Properties

Label 5390.2.a.z
Level $5390$
Weight $2$
Character orbit 5390.a
Self dual yes
Analytic conductor $43.039$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 5390 = 2 \cdot 5 \cdot 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5390.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(43.0393666895\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 770)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + q^{2} - q^{3} + q^{4} + q^{5} - q^{6} + q^{8} - 2 q^{9} + O(q^{10}) \) \( q + q^{2} - q^{3} + q^{4} + q^{5} - q^{6} + q^{8} - 2 q^{9} + q^{10} + q^{11} - q^{12} + q^{13} - q^{15} + q^{16} - 2 q^{18} - 2 q^{19} + q^{20} + q^{22} - 6 q^{23} - q^{24} + q^{25} + q^{26} + 5 q^{27} - 9 q^{29} - q^{30} + 4 q^{31} + q^{32} - q^{33} - 2 q^{36} - 4 q^{37} - 2 q^{38} - q^{39} + q^{40} - 12 q^{41} - 10 q^{43} + q^{44} - 2 q^{45} - 6 q^{46} + 12 q^{47} - q^{48} + q^{50} + q^{52} + 6 q^{53} + 5 q^{54} + q^{55} + 2 q^{57} - 9 q^{58} - 3 q^{59} - q^{60} + 7 q^{61} + 4 q^{62} + q^{64} + q^{65} - q^{66} - 13 q^{67} + 6 q^{69} - 2 q^{72} - 14 q^{73} - 4 q^{74} - q^{75} - 2 q^{76} - q^{78} + 17 q^{79} + q^{80} + q^{81} - 12 q^{82} - 6 q^{83} - 10 q^{86} + 9 q^{87} + q^{88} + 6 q^{89} - 2 q^{90} - 6 q^{92} - 4 q^{93} + 12 q^{94} - 2 q^{95} - q^{96} - 5 q^{97} - 2 q^{99} + O(q^{100}) \)

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

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(5\) \(-1\)
\(7\) \(-1\)
\(11\) \(-1\)

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 5390.2.a.z 1
7.b odd 2 1 5390.2.a.be 1
7.d odd 6 2 770.2.i.a 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
770.2.i.a 2 7.d odd 6 2
5390.2.a.z 1 1.a even 1 1 trivial
5390.2.a.be 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(5390))\):

\( T_{3} + 1 \)
\( T_{13} - 1 \)
\( T_{17} \)
\( T_{19} + 2 \)
\( T_{31} - 4 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( -1 + T \)
$3$ \( 1 + T \)
$5$ \( -1 + T \)
$7$ \( T \)
$11$ \( -1 + T \)
$13$ \( -1 + T \)
$17$ \( T \)
$19$ \( 2 + T \)
$23$ \( 6 + T \)
$29$ \( 9 + T \)
$31$ \( -4 + T \)
$37$ \( 4 + T \)
$41$ \( 12 + T \)
$43$ \( 10 + T \)
$47$ \( -12 + T \)
$53$ \( -6 + T \)
$59$ \( 3 + T \)
$61$ \( -7 + T \)
$67$ \( 13 + T \)
$71$ \( T \)
$73$ \( 14 + T \)
$79$ \( -17 + T \)
$83$ \( 6 + T \)
$89$ \( -6 + T \)
$97$ \( 5 + T \)
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