Newspace parameters
Level: | \( N \) | \(=\) | \( 960 = 2^{6} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 960.a (trivial) |
Newform invariants
Self dual: | yes |
Analytic conductor: | \(153.968467020\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 30) |
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 | −9.00000 | 0 | 25.0000 | 0 | 164.000 | 0 | 81.0000 | 0 | |||||||||||||||||||||
Atkin-Lehner signs
\( p \) | Sign |
---|---|
\(2\) | \(1\) |
\(3\) | \(1\) |
\(5\) | \(-1\) |
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 | 960.6.a.n | 1 | |
4.b | odd | 2 | 1 | 960.6.a.u | 1 | ||
8.b | even | 2 | 1 | 30.6.a.a | ✓ | 1 | |
8.d | odd | 2 | 1 | 240.6.a.a | 1 | ||
24.f | even | 2 | 1 | 720.6.a.m | 1 | ||
24.h | odd | 2 | 1 | 90.6.a.g | 1 | ||
40.f | even | 2 | 1 | 150.6.a.h | 1 | ||
40.i | odd | 4 | 2 | 150.6.c.d | 2 | ||
120.i | odd | 2 | 1 | 450.6.a.b | 1 | ||
120.w | even | 4 | 2 | 450.6.c.b | 2 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
30.6.a.a | ✓ | 1 | 8.b | even | 2 | 1 | |
90.6.a.g | 1 | 24.h | odd | 2 | 1 | ||
150.6.a.h | 1 | 40.f | even | 2 | 1 | ||
150.6.c.d | 2 | 40.i | odd | 4 | 2 | ||
240.6.a.a | 1 | 8.d | odd | 2 | 1 | ||
450.6.a.b | 1 | 120.i | odd | 2 | 1 | ||
450.6.c.b | 2 | 120.w | even | 4 | 2 | ||
720.6.a.m | 1 | 24.f | even | 2 | 1 | ||
960.6.a.n | 1 | 1.a | even | 1 | 1 | trivial | |
960.6.a.u | 1 | 4.b | odd | 2 | 1 |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator
\( T_{7} - 164 \)
acting on \(S_{6}^{\mathrm{new}}(\Gamma_0(960))\).
Hecke characteristic polynomials
$p$
$F_p(T)$
$2$
\( T \)
$3$
\( T + 9 \)
$5$
\( T - 25 \)
$7$
\( T - 164 \)
$11$
\( T + 720 \)
$13$
\( T + 698 \)
$17$
\( T + 2226 \)
$19$
\( T + 356 \)
$23$
\( T + 1800 \)
$29$
\( T + 714 \)
$31$
\( T - 848 \)
$37$
\( T - 11302 \)
$41$
\( T - 9354 \)
$43$
\( T - 5956 \)
$47$
\( T + 11160 \)
$53$
\( T + 14106 \)
$59$
\( T + 7920 \)
$61$
\( T - 13450 \)
$67$
\( T - 65476 \)
$71$
\( T - 34560 \)
$73$
\( T - 86258 \)
$79$
\( T + 108832 \)
$83$
\( T + 10668 \)
$89$
\( T - 10818 \)
$97$
\( T - 4418 \)
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