Properties

Label 280.4.a.d
Level $280$
Weight $4$
Character orbit 280.a
Self dual yes
Analytic conductor $16.521$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 280.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(16.5205348016\)
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

\(f(q)\) \(=\) \( q + 7q^{3} + 5q^{5} + 7q^{7} + 22q^{9} + O(q^{10}) \) \( q + 7q^{3} + 5q^{5} + 7q^{7} + 22q^{9} + 9q^{11} + 23q^{13} + 35q^{15} + 41q^{17} + 34q^{19} + 49q^{21} - 6q^{23} + 25q^{25} - 35q^{27} + 131q^{29} + 4q^{31} + 63q^{33} + 35q^{35} + 26q^{37} + 161q^{39} - 260q^{41} - 190q^{43} + 110q^{45} + 167q^{47} + 49q^{49} + 287q^{51} - 368q^{53} + 45q^{55} + 238q^{57} + 324q^{59} - 164q^{61} + 154q^{63} + 115q^{65} + 200q^{67} - 42q^{69} + 784q^{71} - 410q^{73} + 175q^{75} + 63q^{77} + 1211q^{79} - 839q^{81} - 1132q^{83} + 205q^{85} + 917q^{87} - 72q^{89} + 161q^{91} + 28q^{93} + 170q^{95} - 707q^{97} + 198q^{99} + O(q^{100}) \)

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
0 7.00000 0 5.00000 0 7.00000 0 22.0000 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \(1\)
\(5\) \(-1\)
\(7\) \(-1\)

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 280.4.a.d 1
4.b odd 2 1 560.4.a.d 1
5.b even 2 1 1400.4.a.a 1
5.c odd 4 2 1400.4.g.a 2
7.b odd 2 1 1960.4.a.b 1
8.b even 2 1 2240.4.a.e 1
8.d odd 2 1 2240.4.a.bg 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
280.4.a.d 1 1.a even 1 1 trivial
560.4.a.d 1 4.b odd 2 1
1400.4.a.a 1 5.b even 2 1
1400.4.g.a 2 5.c odd 4 2
1960.4.a.b 1 7.b odd 2 1
2240.4.a.e 1 8.b even 2 1
2240.4.a.bg 1 8.d odd 2 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3} - 7 \) acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(280))\).

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T \)
$3$ \( -7 + T \)
$5$ \( -5 + T \)
$7$ \( -7 + T \)
$11$ \( -9 + T \)
$13$ \( -23 + T \)
$17$ \( -41 + T \)
$19$ \( -34 + T \)
$23$ \( 6 + T \)
$29$ \( -131 + T \)
$31$ \( -4 + T \)
$37$ \( -26 + T \)
$41$ \( 260 + T \)
$43$ \( 190 + T \)
$47$ \( -167 + T \)
$53$ \( 368 + T \)
$59$ \( -324 + T \)
$61$ \( 164 + T \)
$67$ \( -200 + T \)
$71$ \( -784 + T \)
$73$ \( 410 + T \)
$79$ \( -1211 + T \)
$83$ \( 1132 + T \)
$89$ \( 72 + T \)
$97$ \( 707 + T \)
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