Properties

Label 2842.2.a.b
Level $2842$
Weight $2$
Character orbit 2842.a
Self dual yes
Analytic conductor $22.693$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 2842 = 2 \cdot 7^{2} \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2842.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(22.6934842544\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 406)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q - q^{2} - q^{3} + q^{4} + 3 q^{5} + q^{6} - q^{8} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q - q^{2} - q^{3} + q^{4} + 3 q^{5} + q^{6} - q^{8} - 2 q^{9} - 3 q^{10} - 3 q^{11} - q^{12} + q^{13} - 3 q^{15} + q^{16} + 2 q^{18} + 4 q^{19} + 3 q^{20} + 3 q^{22} - 6 q^{23} + q^{24} + 4 q^{25} - q^{26} + 5 q^{27} + q^{29} + 3 q^{30} - 5 q^{31} - q^{32} + 3 q^{33} - 2 q^{36} + 2 q^{37} - 4 q^{38} - q^{39} - 3 q^{40} - 7 q^{43} - 3 q^{44} - 6 q^{45} + 6 q^{46} + 3 q^{47} - q^{48} - 4 q^{50} + q^{52} - 9 q^{53} - 5 q^{54} - 9 q^{55} - 4 q^{57} - q^{58} - 12 q^{59} - 3 q^{60} + 10 q^{61} + 5 q^{62} + q^{64} + 3 q^{65} - 3 q^{66} + 2 q^{67} + 6 q^{69} - 12 q^{71} + 2 q^{72} - 8 q^{73} - 2 q^{74} - 4 q^{75} + 4 q^{76} + q^{78} + 5 q^{79} + 3 q^{80} + q^{81} - 12 q^{83} + 7 q^{86} - q^{87} + 3 q^{88} - 6 q^{89} + 6 q^{90} - 6 q^{92} + 5 q^{93} - 3 q^{94} + 12 q^{95} + q^{96} - 8 q^{97} + 6 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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 3.00000 1.00000 0 −1.00000 −2.00000 −3.00000
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \(1\)
\(7\) \(-1\)
\(29\) \(-1\)

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 2842.2.a.b 1
7.b odd 2 1 406.2.a.b 1
21.c even 2 1 3654.2.a.w 1
28.d even 2 1 3248.2.a.f 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
406.2.a.b 1 7.b odd 2 1
2842.2.a.b 1 1.a even 1 1 trivial
3248.2.a.f 1 28.d even 2 1
3654.2.a.w 1 21.c even 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(2842))\):

\( T_{3} + 1 \) Copy content Toggle raw display
\( T_{5} - 3 \) Copy content Toggle raw display

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T + 1 \) Copy content Toggle raw display
$3$ \( T + 1 \) Copy content Toggle raw display
$5$ \( T - 3 \) Copy content Toggle raw display
$7$ \( T \) Copy content Toggle raw display
$11$ \( T + 3 \) Copy content Toggle raw display
$13$ \( T - 1 \) Copy content Toggle raw display
$17$ \( T \) Copy content Toggle raw display
$19$ \( T - 4 \) Copy content Toggle raw display
$23$ \( T + 6 \) Copy content Toggle raw display
$29$ \( T - 1 \) Copy content Toggle raw display
$31$ \( T + 5 \) Copy content Toggle raw display
$37$ \( T - 2 \) Copy content Toggle raw display
$41$ \( T \) Copy content Toggle raw display
$43$ \( T + 7 \) Copy content Toggle raw display
$47$ \( T - 3 \) Copy content Toggle raw display
$53$ \( T + 9 \) Copy content Toggle raw display
$59$ \( T + 12 \) Copy content Toggle raw display
$61$ \( T - 10 \) Copy content Toggle raw display
$67$ \( T - 2 \) Copy content Toggle raw display
$71$ \( T + 12 \) Copy content Toggle raw display
$73$ \( T + 8 \) Copy content Toggle raw display
$79$ \( T - 5 \) Copy content Toggle raw display
$83$ \( T + 12 \) Copy content Toggle raw display
$89$ \( T + 6 \) Copy content Toggle raw display
$97$ \( T + 8 \) Copy content Toggle raw display
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