Newspace parameters
Level: | \( N \) | \(=\) | \( 27 = 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 27.a (trivial) |
Newform invariants
Self dual: | yes |
Analytic conductor: | \(8.43439568807\) |
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: | $N(\mathrm{U}(1))$ |
$q$-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 | 0 | −128.000 | 0 | 0 | 1763.00 | 0 | 0 | 0 | |||||||||||||||||||||
Atkin-Lehner signs
\( p \) | Sign |
---|---|
\(3\) | \(1\) |
Inner twists
Char | Parity | Ord | Mult | Type |
---|---|---|---|---|
1.a | even | 1 | 1 | trivial |
3.b | odd | 2 | 1 | CM by \(\Q(\sqrt{-3}) \) |
Twists
By twisting character orbit | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Mult | Type | Twist | Min | Dim |
1.a | even | 1 | 1 | trivial | 27.8.a.a | ✓ | 1 |
3.b | odd | 2 | 1 | CM | 27.8.a.a | ✓ | 1 |
4.b | odd | 2 | 1 | 432.8.a.d | 1 | ||
9.c | even | 3 | 2 | 81.8.c.b | 2 | ||
9.d | odd | 6 | 2 | 81.8.c.b | 2 | ||
12.b | even | 2 | 1 | 432.8.a.d | 1 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
27.8.a.a | ✓ | 1 | 1.a | even | 1 | 1 | trivial |
27.8.a.a | ✓ | 1 | 3.b | odd | 2 | 1 | CM |
81.8.c.b | 2 | 9.c | even | 3 | 2 | ||
81.8.c.b | 2 | 9.d | odd | 6 | 2 | ||
432.8.a.d | 1 | 4.b | odd | 2 | 1 | ||
432.8.a.d | 1 | 12.b | even | 2 | 1 |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2} \)
acting on \(S_{8}^{\mathrm{new}}(\Gamma_0(27))\).
Hecke characteristic polynomials
$p$
$F_p(T)$
$2$
\( T \)
$3$
\( T \)
$5$
\( T \)
$7$
\( T - 1763 \)
$11$
\( T \)
$13$
\( T - 12605 \)
$17$
\( T \)
$19$
\( T - 14357 \)
$23$
\( T \)
$29$
\( T \)
$31$
\( T - 178916 \)
$37$
\( T + 615373 \)
$41$
\( T \)
$43$
\( T - 1035224 \)
$47$
\( T \)
$53$
\( T \)
$59$
\( T \)
$61$
\( T - 1537199 \)
$67$
\( T + 4058455 \)
$71$
\( T \)
$73$
\( T - 1236809 \)
$79$
\( T + 4245427 \)
$83$
\( T \)
$89$
\( T \)
$97$
\( T - 5276357 \)
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