Newspace parameters
| Level: | \( N \) | \(=\) | \( 44 = 2^{2} \cdot 11 \) |
| Weight: | \( k \) | \(=\) | \( 4 \) |
| Character orbit: | \([\chi]\) | \(=\) | 44.a (trivial) |
Newform invariants
| Self dual: | yes |
| Analytic conductor: | \(2.59608404025\) |
| 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 |
|
0 | −5.00000 | 0 | −7.00000 | 0 | −26.0000 | 0 | −2.00000 | 0 | |||||||||||||||||||||
Atkin-Lehner signs
| \( p \) | Sign |
|---|---|
| \(2\) | \( -1 \) |
| \(11\) | \( +1 \) |
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 | 44.4.a.a | ✓ | 1 |
| 3.b | odd | 2 | 1 | 396.4.a.e | 1 | ||
| 4.b | odd | 2 | 1 | 176.4.a.e | 1 | ||
| 5.b | even | 2 | 1 | 1100.4.a.d | 1 | ||
| 5.c | odd | 4 | 2 | 1100.4.b.c | 2 | ||
| 7.b | odd | 2 | 1 | 2156.4.a.b | 1 | ||
| 8.b | even | 2 | 1 | 704.4.a.j | 1 | ||
| 8.d | odd | 2 | 1 | 704.4.a.c | 1 | ||
| 11.b | odd | 2 | 1 | 484.4.a.a | 1 | ||
| 12.b | even | 2 | 1 | 1584.4.a.p | 1 | ||
| 44.c | even | 2 | 1 | 1936.4.a.m | 1 | ||
| By twisted newform orbit | |||||||
|---|---|---|---|---|---|---|---|
| Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
| 44.4.a.a | ✓ | 1 | 1.a | even | 1 | 1 | trivial |
| 176.4.a.e | 1 | 4.b | odd | 2 | 1 | ||
| 396.4.a.e | 1 | 3.b | odd | 2 | 1 | ||
| 484.4.a.a | 1 | 11.b | odd | 2 | 1 | ||
| 704.4.a.c | 1 | 8.d | odd | 2 | 1 | ||
| 704.4.a.j | 1 | 8.b | even | 2 | 1 | ||
| 1100.4.a.d | 1 | 5.b | even | 2 | 1 | ||
| 1100.4.b.c | 2 | 5.c | odd | 4 | 2 | ||
| 1584.4.a.p | 1 | 12.b | even | 2 | 1 | ||
| 1936.4.a.m | 1 | 44.c | even | 2 | 1 | ||
| 2156.4.a.b | 1 | 7.b | odd | 2 | 1 | ||
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator
\( T_{3} + 5 \)
acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(44))\).
Hecke characteristic polynomials
| $p$ | $F_p(T)$ |
|---|---|
| $2$ |
\( T \)
|
| $3$ |
\( T + 5 \)
|
| $5$ |
\( T + 7 \)
|
| $7$ |
\( T + 26 \)
|
| $11$ |
\( T + 11 \)
|
| $13$ |
\( T - 52 \)
|
| $17$ |
\( T - 46 \)
|
| $19$ |
\( T + 96 \)
|
| $23$ |
\( T - 27 \)
|
| $29$ |
\( T - 16 \)
|
| $31$ |
\( T + 293 \)
|
| $37$ |
\( T + 29 \)
|
| $41$ |
\( T + 472 \)
|
| $43$ |
\( T + 110 \)
|
| $47$ |
\( T + 224 \)
|
| $53$ |
\( T - 754 \)
|
| $59$ |
\( T - 825 \)
|
| $61$ |
\( T + 548 \)
|
| $67$ |
\( T + 123 \)
|
| $71$ |
\( T - 1001 \)
|
| $73$ |
\( T + 1020 \)
|
| $79$ |
\( T - 526 \)
|
| $83$ |
\( T + 158 \)
|
| $89$ |
\( T + 1217 \)
|
| $97$ |
\( T + 263 \)
|
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