 1
3.b odd 2 1 8379.2.a.d 1
7.b odd 2 1 931.2.a.c 1
7.c even 3 2 931.2.f.a 2
7.d odd 6 2 133.2.f.a 2
21.c even 2 1 8379.2.a.a 1
21.g even 6 2 1197.2.j.c 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
133.2.f.a 2 7.d odd 6 2
931.2.a.b 1 1.a even 1 1 trivial
931.2.a.c 1 7.b odd 2 1
931.2.f.a 2 7.c even 3 2
1197.2.j.c 2 21.g even 6 2
8379.2.a.a 1 21.c even 2 1
8379.2.a.d 1 3.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 \(S_{2}^{\mathrm{new}}(\Gamma_0(931))\):

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

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( -2 + T \)
$3$ \( 2 + T \)
$5$ \( 3 + T \)
$7$ \( T \)
$11$ \( -4 + T \)
$13$ \( -6 + T \)
$17$ \( -7 + T \)
$19$ \( 1 + T \)
$23$ \( -3 + T \)
$29$ \( T \)
$31$ \( T \)
$37$ \( 2 + T \)
$41$ \( -4 + T \)
$43$ \( -5 + T \)
$47$ \( 4 + T \)
$53$ \( -6 + T \)
$59$ \( 8 + T \)
$61$ \( -2 + T \)
$67$ \( -8 + T \)
$71$ \( 2 + T \)
$73$ \( 10 + T \)
$79$ \( -12 + T \)
$83$ \( -3 + T \)
$89$ \( -8 + T \)
$97$ \( 4 + T \)
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