Newspace parameters
| Level: | \( N \) | \(=\) | \( 847 = 7 \cdot 11^{2} \) |
| Weight: | \( k \) | \(=\) | \( 4 \) |
| Character orbit: | \([\chi]\) | \(=\) | 847.a (trivial) |
Newform invariants
| Self dual: | yes |
| Analytic conductor: | \(49.9746177749\) |
| Analytic rank: | \(0\) |
| Dimension: | \(1\) |
| Coefficient field: | \(\mathbb{Q}\) |
| Coefficient ring: | \(\mathbb{Z}\) |
| Coefficient ring index: | \( 1 \) |
| Twist minimal: | no (minimal twist has level 7) |
| 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 |
|
1.00000 | −2.00000 | −7.00000 | 16.0000 | −2.00000 | 7.00000 | −15.0000 | −23.0000 | 16.0000 | |||||||||||||||||||||
Atkin-Lehner signs
| \( p \) | Sign |
|---|---|
| \(7\) | \(-1\) |
| \(11\) | \(-1\) |
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 | 847.4.a.b | 1 | |
| 11.b | odd | 2 | 1 | 7.4.a.a | ✓ | 1 | |
| 33.d | even | 2 | 1 | 63.4.a.b | 1 | ||
| 44.c | even | 2 | 1 | 112.4.a.f | 1 | ||
| 55.d | odd | 2 | 1 | 175.4.a.b | 1 | ||
| 55.e | even | 4 | 2 | 175.4.b.b | 2 | ||
| 77.b | even | 2 | 1 | 49.4.a.b | 1 | ||
| 77.h | odd | 6 | 2 | 49.4.c.c | 2 | ||
| 77.i | even | 6 | 2 | 49.4.c.b | 2 | ||
| 88.b | odd | 2 | 1 | 448.4.a.i | 1 | ||
| 88.g | even | 2 | 1 | 448.4.a.e | 1 | ||
| 132.d | odd | 2 | 1 | 1008.4.a.c | 1 | ||
| 143.d | odd | 2 | 1 | 1183.4.a.b | 1 | ||
| 165.d | even | 2 | 1 | 1575.4.a.e | 1 | ||
| 187.b | odd | 2 | 1 | 2023.4.a.a | 1 | ||
| 231.h | odd | 2 | 1 | 441.4.a.i | 1 | ||
| 231.k | odd | 6 | 2 | 441.4.e.e | 2 | ||
| 231.l | even | 6 | 2 | 441.4.e.h | 2 | ||
| 308.g | odd | 2 | 1 | 784.4.a.g | 1 | ||
| 385.h | even | 2 | 1 | 1225.4.a.j | 1 | ||
| By twisted newform orbit | |||||||
|---|---|---|---|---|---|---|---|
| Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
| 7.4.a.a | ✓ | 1 | 11.b | odd | 2 | 1 | |
| 49.4.a.b | 1 | 77.b | even | 2 | 1 | ||
| 49.4.c.b | 2 | 77.i | even | 6 | 2 | ||
| 49.4.c.c | 2 | 77.h | odd | 6 | 2 | ||
| 63.4.a.b | 1 | 33.d | even | 2 | 1 | ||
| 112.4.a.f | 1 | 44.c | even | 2 | 1 | ||
| 175.4.a.b | 1 | 55.d | odd | 2 | 1 | ||
| 175.4.b.b | 2 | 55.e | even | 4 | 2 | ||
| 441.4.a.i | 1 | 231.h | odd | 2 | 1 | ||
| 441.4.e.e | 2 | 231.k | odd | 6 | 2 | ||
| 441.4.e.h | 2 | 231.l | even | 6 | 2 | ||
| 448.4.a.e | 1 | 88.g | even | 2 | 1 | ||
| 448.4.a.i | 1 | 88.b | odd | 2 | 1 | ||
| 784.4.a.g | 1 | 308.g | odd | 2 | 1 | ||
| 847.4.a.b | 1 | 1.a | even | 1 | 1 | trivial | |
| 1008.4.a.c | 1 | 132.d | odd | 2 | 1 | ||
| 1183.4.a.b | 1 | 143.d | odd | 2 | 1 | ||
| 1225.4.a.j | 1 | 385.h | even | 2 | 1 | ||
| 1575.4.a.e | 1 | 165.d | even | 2 | 1 | ||
| 2023.4.a.a | 1 | 187.b | odd | 2 | 1 | ||
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2} - 1 \)
acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(847))\).
Hecke characteristic polynomials
$p$
$F_p(T)$
$2$
\( T - 1 \)
$3$
\( T + 2 \)
$5$
\( T - 16 \)
$7$
\( T - 7 \)
$11$
\( T \)
$13$
\( T + 28 \)
$17$
\( T + 54 \)
$19$
\( T - 110 \)
$23$
\( T - 48 \)
$29$
\( T - 110 \)
$31$
\( T - 12 \)
$37$
\( T + 246 \)
$41$
\( T + 182 \)
$43$
\( T + 128 \)
$47$
\( T - 324 \)
$53$
\( T + 162 \)
$59$
\( T - 810 \)
$61$
\( T - 488 \)
$67$
\( T - 244 \)
$71$
\( T + 768 \)
$73$
\( T - 702 \)
$79$
\( T + 440 \)
$83$
\( T - 1302 \)
$89$
\( T - 730 \)
$97$
\( T - 294 \)
show more
show less