Properties

Label 5290.2.a.b
Level $5290$
Weight $2$
Character orbit 5290.a
Self dual yes
Analytic conductor $42.241$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 5290 = 2 \cdot 5 \cdot 23^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5290.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(42.2408626693\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q - q^{2} - q^{3} + q^{4} + q^{5} + q^{6} - 2q^{7} - q^{8} - 2q^{9} + O(q^{10}) \) \( q - q^{2} - q^{3} + q^{4} + q^{5} + q^{6} - 2q^{7} - q^{8} - 2q^{9} - q^{10} - 4q^{11} - q^{12} + 4q^{13} + 2q^{14} - q^{15} + q^{16} - 3q^{17} + 2q^{18} - q^{19} + q^{20} + 2q^{21} + 4q^{22} + q^{24} + q^{25} - 4q^{26} + 5q^{27} - 2q^{28} + 8q^{29} + q^{30} + 2q^{31} - q^{32} + 4q^{33} + 3q^{34} - 2q^{35} - 2q^{36} + 2q^{37} + q^{38} - 4q^{39} - q^{40} + 6q^{41} - 2q^{42} - 3q^{43} - 4q^{44} - 2q^{45} + 2q^{47} - q^{48} - 3q^{49} - q^{50} + 3q^{51} + 4q^{52} + 4q^{53} - 5q^{54} - 4q^{55} + 2q^{56} + q^{57} - 8q^{58} + 7q^{59} - q^{60} + 12q^{61} - 2q^{62} + 4q^{63} + q^{64} + 4q^{65} - 4q^{66} + 5q^{67} - 3q^{68} + 2q^{70} - 14q^{71} + 2q^{72} + 11q^{73} - 2q^{74} - q^{75} - q^{76} + 8q^{77} + 4q^{78} - 8q^{79} + q^{80} + q^{81} - 6q^{82} - 7q^{83} + 2q^{84} - 3q^{85} + 3q^{86} - 8q^{87} + 4q^{88} - 18q^{89} + 2q^{90} - 8q^{91} - 2q^{93} - 2q^{94} - q^{95} + q^{96} - 14q^{97} + 3q^{98} + 8q^{99} + O(q^{100}) \)

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

Atkin-Lehner signs

\( p \) Sign
\(2\) \(1\)
\(5\) \(-1\)
\(23\) \(-1\)

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 5290.2.a.b yes 1
23.b odd 2 1 5290.2.a.a 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
5290.2.a.a 1 23.b odd 2 1
5290.2.a.b yes 1 1.a even 1 1 trivial

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(5290))\):

\( T_{3} + 1 \)
\( T_{7} + 2 \)
\( T_{11} + 4 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 1 + T \)
$3$ \( 1 + T \)
$5$ \( -1 + T \)
$7$ \( 2 + T \)
$11$ \( 4 + T \)
$13$ \( -4 + T \)
$17$ \( 3 + T \)
$19$ \( 1 + T \)
$23$ \( T \)
$29$ \( -8 + T \)
$31$ \( -2 + T \)
$37$ \( -2 + T \)
$41$ \( -6 + T \)
$43$ \( 3 + T \)
$47$ \( -2 + T \)
$53$ \( -4 + T \)
$59$ \( -7 + T \)
$61$ \( -12 + T \)
$67$ \( -5 + T \)
$71$ \( 14 + T \)
$73$ \( -11 + T \)
$79$ \( 8 + T \)
$83$ \( 7 + T \)
$89$ \( 18 + T \)
$97$ \( 14 + T \)
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