Newspace parameters
Level: | \( N \) | \(=\) | \( 55 = 5 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 55.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
Self dual: | yes |
Analytic conductor: | \(5.68534796961\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{2}]$ |
$q$-expansion
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/55\mathbb{Z}\right)^\times\).
\(n\) | \(12\) | \(46\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 | \(\iota_m(\nu)\) | \( a_{2} \) | \( a_{3} \) | \( a_{4} \) | \( a_{5} \) | \( a_{6} \) | \( a_{7} \) | \( a_{8} \) | \( a_{9} \) | \( a_{10} \) | |||||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
54.1 |
|
3.00000 | 0 | −7.00000 | 25.0000 | 0 | 78.0000 | −69.0000 | 81.0000 | 75.0000 | |||||||||||||||||||||
Inner twists
Char | Parity | Ord | Mult | Type |
---|---|---|---|---|
1.a | even | 1 | 1 | trivial |
55.d | odd | 2 | 1 | CM by \(\Q(\sqrt{-55}) \) |
Twists
By twisting character orbit | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Mult | Type | Twist | Min | Dim |
1.a | even | 1 | 1 | trivial | 55.5.d.b | yes | 1 |
5.b | even | 2 | 1 | 55.5.d.a | ✓ | 1 | |
5.c | odd | 4 | 2 | 275.5.c.c | 2 | ||
11.b | odd | 2 | 1 | 55.5.d.a | ✓ | 1 | |
55.d | odd | 2 | 1 | CM | 55.5.d.b | yes | 1 |
55.e | even | 4 | 2 | 275.5.c.c | 2 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
55.5.d.a | ✓ | 1 | 5.b | even | 2 | 1 | |
55.5.d.a | ✓ | 1 | 11.b | odd | 2 | 1 | |
55.5.d.b | yes | 1 | 1.a | even | 1 | 1 | trivial |
55.5.d.b | yes | 1 | 55.d | odd | 2 | 1 | CM |
275.5.c.c | 2 | 5.c | odd | 4 | 2 | ||
275.5.c.c | 2 | 55.e | even | 4 | 2 |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2} - 3 \)
acting on \(S_{5}^{\mathrm{new}}(55, [\chi])\).
Hecke characteristic polynomials
$p$
$F_p(T)$
$2$
\( T - 3 \)
$3$
\( T \)
$5$
\( T - 25 \)
$7$
\( T - 78 \)
$11$
\( T - 121 \)
$13$
\( T + 162 \)
$17$
\( T + 402 \)
$19$
\( T \)
$23$
\( T \)
$29$
\( T \)
$31$
\( T + 1598 \)
$37$
\( T \)
$41$
\( T \)
$43$
\( T + 3522 \)
$47$
\( T \)
$53$
\( T \)
$59$
\( T - 3442 \)
$61$
\( T \)
$67$
\( T \)
$71$
\( T + 3998 \)
$73$
\( T - 10638 \)
$79$
\( T \)
$83$
\( T + 13602 \)
$89$
\( T + 15838 \)
$97$
\( T \)
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