Newspace parameters
Level: | \( N \) | \(=\) | \( 22 = 2 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 22.a (trivial) |
Newform invariants
Self dual: | yes |
Analytic conductor: | \(1.29804202013\) |
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 |
|
−2.00000 | −7.00000 | 4.00000 | −19.0000 | 14.0000 | 14.0000 | −8.00000 | 22.0000 | 38.0000 | |||||||||||||||||||||
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 | 22.4.a.a | ✓ | 1 |
3.b | odd | 2 | 1 | 198.4.a.g | 1 | ||
4.b | odd | 2 | 1 | 176.4.a.f | 1 | ||
5.b | even | 2 | 1 | 550.4.a.n | 1 | ||
5.c | odd | 4 | 2 | 550.4.b.k | 2 | ||
7.b | odd | 2 | 1 | 1078.4.a.d | 1 | ||
8.b | even | 2 | 1 | 704.4.a.l | 1 | ||
8.d | odd | 2 | 1 | 704.4.a.b | 1 | ||
11.b | odd | 2 | 1 | 242.4.a.d | 1 | ||
11.c | even | 5 | 4 | 242.4.c.l | 4 | ||
11.d | odd | 10 | 4 | 242.4.c.e | 4 | ||
12.b | even | 2 | 1 | 1584.4.a.v | 1 | ||
33.d | even | 2 | 1 | 2178.4.a.l | 1 | ||
44.c | even | 2 | 1 | 1936.4.a.n | 1 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
22.4.a.a | ✓ | 1 | 1.a | even | 1 | 1 | trivial |
176.4.a.f | 1 | 4.b | odd | 2 | 1 | ||
198.4.a.g | 1 | 3.b | odd | 2 | 1 | ||
242.4.a.d | 1 | 11.b | odd | 2 | 1 | ||
242.4.c.e | 4 | 11.d | odd | 10 | 4 | ||
242.4.c.l | 4 | 11.c | even | 5 | 4 | ||
550.4.a.n | 1 | 5.b | even | 2 | 1 | ||
550.4.b.k | 2 | 5.c | odd | 4 | 2 | ||
704.4.a.b | 1 | 8.d | odd | 2 | 1 | ||
704.4.a.l | 1 | 8.b | even | 2 | 1 | ||
1078.4.a.d | 1 | 7.b | odd | 2 | 1 | ||
1584.4.a.v | 1 | 12.b | even | 2 | 1 | ||
1936.4.a.n | 1 | 44.c | even | 2 | 1 | ||
2178.4.a.l | 1 | 33.d | even | 2 | 1 |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator
\( T_{3} + 7 \)
acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(22))\).
Hecke characteristic polynomials
$p$
$F_p(T)$
$2$
\( T + 2 \)
$3$
\( T + 7 \)
$5$
\( T + 19 \)
$7$
\( T - 14 \)
$11$
\( T - 11 \)
$13$
\( T + 72 \)
$17$
\( T + 46 \)
$19$
\( T + 20 \)
$23$
\( T + 107 \)
$29$
\( T - 120 \)
$31$
\( T - 117 \)
$37$
\( T + 201 \)
$41$
\( T + 228 \)
$43$
\( T + 242 \)
$47$
\( T + 96 \)
$53$
\( T - 458 \)
$59$
\( T - 435 \)
$61$
\( T + 668 \)
$67$
\( T - 439 \)
$71$
\( T + 1113 \)
$73$
\( T + 72 \)
$79$
\( T + 70 \)
$83$
\( T - 358 \)
$89$
\( T - 895 \)
$97$
\( T - 409 \)
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