Properties

Label 5390.2.a.i
Level $5390$
Weight $2$
Character orbit 5390.a
Self dual yes
Analytic conductor $43.039$
Analytic rank $0$
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: \(0\)
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

\(f(q)\) \(=\) \( q - q^{2} + q^{4} - q^{5} - q^{8} - 3 q^{9} + O(q^{10}) \) \( q - q^{2} + q^{4} - q^{5} - q^{8} - 3 q^{9} + q^{10} - q^{11} - 2 q^{13} + q^{16} - 6 q^{17} + 3 q^{18} - 4 q^{19} - q^{20} + q^{22} + 4 q^{23} + q^{25} + 2 q^{26} - 2 q^{29} - 8 q^{31} - q^{32} + 6 q^{34} - 3 q^{36} - 10 q^{37} + 4 q^{38} + q^{40} + 6 q^{41} + 12 q^{43} - q^{44} + 3 q^{45} - 4 q^{46} - 12 q^{47} - q^{50} - 2 q^{52} + 6 q^{53} + q^{55} + 2 q^{58} + 12 q^{59} - 6 q^{61} + 8 q^{62} + q^{64} + 2 q^{65} + 8 q^{67} - 6 q^{68} - 8 q^{71} + 3 q^{72} - 14 q^{73} + 10 q^{74} - 4 q^{76} - q^{80} + 9 q^{81} - 6 q^{82} - 4 q^{83} + 6 q^{85} - 12 q^{86} + q^{88} + 6 q^{89} - 3 q^{90} + 4 q^{92} + 12 q^{94} + 4 q^{95} + 14 q^{97} + 3 q^{99} + O(q^{100}) \)

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 0 1.00000 −1.00000 0 0 −1.00000 −3.00000 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.i 1
7.b odd 2 1 770.2.a.c 1
21.c even 2 1 6930.2.a.u 1
28.d even 2 1 6160.2.a.i 1
35.c odd 2 1 3850.2.a.t 1
35.f even 4 2 3850.2.c.h 2
77.b even 2 1 8470.2.a.ba 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
770.2.a.c 1 7.b odd 2 1
3850.2.a.t 1 35.c odd 2 1
3850.2.c.h 2 35.f even 4 2
5390.2.a.i 1 1.a even 1 1 trivial
6160.2.a.i 1 28.d even 2 1
6930.2.a.u 1 21.c even 2 1
8470.2.a.ba 1 77.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 \(S_{2}^{\mathrm{new}}(\Gamma_0(5390))\):

\( T_{3} \)
\( T_{13} + 2 \)
\( T_{17} + 6 \)
\( T_{19} + 4 \)
\( T_{31} + 8 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 1 + T \)
$3$ \( T \)
$5$ \( 1 + T \)
$7$ \( T \)
$11$ \( 1 + T \)
$13$ \( 2 + T \)
$17$ \( 6 + T \)
$19$ \( 4 + T \)
$23$ \( -4 + T \)
$29$ \( 2 + T \)
$31$ \( 8 + T \)
$37$ \( 10 + T \)
$41$ \( -6 + T \)
$43$ \( -12 + T \)
$47$ \( 12 + T \)
$53$ \( -6 + T \)
$59$ \( -12 + T \)
$61$ \( 6 + T \)
$67$ \( -8 + T \)
$71$ \( 8 + T \)
$73$ \( 14 + T \)
$79$ \( T \)
$83$ \( 4 + T \)
$89$ \( -6 + T \)
$97$ \( -14 + T \)
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