Newspace parameters
Level: | \( N \) | \(=\) | \( 27 = 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 27.a (trivial) |
Newform invariants
Self dual: | yes |
Analytic conductor: | \(1.59305157015\) |
Analytic rank: | \(1\) |
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 |
|
−3.00000 | 0 | 1.00000 | −15.0000 | 0 | −25.0000 | 21.0000 | 0 | 45.0000 | |||||||||||||||||||||
Atkin-Lehner signs
\( p \) | Sign |
---|---|
\(3\) | \(-1\) |
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 | 27.4.a.a | ✓ | 1 |
3.b | odd | 2 | 1 | 27.4.a.b | yes | 1 | |
4.b | odd | 2 | 1 | 432.4.a.a | 1 | ||
5.b | even | 2 | 1 | 675.4.a.j | 1 | ||
5.c | odd | 4 | 2 | 675.4.b.b | 2 | ||
7.b | odd | 2 | 1 | 1323.4.a.d | 1 | ||
8.b | even | 2 | 1 | 1728.4.a.bc | 1 | ||
8.d | odd | 2 | 1 | 1728.4.a.bd | 1 | ||
9.c | even | 3 | 2 | 81.4.c.c | 2 | ||
9.d | odd | 6 | 2 | 81.4.c.a | 2 | ||
12.b | even | 2 | 1 | 432.4.a.n | 1 | ||
15.d | odd | 2 | 1 | 675.4.a.a | 1 | ||
15.e | even | 4 | 2 | 675.4.b.a | 2 | ||
21.c | even | 2 | 1 | 1323.4.a.k | 1 | ||
24.f | even | 2 | 1 | 1728.4.a.d | 1 | ||
24.h | odd | 2 | 1 | 1728.4.a.c | 1 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
27.4.a.a | ✓ | 1 | 1.a | even | 1 | 1 | trivial |
27.4.a.b | yes | 1 | 3.b | odd | 2 | 1 | |
81.4.c.a | 2 | 9.d | odd | 6 | 2 | ||
81.4.c.c | 2 | 9.c | even | 3 | 2 | ||
432.4.a.a | 1 | 4.b | odd | 2 | 1 | ||
432.4.a.n | 1 | 12.b | even | 2 | 1 | ||
675.4.a.a | 1 | 15.d | odd | 2 | 1 | ||
675.4.a.j | 1 | 5.b | even | 2 | 1 | ||
675.4.b.a | 2 | 15.e | even | 4 | 2 | ||
675.4.b.b | 2 | 5.c | odd | 4 | 2 | ||
1323.4.a.d | 1 | 7.b | odd | 2 | 1 | ||
1323.4.a.k | 1 | 21.c | even | 2 | 1 | ||
1728.4.a.c | 1 | 24.h | odd | 2 | 1 | ||
1728.4.a.d | 1 | 24.f | even | 2 | 1 | ||
1728.4.a.bc | 1 | 8.b | even | 2 | 1 | ||
1728.4.a.bd | 1 | 8.d | odd | 2 | 1 |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2} + 3 \)
acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(27))\).
Hecke characteristic polynomials
$p$
$F_p(T)$
$2$
\( T + 3 \)
$3$
\( T \)
$5$
\( T + 15 \)
$7$
\( T + 25 \)
$11$
\( T - 15 \)
$13$
\( T - 20 \)
$17$
\( T + 72 \)
$19$
\( T - 2 \)
$23$
\( T + 114 \)
$29$
\( T + 30 \)
$31$
\( T - 101 \)
$37$
\( T + 430 \)
$41$
\( T - 30 \)
$43$
\( T - 110 \)
$47$
\( T - 330 \)
$53$
\( T + 621 \)
$59$
\( T - 660 \)
$61$
\( T + 376 \)
$67$
\( T + 250 \)
$71$
\( T - 360 \)
$73$
\( T - 785 \)
$79$
\( T - 488 \)
$83$
\( T + 489 \)
$89$
\( T - 450 \)
$97$
\( T + 1105 \)
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