Newspace parameters
Level: | \( N \) | \(=\) | \( 560 = 2^{4} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 560.p (of order \(2\), degree \(1\), not minimal) |
Newform invariants
Self dual: | yes |
Analytic conductor: | \(57.8871793270\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 35) |
Sato-Tate group: | $\mathrm{U}(1)[D_{2}]$ |
$q$-expansion
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/560\mathbb{Z}\right)^\times\).
\(n\) | \(241\) | \(337\) | \(351\) | \(421\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) | \(1\) |
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 | \(\iota_m(\nu)\) | \( a_{2} \) | \( a_{3} \) | \( a_{4} \) | \( a_{5} \) | \( a_{6} \) | \( a_{7} \) | \( a_{8} \) | \( a_{9} \) | \( a_{10} \) | |||||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
209.1 |
|
0 | −17.0000 | 0 | −25.0000 | 0 | 49.0000 | 0 | 208.000 | 0 | |||||||||||||||||||||
Inner twists
Char | Parity | Ord | Mult | Type |
---|---|---|---|---|
1.a | even | 1 | 1 | trivial |
35.c | odd | 2 | 1 | CM by \(\Q(\sqrt{-35}) \) |
Twists
By twisting character orbit | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Mult | Type | Twist | Min | Dim |
1.a | even | 1 | 1 | trivial | 560.5.p.a | 1 | |
4.b | odd | 2 | 1 | 35.5.c.b | yes | 1 | |
5.b | even | 2 | 1 | 560.5.p.b | 1 | ||
7.b | odd | 2 | 1 | 560.5.p.b | 1 | ||
12.b | even | 2 | 1 | 315.5.e.b | 1 | ||
20.d | odd | 2 | 1 | 35.5.c.a | ✓ | 1 | |
20.e | even | 4 | 2 | 175.5.d.c | 2 | ||
28.d | even | 2 | 1 | 35.5.c.a | ✓ | 1 | |
35.c | odd | 2 | 1 | CM | 560.5.p.a | 1 | |
60.h | even | 2 | 1 | 315.5.e.a | 1 | ||
84.h | odd | 2 | 1 | 315.5.e.a | 1 | ||
140.c | even | 2 | 1 | 35.5.c.b | yes | 1 | |
140.j | odd | 4 | 2 | 175.5.d.c | 2 | ||
420.o | odd | 2 | 1 | 315.5.e.b | 1 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
35.5.c.a | ✓ | 1 | 20.d | odd | 2 | 1 | |
35.5.c.a | ✓ | 1 | 28.d | even | 2 | 1 | |
35.5.c.b | yes | 1 | 4.b | odd | 2 | 1 | |
35.5.c.b | yes | 1 | 140.c | even | 2 | 1 | |
175.5.d.c | 2 | 20.e | even | 4 | 2 | ||
175.5.d.c | 2 | 140.j | odd | 4 | 2 | ||
315.5.e.a | 1 | 60.h | even | 2 | 1 | ||
315.5.e.a | 1 | 84.h | odd | 2 | 1 | ||
315.5.e.b | 1 | 12.b | even | 2 | 1 | ||
315.5.e.b | 1 | 420.o | odd | 2 | 1 | ||
560.5.p.a | 1 | 1.a | even | 1 | 1 | trivial | |
560.5.p.a | 1 | 35.c | odd | 2 | 1 | CM | |
560.5.p.b | 1 | 5.b | even | 2 | 1 | ||
560.5.p.b | 1 | 7.b | odd | 2 | 1 |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator
\( T_{3} + 17 \)
acting on \(S_{5}^{\mathrm{new}}(560, [\chi])\).
Hecke characteristic polynomials
$p$
$F_p(T)$
$2$
\( T \)
$3$
\( T + 17 \)
$5$
\( T + 25 \)
$7$
\( T - 49 \)
$11$
\( T - 73 \)
$13$
\( T + 23 \)
$17$
\( T + 263 \)
$19$
\( T \)
$23$
\( T \)
$29$
\( T + 1153 \)
$31$
\( T \)
$37$
\( T \)
$41$
\( T \)
$43$
\( T \)
$47$
\( T + 3457 \)
$53$
\( T \)
$59$
\( T \)
$61$
\( T \)
$67$
\( T \)
$71$
\( T - 10078 \)
$73$
\( T - 9502 \)
$79$
\( T + 12167 \)
$83$
\( T + 6382 \)
$89$
\( T \)
$97$
\( T + 3383 \)
show more
show less