Properties

Label 2842.2.a.f
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

\(f(q)\) \(=\) \( q + q^{2} + q^{3} + q^{4} + 3 q^{5} + q^{6} + q^{8} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q + q^{2} + q^{3} + q^{4} + 3 q^{5} + q^{6} + q^{8} - 2 q^{9} + 3 q^{10} - q^{11} + q^{12} + q^{13} + 3 q^{15} + q^{16} + 4 q^{17} - 2 q^{18} + 4 q^{19} + 3 q^{20} - q^{22} - 2 q^{23} + q^{24} + 4 q^{25} + q^{26} - 5 q^{27} + q^{29} + 3 q^{30} + q^{31} + q^{32} - q^{33} + 4 q^{34} - 2 q^{36} + 6 q^{37} + 4 q^{38} + q^{39} + 3 q^{40} + 3 q^{43} - q^{44} - 6 q^{45} - 2 q^{46} + 9 q^{47} + q^{48} + 4 q^{50} + 4 q^{51} + q^{52} + 3 q^{53} - 5 q^{54} - 3 q^{55} + 4 q^{57} + q^{58} + 3 q^{60} - 6 q^{61} + q^{62} + q^{64} + 3 q^{65} - q^{66} + 2 q^{67} + 4 q^{68} - 2 q^{69} - 8 q^{71} - 2 q^{72} + 6 q^{74} + 4 q^{75} + 4 q^{76} + q^{78} - 13 q^{79} + 3 q^{80} + q^{81} + 12 q^{85} + 3 q^{86} + q^{87} - q^{88} + 14 q^{89} - 6 q^{90} - 2 q^{92} + q^{93} + 9 q^{94} + 12 q^{95} + q^{96} - 16 q^{97} + 2 q^{99}+O(q^{100}) \) 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.f 1
7.b odd 2 1 406.2.a.d 1
21.c even 2 1 3654.2.a.l 1
28.d even 2 1 3248.2.a.k 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
406.2.a.d 1 7.b odd 2 1
2842.2.a.f 1 1.a even 1 1 trivial
3248.2.a.k 1 28.d even 2 1
3654.2.a.l 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
$11$ \( T + 1 \) Copy content Toggle raw display
$13$ \( T - 1 \) Copy content Toggle raw display
$17$ \( T - 4 \) Copy content Toggle raw display
$19$ \( T - 4 \) Copy content Toggle raw display
$23$ \( T + 2 \) Copy content Toggle raw display
$29$ \( T - 1 \) Copy content Toggle raw display
$31$ \( T - 1 \) Copy content Toggle raw display
$37$ \( T - 6 \) Copy content Toggle raw display
$41$ \( T \) Copy content Toggle raw display
$43$ \( T - 3 \) Copy content Toggle raw display
$47$ \( T - 9 \) Copy content Toggle raw display
$53$ \( T - 3 \) Copy content Toggle raw display
$59$ \( T \) Copy content Toggle raw display
$61$ \( T + 6 \) Copy content Toggle raw display
$67$ \( T - 2 \) Copy content Toggle raw display
$71$ \( T + 8 \) Copy content Toggle raw display
$73$ \( T \) Copy content Toggle raw display
$79$ \( T + 13 \) Copy content Toggle raw display
$83$ \( T \) Copy content Toggle raw display
$89$ \( T - 14 \) Copy content Toggle raw display
$97$ \( T + 16 \) Copy content Toggle raw display
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