Properties

Label 5586.2.a.v
Level $5586$
Weight $2$
Character orbit 5586.a
Self dual yes
Analytic conductor $44.604$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 5586 = 2 \cdot 3 \cdot 7^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5586.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(44.6044345691\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 798)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + q^{2} - q^{3} + q^{4} + q^{5} - q^{6} + q^{8} + q^{9} + O(q^{10}) \) \( q + q^{2} - q^{3} + q^{4} + q^{5} - q^{6} + q^{8} + q^{9} + q^{10} - q^{11} - q^{12} - 6q^{13} - q^{15} + q^{16} + 2q^{17} + q^{18} + q^{19} + q^{20} - q^{22} - q^{23} - q^{24} - 4q^{25} - 6q^{26} - q^{27} + 4q^{29} - q^{30} + q^{32} + q^{33} + 2q^{34} + q^{36} + 8q^{37} + q^{38} + 6q^{39} + q^{40} - 12q^{41} - 7q^{43} - q^{44} + q^{45} - q^{46} - 9q^{47} - q^{48} - 4q^{50} - 2q^{51} - 6q^{52} - q^{54} - q^{55} - q^{57} + 4q^{58} - 2q^{59} - q^{60} - 3q^{61} + q^{64} - 6q^{65} + q^{66} - 2q^{67} + 2q^{68} + q^{69} + 2q^{71} + q^{72} + q^{73} + 8q^{74} + 4q^{75} + q^{76} + 6q^{78} + 12q^{79} + q^{80} + q^{81} - 12q^{82} - q^{83} + 2q^{85} - 7q^{86} - 4q^{87} - q^{88} - 18q^{89} + q^{90} - q^{92} - 9q^{94} + q^{95} - q^{96} + 4q^{97} - q^{99} + O(q^{100}) \)

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

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(3\) \(1\)
\(7\) \(1\)
\(19\) \(-1\)

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 5586.2.a.v 1
7.b odd 2 1 5586.2.a.ba 1
7.c even 3 2 798.2.j.a 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
798.2.j.a 2 7.c even 3 2
5586.2.a.v 1 1.a even 1 1 trivial
5586.2.a.ba 1 7.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 \(S_{2}^{\mathrm{new}}(\Gamma_0(5586))\):

\( T_{5} - 1 \)
\( T_{11} + 1 \)
\( T_{13} + 6 \)
\( T_{17} - 2 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( -1 + T \)
$3$ \( 1 + T \)
$5$ \( -1 + T \)
$7$ \( T \)
$11$ \( 1 + T \)
$13$ \( 6 + T \)
$17$ \( -2 + T \)
$19$ \( -1 + T \)
$23$ \( 1 + T \)
$29$ \( -4 + T \)
$31$ \( T \)
$37$ \( -8 + T \)
$41$ \( 12 + T \)
$43$ \( 7 + T \)
$47$ \( 9 + T \)
$53$ \( T \)
$59$ \( 2 + T \)
$61$ \( 3 + T \)
$67$ \( 2 + T \)
$71$ \( -2 + T \)
$73$ \( -1 + T \)
$79$ \( -12 + T \)
$83$ \( 1 + T \)
$89$ \( 18 + T \)
$97$ \( -4 + T \)
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