Newspace parameters
| Level: | \( N \) | \(=\) | \( 1274 = 2 \cdot 7^{2} \cdot 13 \) |
| Weight: | \( k \) | \(=\) | \( 4 \) |
| Character orbit: | \([\chi]\) | \(=\) | 1274.a (trivial) |
Newform invariants
| Self dual: | yes |
| Analytic conductor: | \(75.1684333473\) |
| Analytic rank: | \(0\) |
| Dimension: | \(1\) |
| Coefficient field: | \(\mathbb{Q}\) |
| Coefficient ring: | \(\mathbb{Z}\) |
| Coefficient ring index: | \( 1 \) |
| Twist minimal: | no (minimal twist has level 26) |
| 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 | −3.00000 | 4.00000 | −11.0000 | 6.00000 | 0 | −8.00000 | −18.0000 | 22.0000 | |||||||||||||||||||||
Atkin-Lehner signs
| \( p \) | Sign |
|---|---|
| \(2\) | \( +1 \) |
| \(7\) | \( -1 \) |
| \(13\) | \( -1 \) |
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 | 1274.4.a.b | 1 | |
| 7.b | odd | 2 | 1 | 26.4.a.a | ✓ | 1 | |
| 21.c | even | 2 | 1 | 234.4.a.g | 1 | ||
| 28.d | even | 2 | 1 | 208.4.a.c | 1 | ||
| 35.c | odd | 2 | 1 | 650.4.a.f | 1 | ||
| 35.f | even | 4 | 2 | 650.4.b.b | 2 | ||
| 56.e | even | 2 | 1 | 832.4.a.m | 1 | ||
| 56.h | odd | 2 | 1 | 832.4.a.e | 1 | ||
| 84.h | odd | 2 | 1 | 1872.4.a.c | 1 | ||
| 91.b | odd | 2 | 1 | 338.4.a.e | 1 | ||
| 91.i | even | 4 | 2 | 338.4.b.c | 2 | ||
| 91.n | odd | 6 | 2 | 338.4.c.f | 2 | ||
| 91.t | odd | 6 | 2 | 338.4.c.b | 2 | ||
| 91.bc | even | 12 | 4 | 338.4.e.b | 4 | ||
| By twisted newform orbit | |||||||
|---|---|---|---|---|---|---|---|
| Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
| 26.4.a.a | ✓ | 1 | 7.b | odd | 2 | 1 | |
| 208.4.a.c | 1 | 28.d | even | 2 | 1 | ||
| 234.4.a.g | 1 | 21.c | even | 2 | 1 | ||
| 338.4.a.e | 1 | 91.b | odd | 2 | 1 | ||
| 338.4.b.c | 2 | 91.i | even | 4 | 2 | ||
| 338.4.c.b | 2 | 91.t | odd | 6 | 2 | ||
| 338.4.c.f | 2 | 91.n | odd | 6 | 2 | ||
| 338.4.e.b | 4 | 91.bc | even | 12 | 4 | ||
| 650.4.a.f | 1 | 35.c | odd | 2 | 1 | ||
| 650.4.b.b | 2 | 35.f | even | 4 | 2 | ||
| 832.4.a.e | 1 | 56.h | odd | 2 | 1 | ||
| 832.4.a.m | 1 | 56.e | even | 2 | 1 | ||
| 1274.4.a.b | 1 | 1.a | even | 1 | 1 | trivial | |
| 1872.4.a.c | 1 | 84.h | odd | 2 | 1 | ||
Hecke kernels
This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(1274))\):
|
\( T_{3} + 3 \)
|
|
\( T_{5} + 11 \)
|
Hecke characteristic polynomials
| $p$ | $F_p(T)$ |
|---|---|
| $2$ |
\( T + 2 \)
|
| $3$ |
\( T + 3 \)
|
| $5$ |
\( T + 11 \)
|
| $7$ |
\( T \)
|
| $11$ |
\( T + 38 \)
|
| $13$ |
\( T - 13 \)
|
| $17$ |
\( T - 51 \)
|
| $19$ |
\( T + 90 \)
|
| $23$ |
\( T + 52 \)
|
| $29$ |
\( T + 190 \)
|
| $31$ |
\( T + 292 \)
|
| $37$ |
\( T + 441 \)
|
| $41$ |
\( T + 312 \)
|
| $43$ |
\( T - 373 \)
|
| $47$ |
\( T - 41 \)
|
| $53$ |
\( T - 468 \)
|
| $59$ |
\( T + 530 \)
|
| $61$ |
\( T + 592 \)
|
| $67$ |
\( T + 206 \)
|
| $71$ |
\( T + 863 \)
|
| $73$ |
\( T - 322 \)
|
| $79$ |
\( T + 460 \)
|
| $83$ |
\( T + 528 \)
|
| $89$ |
\( T + 870 \)
|
| $97$ |
\( T - 346 \)
|
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