Properties

Label 1290.2.a.b
Level $1290$
Weight $2$
Character orbit 1290.a
Self dual yes
Analytic conductor $10.301$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1290 = 2 \cdot 3 \cdot 5 \cdot 43 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1290.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(10.3007018607\)
Analytic rank: \(0\)
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

\(f(q)\) \(=\) \( q - q^{2} - q^{3} + q^{4} + q^{5} + q^{6} - q^{8} + q^{9} + O(q^{10}) \) \( q - q^{2} - q^{3} + q^{4} + q^{5} + q^{6} - q^{8} + q^{9} - q^{10} + 6q^{11} - q^{12} + 2q^{13} - q^{15} + q^{16} - q^{18} - 2q^{19} + q^{20} - 6q^{22} - 4q^{23} + q^{24} + q^{25} - 2q^{26} - q^{27} + 2q^{29} + q^{30} + 8q^{31} - q^{32} - 6q^{33} + q^{36} - 8q^{37} + 2q^{38} - 2q^{39} - q^{40} - 2q^{41} - q^{43} + 6q^{44} + q^{45} + 4q^{46} + 12q^{47} - q^{48} - 7q^{49} - q^{50} + 2q^{52} + 8q^{53} + q^{54} + 6q^{55} + 2q^{57} - 2q^{58} + 2q^{59} - q^{60} - 6q^{61} - 8q^{62} + q^{64} + 2q^{65} + 6q^{66} - 4q^{67} + 4q^{69} + 12q^{71} - q^{72} + 8q^{74} - q^{75} - 2q^{76} + 2q^{78} + q^{80} + q^{81} + 2q^{82} + 12q^{83} + q^{86} - 2q^{87} - 6q^{88} + 6q^{89} - q^{90} - 4q^{92} - 8q^{93} - 12q^{94} - 2q^{95} + q^{96} - 2q^{97} + 7q^{98} + 6q^{99} + O(q^{100}) \)

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
\(2\) \(1\)
\(3\) \(1\)
\(5\) \(-1\)
\(43\) \(1\)

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 1290.2.a.b 1
3.b odd 2 1 3870.2.a.p 1
5.b even 2 1 6450.2.a.bk 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1290.2.a.b 1 1.a even 1 1 trivial
3870.2.a.p 1 3.b odd 2 1
6450.2.a.bk 1 5.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 \(S_{2}^{\mathrm{new}}(\Gamma_0(1290))\):

\( T_{7} \)
\( T_{11} - 6 \)

Hecke characteristic polynomials

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