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
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 | −12.0000 | 0 | 25.0000 | 0 | −49.0000 | 0 | −99.0000 | 0 | |||||||||||||||||||||
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
$p$
$F_p(T)$
$2$
\( T \)
$3$
\( T + 12 \)
$5$
\( T - 25 \)
$7$
\( T + 49 \)
$11$
\( T - 556 \)
$13$
\( T + 354 \)
$17$
\( T - 770 \)
$19$
\( T + 2684 \)
$23$
\( T + 1528 \)
$29$
\( T + 2418 \)
$31$
\( T - 7840 \)
$37$
\( T + 314 \)
$41$
\( T + 17878 \)
$43$
\( T - 16476 \)
$47$
\( T - 5376 \)
$53$
\( T - 1654 \)
$59$
\( T + 29492 \)
$61$
\( T - 27630 \)
$67$
\( T - 57716 \)
$71$
\( T - 70648 \)
$73$
\( T - 74202 \)
$79$
\( T - 74336 \)
$83$
\( T - 44068 \)
$89$
\( T - 129306 \)
$97$
\( T + 137646 \)
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