Newspace parameters
Level: | \( N \) | \(=\) | \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 546.a (trivial) |
Newform invariants
Self dual: | yes |
Analytic conductor: | \(170.562223914\) |
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 | 27.0000 | 64.0000 | −10.0000 | 216.000 | −343.000 | 512.000 | 729.000 | −80.0000 | |||||||||||||||||||||
Atkin-Lehner signs
\( p \) | Sign |
---|---|
\(2\) | \(-1\) |
\(3\) | \(-1\) |
\(7\) | \(1\) |
\(13\) | \(-1\) |
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 | 546.8.a.c | ✓ | 1 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
546.8.a.c | ✓ | 1 | 1.a | even | 1 | 1 | trivial |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator
\( T_{5} + 10 \)
acting on \(S_{8}^{\mathrm{new}}(\Gamma_0(546))\).
Hecke characteristic polynomials
$p$
$F_p(T)$
$2$
\( T - 8 \)
$3$
\( T - 27 \)
$5$
\( T + 10 \)
$7$
\( T + 343 \)
$11$
\( T - 1508 \)
$13$
\( T - 2197 \)
$17$
\( T + 1042 \)
$19$
\( T + 9068 \)
$23$
\( T + 98988 \)
$29$
\( T + 213642 \)
$31$
\( T + 22048 \)
$37$
\( T - 418246 \)
$41$
\( T + 76414 \)
$43$
\( T + 177524 \)
$47$
\( T - 631916 \)
$53$
\( T + 982354 \)
$59$
\( T + 596384 \)
$61$
\( T - 1863406 \)
$67$
\( T + 1845652 \)
$71$
\( T - 1632280 \)
$73$
\( T - 216650 \)
$79$
\( T + 6460168 \)
$83$
\( T - 3592152 \)
$89$
\( T + 9482662 \)
$97$
\( T - 840226 \)
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