Newspace parameters
Level: | \( N \) | \(=\) | \( 464 = 2^{4} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 464.h (of order \(2\), degree \(1\), minimal) |
Newform invariants
Self dual: | yes |
Analytic conductor: | \(0.231566165862\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Projective image: | \(D_{2}\) |
Projective field: | Galois closure of \(\Q(i, \sqrt{29})\) |
Artin image: | $D_4$ |
Artin field: | Galois closure of 4.0.1856.1 |
$q$-expansion
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/464\mathbb{Z}\right)^\times\).
\(n\) | \(117\) | \(175\) | \(321\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 | \(\iota_m(\nu)\) | \( a_{2} \) | \( a_{3} \) | \( a_{4} \) | \( a_{5} \) | \( a_{6} \) | \( a_{7} \) | \( a_{8} \) | \( a_{9} \) | \( a_{10} \) | |||||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
463.1 |
|
0 | 0 | 0 | 2.00000 | 0 | 0 | 0 | −1.00000 | 0 | |||||||||||||||||||||
Inner twists
Char | Parity | Ord | Mult | Type |
---|---|---|---|---|
1.a | even | 1 | 1 | trivial |
4.b | odd | 2 | 1 | CM by \(\Q(\sqrt{-1}) \) |
29.b | even | 2 | 1 | RM by \(\Q(\sqrt{29}) \) |
116.d | odd | 2 | 1 | CM by \(\Q(\sqrt{-29}) \) |
Twists
By twisting character orbit | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Mult | Type | Twist | Min | Dim |
1.a | even | 1 | 1 | trivial | 464.1.h.a | ✓ | 1 |
4.b | odd | 2 | 1 | CM | 464.1.h.a | ✓ | 1 |
8.b | even | 2 | 1 | 1856.1.h.b | 1 | ||
8.d | odd | 2 | 1 | 1856.1.h.b | 1 | ||
29.b | even | 2 | 1 | RM | 464.1.h.a | ✓ | 1 |
116.d | odd | 2 | 1 | CM | 464.1.h.a | ✓ | 1 |
232.b | odd | 2 | 1 | 1856.1.h.b | 1 | ||
232.g | even | 2 | 1 | 1856.1.h.b | 1 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
464.1.h.a | ✓ | 1 | 1.a | even | 1 | 1 | trivial |
464.1.h.a | ✓ | 1 | 4.b | odd | 2 | 1 | CM |
464.1.h.a | ✓ | 1 | 29.b | even | 2 | 1 | RM |
464.1.h.a | ✓ | 1 | 116.d | odd | 2 | 1 | CM |
1856.1.h.b | 1 | 8.b | even | 2 | 1 | ||
1856.1.h.b | 1 | 8.d | odd | 2 | 1 | ||
1856.1.h.b | 1 | 232.b | odd | 2 | 1 | ||
1856.1.h.b | 1 | 232.g | even | 2 | 1 |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator
\( T_{3} \)
acting on \(S_{1}^{\mathrm{new}}(464, [\chi])\).
Hecke characteristic polynomials
$p$
$F_p(T)$
$2$
\( T \)
$3$
\( T \)
$5$
\( T - 2 \)
$7$
\( T \)
$11$
\( T \)
$13$
\( T + 2 \)
$17$
\( T \)
$19$
\( T \)
$23$
\( T \)
$29$
\( T + 1 \)
$31$
\( T \)
$37$
\( T \)
$41$
\( T \)
$43$
\( T \)
$47$
\( T \)
$53$
\( T + 2 \)
$59$
\( T \)
$61$
\( T \)
$67$
\( T \)
$71$
\( T \)
$73$
\( T \)
$79$
\( T \)
$83$
\( T \)
$89$
\( T \)
$97$
\( T \)
show more
show less