Newspace parameters
| Level: | \( N \) | \(=\) | \( 11 \) |
| Weight: | \( k \) | \(=\) | \( 7 \) |
| Character orbit: | \([\chi]\) | \(=\) | 11.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
| Self dual: | yes |
| Analytic conductor: | \(2.53059491982\) |
| 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 \(\left(\mathbb{Z}/11\mathbb{Z}\right)^\times\).
| \(n\) | \(2\) |
| \(\chi(n)\) | \(-1\) |
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 | \(\iota_m(\nu)\) | \( a_{2} \) | \( a_{3} \) | \( a_{4} \) | \( a_{5} \) | \( a_{6} \) | \( a_{7} \) | \( a_{8} \) | \( a_{9} \) | \( a_{10} \) | |||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 10.1 |
|
0 | 10.0000 | 64.0000 | 74.0000 | 0 | 0 | 0 | −629.000 | 0 | |||||||||||||||||||||
Inner twists
| Char | Parity | Ord | Mult | Type |
|---|---|---|---|---|
| 1.a | even | 1 | 1 | trivial |
| 11.b | odd | 2 | 1 | CM by \(\Q(\sqrt{-11}) \) |
Twists
| By twisting character orbit | |||||||
|---|---|---|---|---|---|---|---|
| Char | Parity | Ord | Mult | Type | Twist | Min | Dim |
| 1.a | even | 1 | 1 | trivial | 11.7.b.a | ✓ | 1 |
| 3.b | odd | 2 | 1 | 99.7.c.a | 1 | ||
| 4.b | odd | 2 | 1 | 176.7.h.a | 1 | ||
| 11.b | odd | 2 | 1 | CM | 11.7.b.a | ✓ | 1 |
| 33.d | even | 2 | 1 | 99.7.c.a | 1 | ||
| 44.c | even | 2 | 1 | 176.7.h.a | 1 | ||
| By twisted newform orbit | |||||||
|---|---|---|---|---|---|---|---|
| Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
| 11.7.b.a | ✓ | 1 | 1.a | even | 1 | 1 | trivial |
| 11.7.b.a | ✓ | 1 | 11.b | odd | 2 | 1 | CM |
| 99.7.c.a | 1 | 3.b | odd | 2 | 1 | ||
| 99.7.c.a | 1 | 33.d | even | 2 | 1 | ||
| 176.7.h.a | 1 | 4.b | odd | 2 | 1 | ||
| 176.7.h.a | 1 | 44.c | even | 2 | 1 | ||
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2} \)
acting on \(S_{7}^{\mathrm{new}}(11, [\chi])\).
Hecke characteristic polynomials
$p$
$F_p(T)$
$2$
\( T \)
$3$
\( T - 10 \)
$5$
\( T - 74 \)
$7$
\( T \)
$11$
\( T + 1331 \)
$13$
\( T \)
$17$
\( T \)
$19$
\( T \)
$23$
\( T + 12670 \)
$29$
\( T \)
$31$
\( T - 56018 \)
$37$
\( T - 87050 \)
$41$
\( T \)
$43$
\( T \)
$47$
\( T + 206350 \)
$53$
\( T - 246890 \)
$59$
\( T - 107642 \)
$61$
\( T \)
$67$
\( T + 428470 \)
$71$
\( T + 341278 \)
$73$
\( T \)
$79$
\( T \)
$83$
\( T \)
$89$
\( T - 1392338 \)
$97$
\( T + 1824190 \)
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