Newspace parameters
| Level: | \( N \) | \(=\) | \( 1078 = 2 \cdot 7^{2} \cdot 11 \) |
| Weight: | \( k \) | \(=\) | \( 4 \) |
| Character orbit: | \([\chi]\) | \(=\) | 1078.a (trivial) |
Newform invariants
| Self dual: | yes |
| Analytic conductor: | \(63.6040589862\) |
| Analytic rank: | \(0\) |
| Dimension: | \(1\) |
| Coefficient field: | \(\mathbb{Q}\) |
| Coefficient ring: | \(\mathbb{Z}\) |
| Coefficient ring index: | \( 1 \) |
| Twist minimal: | no (minimal twist has level 154) |
| 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 |
|
2.00000 | 10.0000 | 4.00000 | 14.0000 | 20.0000 | 0 | 8.00000 | 73.0000 | 28.0000 | |||||||||||||||||||||
Atkin-Lehner signs
| \( p \) | Sign |
|---|---|
| \(2\) | \(-1\) |
| \(7\) | \(-1\) |
| \(11\) | \(1\) |
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 | 1078.4.a.h | 1 | |
| 7.b | odd | 2 | 1 | 154.4.a.c | ✓ | 1 | |
| 21.c | even | 2 | 1 | 1386.4.a.g | 1 | ||
| 28.d | even | 2 | 1 | 1232.4.a.i | 1 | ||
| 77.b | even | 2 | 1 | 1694.4.a.a | 1 | ||
| By twisted newform orbit | |||||||
|---|---|---|---|---|---|---|---|
| Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
| 154.4.a.c | ✓ | 1 | 7.b | odd | 2 | 1 | |
| 1078.4.a.h | 1 | 1.a | even | 1 | 1 | trivial | |
| 1232.4.a.i | 1 | 28.d | even | 2 | 1 | ||
| 1386.4.a.g | 1 | 21.c | even | 2 | 1 | ||
| 1694.4.a.a | 1 | 77.b | even | 2 | 1 | ||
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator
\( T_{3} - 10 \)
acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(1078))\).
Hecke characteristic polynomials
$p$
$F_p(T)$
$2$
\( T - 2 \)
$3$
\( T - 10 \)
$5$
\( T - 14 \)
$7$
\( T \)
$11$
\( T + 11 \)
$13$
\( T - 16 \)
$17$
\( T + 108 \)
$19$
\( T + 116 \)
$23$
\( T - 68 \)
$29$
\( T - 122 \)
$31$
\( T - 262 \)
$37$
\( T - 130 \)
$41$
\( T + 204 \)
$43$
\( T + 396 \)
$47$
\( T + 166 \)
$53$
\( T - 442 \)
$59$
\( T + 702 \)
$61$
\( T + 196 \)
$67$
\( T + 416 \)
$71$
\( T - 492 \)
$73$
\( T + 408 \)
$79$
\( T - 600 \)
$83$
\( T - 1212 \)
$89$
\( T + 1146 \)
$97$
\( T - 482 \)
show more
show less