Newspace parameters
Level: | \( N \) | \(=\) | \( 54 = 2 \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 54.a (trivial) |
Newform invariants
Self dual: | yes |
Analytic conductor: | \(16.8687913761\) |
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 |
|
8.00000 | 0 | 64.0000 | −105.000 | 0 | −937.000 | 512.000 | 0 | −840.000 | |||||||||||||||||||||
Atkin-Lehner signs
\( p \) | Sign |
---|---|
\(2\) | \(-1\) |
\(3\) | \(1\) |
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 | 54.8.a.e | yes | 1 |
3.b | odd | 2 | 1 | 54.8.a.b | ✓ | 1 | |
4.b | odd | 2 | 1 | 432.8.a.c | 1 | ||
9.c | even | 3 | 2 | 162.8.c.c | 2 | ||
9.d | odd | 6 | 2 | 162.8.c.j | 2 | ||
12.b | even | 2 | 1 | 432.8.a.f | 1 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
54.8.a.b | ✓ | 1 | 3.b | odd | 2 | 1 | |
54.8.a.e | yes | 1 | 1.a | even | 1 | 1 | trivial |
162.8.c.c | 2 | 9.c | even | 3 | 2 | ||
162.8.c.j | 2 | 9.d | odd | 6 | 2 | ||
432.8.a.c | 1 | 4.b | odd | 2 | 1 | ||
432.8.a.f | 1 | 12.b | even | 2 | 1 |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator
\( T_{5} + 105 \)
acting on \(S_{8}^{\mathrm{new}}(\Gamma_0(54))\).
Hecke characteristic polynomials
$p$
$F_p(T)$
$2$
\( T - 8 \)
$3$
\( T \)
$5$
\( T + 105 \)
$7$
\( T + 937 \)
$11$
\( T + 5943 \)
$13$
\( T - 68 \)
$17$
\( T - 5400 \)
$19$
\( T + 48382 \)
$23$
\( T - 642 \)
$29$
\( T - 125934 \)
$31$
\( T + 161275 \)
$37$
\( T + 414286 \)
$41$
\( T - 627474 \)
$43$
\( T - 570590 \)
$47$
\( T + 538698 \)
$53$
\( T + 356283 \)
$59$
\( T - 2910828 \)
$61$
\( T - 2684168 \)
$67$
\( T - 2681078 \)
$71$
\( T - 3705480 \)
$73$
\( T + 153151 \)
$79$
\( T + 7579288 \)
$83$
\( T + 9345999 \)
$89$
\( T + 4033602 \)
$97$
\( T + 5754097 \)
show more
show less