Properties

Label 5586.2.a.b
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

\(f(q)\) \(=\) \( q - q^{2} - q^{3} + q^{4} - 2q^{5} + q^{6} - q^{8} + q^{9} + O(q^{10}) \) \( q - q^{2} - q^{3} + q^{4} - 2q^{5} + q^{6} - q^{8} + q^{9} + 2q^{10} - q^{12} - 2q^{13} + 2q^{15} + q^{16} - 2q^{17} - q^{18} + q^{19} - 2q^{20} + 8q^{23} + q^{24} - q^{25} + 2q^{26} - q^{27} + 2q^{29} - 2q^{30} - 4q^{31} - q^{32} + 2q^{34} + q^{36} + 2q^{37} - q^{38} + 2q^{39} + 2q^{40} - 6q^{41} - 12q^{43} - 2q^{45} - 8q^{46} + 8q^{47} - q^{48} + q^{50} + 2q^{51} - 2q^{52} + 10q^{53} + q^{54} - q^{57} - 2q^{58} + 4q^{59} + 2q^{60} + 10q^{61} + 4q^{62} + q^{64} + 4q^{65} + 4q^{67} - 2q^{68} - 8q^{69} + 8q^{71} - q^{72} - 10q^{73} - 2q^{74} + q^{75} + q^{76} - 2q^{78} - 4q^{79} - 2q^{80} + q^{81} + 6q^{82} + 4q^{85} + 12q^{86} - 2q^{87} - 6q^{89} + 2q^{90} + 8q^{92} + 4q^{93} - 8q^{94} - 2q^{95} + q^{96} + 6q^{97} + O(q^{100}) \)

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 −2.00000 1.00000 0 −1.00000 1.00000 2.00000
\(n\): 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.b 1
7.b odd 2 1 798.2.a.e 1
21.c even 2 1 2394.2.a.h 1
28.d even 2 1 6384.2.a.n 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
798.2.a.e 1 7.b odd 2 1
2394.2.a.h 1 21.c even 2 1
5586.2.a.b 1 1.a even 1 1 trivial
6384.2.a.n 1 28.d even 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(5586))\):

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

Hecke characteristic polynomials

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