Newspace parameters
Level: | \( N \) | \(=\) | \( 176 = 2^{4} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 176.a (trivial) |
Newform invariants
Self dual: | yes |
Analytic conductor: | \(10.3843361610\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 88) |
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 | −7.00000 | 0 | 9.00000 | 0 | −2.00000 | 0 | 22.0000 | 0 | |||||||||||||||||||||
Atkin-Lehner signs
\( p \) | Sign |
---|---|
\(2\) | \(1\) |
\(11\) | \(-1\) |
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 | 176.4.a.a | 1 | |
3.b | odd | 2 | 1 | 1584.4.a.g | 1 | ||
4.b | odd | 2 | 1 | 88.4.a.b | ✓ | 1 | |
8.b | even | 2 | 1 | 704.4.a.k | 1 | ||
8.d | odd | 2 | 1 | 704.4.a.a | 1 | ||
11.b | odd | 2 | 1 | 1936.4.a.b | 1 | ||
12.b | even | 2 | 1 | 792.4.a.b | 1 | ||
20.d | odd | 2 | 1 | 2200.4.a.a | 1 | ||
44.c | even | 2 | 1 | 968.4.a.e | 1 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
88.4.a.b | ✓ | 1 | 4.b | odd | 2 | 1 | |
176.4.a.a | 1 | 1.a | even | 1 | 1 | trivial | |
704.4.a.a | 1 | 8.d | odd | 2 | 1 | ||
704.4.a.k | 1 | 8.b | even | 2 | 1 | ||
792.4.a.b | 1 | 12.b | even | 2 | 1 | ||
968.4.a.e | 1 | 44.c | even | 2 | 1 | ||
1584.4.a.g | 1 | 3.b | odd | 2 | 1 | ||
1936.4.a.b | 1 | 11.b | odd | 2 | 1 | ||
2200.4.a.a | 1 | 20.d | odd | 2 | 1 |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator
\( T_{3} + 7 \)
acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(176))\).
Hecke characteristic polynomials
$p$
$F_p(T)$
$2$
\( T \)
$3$
\( T + 7 \)
$5$
\( T - 9 \)
$7$
\( T + 2 \)
$11$
\( T - 11 \)
$13$
\( T \)
$17$
\( T + 38 \)
$19$
\( T + 44 \)
$23$
\( T + 175 \)
$29$
\( T + 264 \)
$31$
\( T + 159 \)
$37$
\( T + 173 \)
$41$
\( T + 220 \)
$43$
\( T - 542 \)
$47$
\( T - 264 \)
$53$
\( T - 682 \)
$59$
\( T + 421 \)
$61$
\( T - 308 \)
$67$
\( T + 177 \)
$71$
\( T + 365 \)
$73$
\( T + 528 \)
$79$
\( T + 686 \)
$83$
\( T + 698 \)
$89$
\( T - 967 \)
$97$
\( T + 1127 \)
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