Newspace parameters
| Level: | \( N \) | \(=\) | \( 6253 = 13^{2} \cdot 37 \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 6253.a (trivial) |
Newform invariants
| Self dual: | yes |
| Analytic conductor: | \(49.9304563839\) |
| Analytic rank: | \(0\) |
| Dimension: | \(1\) |
| Coefficient field: | \(\mathbb{Q}\) |
| Coefficient ring: | \(\mathbb{Z}\) |
| Coefficient ring index: | \( 1 \) |
| Twist minimal: | no (minimal twist has level 37) |
| 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 | 2.00000 | 2.00000 | −6.00000 | 1.00000 | 0 | 6.00000 | 4.00000 | |||||||||||||||||||||
Atkin-Lehner signs
| \( p \) | Sign |
|---|---|
| \(13\) | \( +1 \) |
| \(37\) | \( -1 \) |
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 | 6253.2.a.c | 1 | |
| 13.b | even | 2 | 1 | 37.2.a.a | ✓ | 1 | |
| 39.d | odd | 2 | 1 | 333.2.a.d | 1 | ||
| 52.b | odd | 2 | 1 | 592.2.a.e | 1 | ||
| 65.d | even | 2 | 1 | 925.2.a.e | 1 | ||
| 65.h | odd | 4 | 2 | 925.2.b.b | 2 | ||
| 91.b | odd | 2 | 1 | 1813.2.a.a | 1 | ||
| 104.e | even | 2 | 1 | 2368.2.a.q | 1 | ||
| 104.h | odd | 2 | 1 | 2368.2.a.b | 1 | ||
| 143.d | odd | 2 | 1 | 4477.2.a.b | 1 | ||
| 156.h | even | 2 | 1 | 5328.2.a.r | 1 | ||
| 195.e | odd | 2 | 1 | 8325.2.a.e | 1 | ||
| 481.d | even | 2 | 1 | 1369.2.a.e | 1 | ||
| 481.j | odd | 4 | 2 | 1369.2.b.c | 2 | ||
| By twisted newform orbit | |||||||
|---|---|---|---|---|---|---|---|
| Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
| 37.2.a.a | ✓ | 1 | 13.b | even | 2 | 1 | |
| 333.2.a.d | 1 | 39.d | odd | 2 | 1 | ||
| 592.2.a.e | 1 | 52.b | odd | 2 | 1 | ||
| 925.2.a.e | 1 | 65.d | even | 2 | 1 | ||
| 925.2.b.b | 2 | 65.h | odd | 4 | 2 | ||
| 1369.2.a.e | 1 | 481.d | even | 2 | 1 | ||
| 1369.2.b.c | 2 | 481.j | odd | 4 | 2 | ||
| 1813.2.a.a | 1 | 91.b | odd | 2 | 1 | ||
| 2368.2.a.b | 1 | 104.h | odd | 2 | 1 | ||
| 2368.2.a.q | 1 | 104.e | even | 2 | 1 | ||
| 4477.2.a.b | 1 | 143.d | odd | 2 | 1 | ||
| 5328.2.a.r | 1 | 156.h | even | 2 | 1 | ||
| 6253.2.a.c | 1 | 1.a | even | 1 | 1 | trivial | |
| 8325.2.a.e | 1 | 195.e | odd | 2 | 1 | ||
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2} - 2 \)
acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(6253))\).
Hecke characteristic polynomials
| $p$ | $F_p(T)$ |
|---|---|
| $2$ |
\( T - 2 \)
|
| $3$ |
\( T + 3 \)
|
| $5$ |
\( T - 2 \)
|
| $7$ |
\( T - 1 \)
|
| $11$ |
\( T - 5 \)
|
| $13$ |
\( T \)
|
| $17$ |
\( T \)
|
| $19$ |
\( T \)
|
| $23$ |
\( T - 2 \)
|
| $29$ |
\( T - 6 \)
|
| $31$ |
\( T - 4 \)
|
| $37$ |
\( T - 1 \)
|
| $41$ |
\( T - 9 \)
|
| $43$ |
\( T - 2 \)
|
| $47$ |
\( T - 9 \)
|
| $53$ |
\( T - 1 \)
|
| $59$ |
\( T + 8 \)
|
| $61$ |
\( T + 8 \)
|
| $67$ |
\( T + 8 \)
|
| $71$ |
\( T + 9 \)
|
| $73$ |
\( T - 1 \)
|
| $79$ |
\( T - 4 \)
|
| $83$ |
\( T - 15 \)
|
| $89$ |
\( T + 4 \)
|
| $97$ |
\( T + 4 \)
|
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