Properties

Label 2842.2.a.a
Level $2842$
Weight $2$
Character orbit 2842.a
Self dual yes
Analytic conductor $22.693$
Analytic rank $0$
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: \(0\)
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

\(f(q)\) \(=\) \( q - q^{2} - 2 q^{3} + q^{4} - 2 q^{5} + 2 q^{6} - q^{8} + q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q - q^{2} - 2 q^{3} + q^{4} - 2 q^{5} + 2 q^{6} - q^{8} + q^{9} + 2 q^{10} + 4 q^{11} - 2 q^{12} + 2 q^{13} + 4 q^{15} + q^{16} + 4 q^{17} - q^{18} - 2 q^{19} - 2 q^{20} - 4 q^{22} + 2 q^{24} - q^{25} - 2 q^{26} + 4 q^{27} - q^{29} - 4 q^{30} + 2 q^{31} - q^{32} - 8 q^{33} - 4 q^{34} + q^{36} + 2 q^{37} + 2 q^{38} - 4 q^{39} + 2 q^{40} - 8 q^{41} - 8 q^{43} + 4 q^{44} - 2 q^{45} - 6 q^{47} - 2 q^{48} + q^{50} - 8 q^{51} + 2 q^{52} + 6 q^{53} - 4 q^{54} - 8 q^{55} + 4 q^{57} + q^{58} + 4 q^{59} + 4 q^{60} - 4 q^{61} - 2 q^{62} + q^{64} - 4 q^{65} + 8 q^{66} - 4 q^{67} + 4 q^{68} + 8 q^{71} - q^{72} + 12 q^{73} - 2 q^{74} + 2 q^{75} - 2 q^{76} + 4 q^{78} - 12 q^{79} - 2 q^{80} - 11 q^{81} + 8 q^{82} - 8 q^{85} + 8 q^{86} + 2 q^{87} - 4 q^{88} - 4 q^{89} + 2 q^{90} - 4 q^{93} + 6 q^{94} + 4 q^{95} + 2 q^{96} - 4 q^{97} + 4 q^{99}+O(q^{100}) \) 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 −2.00000 1.00000 −2.00000 2.00000 0 −1.00000 1.00000 2.00000
\(n\): 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.a 1
7.b odd 2 1 406.2.a.c 1
21.c even 2 1 3654.2.a.n 1
28.d even 2 1 3248.2.a.c 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
406.2.a.c 1 7.b odd 2 1
2842.2.a.a 1 1.a even 1 1 trivial
3248.2.a.c 1 28.d even 2 1
3654.2.a.n 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(2842))\):

\( T_{3} + 2 \) Copy content Toggle raw display
\( T_{5} + 2 \) Copy content Toggle raw display

Hecke characteristic polynomials

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