Newspace parameters
Level: | \( N \) | \(=\) | \( 891 = 3^{4} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 891.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
Self dual: | yes |
Analytic conductor: | \(0.444666926256\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 99) |
Projective image: | \(D_{3}\) |
Projective field: | Galois closure of 3.1.891.1 |
Artin image: | $S_3$ |
Artin field: | Galois closure of 3.1.891.1 |
$q$-expansion
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/891\mathbb{Z}\right)^\times\).
\(n\) | \(244\) | \(650\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 | \(\iota_m(\nu)\) | \( a_{2} \) | \( a_{3} \) | \( a_{4} \) | \( a_{5} \) | \( a_{6} \) | \( a_{7} \) | \( a_{8} \) | \( a_{9} \) | \( a_{10} \) | |||||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
406.1 |
|
0 | 0 | 1.00000 | −1.00000 | 0 | 0 | 0 | 0 | 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 | 891.1.c.a | 1 | |
3.b | odd | 2 | 1 | 891.1.c.b | 1 | ||
9.c | even | 3 | 2 | 99.1.h.a | ✓ | 2 | |
9.d | odd | 6 | 2 | 297.1.h.a | 2 | ||
11.b | odd | 2 | 1 | CM | 891.1.c.a | 1 | |
33.d | even | 2 | 1 | 891.1.c.b | 1 | ||
36.f | odd | 6 | 2 | 1584.1.bf.b | 2 | ||
45.j | even | 6 | 2 | 2475.1.y.a | 2 | ||
45.k | odd | 12 | 4 | 2475.1.t.a | 4 | ||
99.g | even | 6 | 2 | 297.1.h.a | 2 | ||
99.h | odd | 6 | 2 | 99.1.h.a | ✓ | 2 | |
99.m | even | 15 | 8 | 1089.1.s.a | 8 | ||
99.n | odd | 30 | 8 | 3267.1.w.a | 8 | ||
99.o | odd | 30 | 8 | 1089.1.s.a | 8 | ||
99.p | even | 30 | 8 | 3267.1.w.a | 8 | ||
396.k | even | 6 | 2 | 1584.1.bf.b | 2 | ||
495.o | odd | 6 | 2 | 2475.1.y.a | 2 | ||
495.bf | even | 12 | 4 | 2475.1.t.a | 4 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
99.1.h.a | ✓ | 2 | 9.c | even | 3 | 2 | |
99.1.h.a | ✓ | 2 | 99.h | odd | 6 | 2 | |
297.1.h.a | 2 | 9.d | odd | 6 | 2 | ||
297.1.h.a | 2 | 99.g | even | 6 | 2 | ||
891.1.c.a | 1 | 1.a | even | 1 | 1 | trivial | |
891.1.c.a | 1 | 11.b | odd | 2 | 1 | CM | |
891.1.c.b | 1 | 3.b | odd | 2 | 1 | ||
891.1.c.b | 1 | 33.d | even | 2 | 1 | ||
1089.1.s.a | 8 | 99.m | even | 15 | 8 | ||
1089.1.s.a | 8 | 99.o | odd | 30 | 8 | ||
1584.1.bf.b | 2 | 36.f | odd | 6 | 2 | ||
1584.1.bf.b | 2 | 396.k | even | 6 | 2 | ||
2475.1.t.a | 4 | 45.k | odd | 12 | 4 | ||
2475.1.t.a | 4 | 495.bf | even | 12 | 4 | ||
2475.1.y.a | 2 | 45.j | even | 6 | 2 | ||
2475.1.y.a | 2 | 495.o | odd | 6 | 2 | ||
3267.1.w.a | 8 | 99.n | odd | 30 | 8 | ||
3267.1.w.a | 8 | 99.p | even | 30 | 8 |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator
\( T_{5} + 1 \)
acting on \(S_{1}^{\mathrm{new}}(891, [\chi])\).
Hecke characteristic polynomials
$p$
$F_p(T)$
$2$
\( T \)
$3$
\( T \)
$5$
\( T + 1 \)
$7$
\( T \)
$11$
\( T - 1 \)
$13$
\( T \)
$17$
\( T \)
$19$
\( T \)
$23$
\( T - 2 \)
$29$
\( T \)
$31$
\( T + 1 \)
$37$
\( T + 1 \)
$41$
\( T \)
$43$
\( T \)
$47$
\( T + 1 \)
$53$
\( T + 1 \)
$59$
\( T + 1 \)
$61$
\( T \)
$67$
\( T + 1 \)
$71$
\( T + 1 \)
$73$
\( T \)
$79$
\( T \)
$83$
\( T \)
$89$
\( T - 2 \)
$97$
\( T + 1 \)
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