Properties

Label 280.6.a.a
Level $280$
Weight $6$
Character orbit 280.a
Self dual yes
Analytic conductor $44.907$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

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: \(0\)
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

\(f(q)\) \(=\) \( q - 12q^{3} + 25q^{5} - 49q^{7} - 99q^{9} + O(q^{10}) \) \( q - 12q^{3} + 25q^{5} - 49q^{7} - 99q^{9} + 556q^{11} - 354q^{13} - 300q^{15} + 770q^{17} - 2684q^{19} + 588q^{21} - 1528q^{23} + 625q^{25} + 4104q^{27} - 2418q^{29} + 7840q^{31} - 6672q^{33} - 1225q^{35} - 314q^{37} + 4248q^{39} - 17878q^{41} + 16476q^{43} - 2475q^{45} + 5376q^{47} + 2401q^{49} - 9240q^{51} + 1654q^{53} + 13900q^{55} + 32208q^{57} - 29492q^{59} + 27630q^{61} + 4851q^{63} - 8850q^{65} + 57716q^{67} + 18336q^{69} + 70648q^{71} + 74202q^{73} - 7500q^{75} - 27244q^{77} + 74336q^{79} - 25191q^{81} + 44068q^{83} + 19250q^{85} + 29016q^{87} + 129306q^{89} + 17346q^{91} - 94080q^{93} - 67100q^{95} - 137646q^{97} - 55044q^{99} + O(q^{100}) \)

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 −12.0000 0 25.0000 0 −49.0000 0 −99.0000 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 280.6.a.a 1
4.b odd 2 1 560.6.a.g 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
280.6.a.a 1 1.a even 1 1 trivial
560.6.a.g 1 4.b odd 2 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3} + 12 \) acting on \(S_{6}^{\mathrm{new}}(\Gamma_0(280))\).

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T \)
$3$ \( 12 + T \)
$5$ \( -25 + T \)
$7$ \( 49 + T \)
$11$ \( -556 + T \)
$13$ \( 354 + T \)
$17$ \( -770 + T \)
$19$ \( 2684 + T \)
$23$ \( 1528 + T \)
$29$ \( 2418 + T \)
$31$ \( -7840 + T \)
$37$ \( 314 + T \)
$41$ \( 17878 + T \)
$43$ \( -16476 + T \)
$47$ \( -5376 + T \)
$53$ \( -1654 + T \)
$59$ \( 29492 + T \)
$61$ \( -27630 + T \)
$67$ \( -57716 + T \)
$71$ \( -70648 + T \)
$73$ \( -74202 + T \)
$79$ \( -74336 + T \)
$83$ \( -44068 + T \)
$89$ \( -129306 + T \)
$97$ \( 137646 + T \)
show more
show less