Newspace parameters
| Level: | \( N \) | \(=\) | \( 6 = 2 \cdot 3 \) |
| Weight: | \( k \) | \(=\) | \( 28 \) |
| Character orbit: | \([\chi]\) | \(=\) | 6.a (trivial) |
Newform invariants
| Self dual: | yes |
| Analytic conductor: | \(27.7113344903\) |
| 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 |
|
8192.00 | −1.59432e6 | 6.71089e7 | 2.90426e9 | −1.30607e10 | −4.93494e11 | 5.49756e11 | 2.54187e12 | 2.37917e13 | |||||||||||||||||||||
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 | 6.28.a.b | ✓ | 1 |
| 3.b | odd | 2 | 1 | 18.28.a.a | 1 | ||
| 4.b | odd | 2 | 1 | 48.28.a.c | 1 | ||
| By twisted newform orbit | |||||||
|---|---|---|---|---|---|---|---|
| Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
| 6.28.a.b | ✓ | 1 | 1.a | even | 1 | 1 | trivial |
| 18.28.a.a | 1 | 3.b | odd | 2 | 1 | ||
| 48.28.a.c | 1 | 4.b | odd | 2 | 1 | ||
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator
\( T_{5} - 2904255750 \)
acting on \(S_{28}^{\mathrm{new}}(\Gamma_0(6))\).
Hecke characteristic polynomials
$p$
$F_p(T)$
$2$
\( T - 8192 \)
$3$
\( T + 1594323 \)
$5$
\( T - 2904255750 \)
$7$
\( T + 493494294832 \)
$11$
\( T + 20157692940660 \)
$13$
\( T - 1313545153005254 \)
$17$
\( T + 62\!\cdots\!62 \)
$19$
\( T + 17\!\cdots\!36 \)
$23$
\( T + 26\!\cdots\!00 \)
$29$
\( T + 62\!\cdots\!54 \)
$31$
\( T + 17\!\cdots\!52 \)
$37$
\( T - 18\!\cdots\!46 \)
$41$
\( T - 81\!\cdots\!54 \)
$43$
\( T + 89\!\cdots\!88 \)
$47$
\( T - 22\!\cdots\!60 \)
$53$
\( T + 18\!\cdots\!02 \)
$59$
\( T + 25\!\cdots\!40 \)
$61$
\( T + 92\!\cdots\!90 \)
$67$
\( T - 84\!\cdots\!68 \)
$71$
\( T - 11\!\cdots\!20 \)
$73$
\( T - 16\!\cdots\!34 \)
$79$
\( T + 20\!\cdots\!68 \)
$83$
\( T - 59\!\cdots\!44 \)
$89$
\( T + 84\!\cdots\!38 \)
$97$
\( T - 11\!\cdots\!46 \)
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