Newspace parameters
| Level: | \( N \) | \(=\) | \( 224 = 2^{5} \cdot 7 \) |
| Weight: | \( k \) | \(=\) | \( 6 \) |
| Character orbit: | \([\chi]\) | \(=\) | 224.a (trivial) |
Newform invariants
| Self dual: | yes |
| Analytic conductor: | \(35.9259756381\) |
| 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 | 14.0000 | 0 | −64.0000 | 0 | −49.0000 | 0 | −47.0000 | 0 | |||||||||||||||||||||
Atkin-Lehner signs
| \( p \) | Sign |
|---|---|
| \(2\) | \(-1\) |
| \(7\) | \(1\) |
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 | 224.6.a.b | yes | 1 |
| 4.b | odd | 2 | 1 | 224.6.a.a | ✓ | 1 | |
| 8.b | even | 2 | 1 | 448.6.a.d | 1 | ||
| 8.d | odd | 2 | 1 | 448.6.a.n | 1 | ||
| By twisted newform orbit | |||||||
|---|---|---|---|---|---|---|---|
| Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
| 224.6.a.a | ✓ | 1 | 4.b | odd | 2 | 1 | |
| 224.6.a.b | yes | 1 | 1.a | even | 1 | 1 | trivial |
| 448.6.a.d | 1 | 8.b | even | 2 | 1 | ||
| 448.6.a.n | 1 | 8.d | odd | 2 | 1 | ||
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator
\( T_{3} - 14 \)
acting on \(S_{6}^{\mathrm{new}}(\Gamma_0(224))\).
Hecke characteristic polynomials
$p$
$F_p(T)$
$2$
\( T \)
$3$
\( T - 14 \)
$5$
\( T + 64 \)
$7$
\( T + 49 \)
$11$
\( T + 420 \)
$13$
\( T - 860 \)
$17$
\( T - 830 \)
$19$
\( T - 490 \)
$23$
\( T - 4872 \)
$29$
\( T - 8754 \)
$31$
\( T - 5628 \)
$37$
\( T - 1434 \)
$41$
\( T + 9258 \)
$43$
\( T - 14756 \)
$47$
\( T + 10108 \)
$53$
\( T + 23058 \)
$59$
\( T + 13734 \)
$61$
\( T + 25352 \)
$67$
\( T - 19768 \)
$71$
\( T - 1792 \)
$73$
\( T - 37914 \)
$79$
\( T - 95984 \)
$83$
\( T - 88242 \)
$89$
\( T - 43762 \)
$97$
\( T - 65790 \)
show more
show less