Properties

Label 280.6.a.b
Level $280$
Weight $6$
Character orbit 280.a
Self dual yes
Analytic conductor $44.907$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 280.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(44.9074695476\)
Analytic rank: \(1\)
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

\(f(q)\) \(=\) \( q + 4 q^{3} + 25 q^{5} - 49 q^{7} - 227 q^{9} + O(q^{10}) \) \( q + 4 q^{3} + 25 q^{5} - 49 q^{7} - 227 q^{9} + 124 q^{11} + 766 q^{13} + 100 q^{15} - 1102 q^{17} - 764 q^{19} - 196 q^{21} + 168 q^{23} + 625 q^{25} - 1880 q^{27} - 6866 q^{29} - 4096 q^{31} + 496 q^{33} - 1225 q^{35} - 4682 q^{37} + 3064 q^{39} + 13130 q^{41} + 18220 q^{43} - 5675 q^{45} - 7104 q^{47} + 2401 q^{49} - 4408 q^{51} - 20026 q^{53} + 3100 q^{55} - 3056 q^{57} - 38964 q^{59} - 56274 q^{61} + 11123 q^{63} + 19150 q^{65} - 24060 q^{67} + 672 q^{69} - 31896 q^{71} - 23670 q^{73} + 2500 q^{75} - 6076 q^{77} + 37744 q^{79} + 47641 q^{81} - 68204 q^{83} - 27550 q^{85} - 27464 q^{87} - 19078 q^{89} - 37534 q^{91} - 16384 q^{93} - 19100 q^{95} - 115646 q^{97} - 28148 q^{99} + O(q^{100}) \)

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 4.00000 0 25.0000 0 −49.0000 0 −227.000 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 280.6.a.b 1
4.b odd 2 1 560.6.a.b 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
280.6.a.b 1 1.a even 1 1 trivial
560.6.a.b 1 4.b odd 2 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3} - 4 \) acting on \(S_{6}^{\mathrm{new}}(\Gamma_0(280))\).

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T \)
$3$ \( -4 + T \)
$5$ \( -25 + T \)
$7$ \( 49 + T \)
$11$ \( -124 + T \)
$13$ \( -766 + T \)
$17$ \( 1102 + T \)
$19$ \( 764 + T \)
$23$ \( -168 + T \)
$29$ \( 6866 + T \)
$31$ \( 4096 + T \)
$37$ \( 4682 + T \)
$41$ \( -13130 + T \)
$43$ \( -18220 + T \)
$47$ \( 7104 + T \)
$53$ \( 20026 + T \)
$59$ \( 38964 + T \)
$61$ \( 56274 + T \)
$67$ \( 24060 + T \)
$71$ \( 31896 + T \)
$73$ \( 23670 + T \)
$79$ \( -37744 + T \)
$83$ \( 68204 + T \)
$89$ \( 19078 + T \)
$97$ \( 115646 + T \)
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