Newform orbit 459.1.c.b

• Label: 459.1.c.b
• Level: $459$
• Weight: $1$
• Character orbit: 459.c
• Self dual: yes
• Analytic conductor: $0.229$
• Analytic rank: $0$
• Dimension: $1$
• Projective image: $D_{3}$
• CM discriminant: -51
• Inner twists: $2$

Newspace parameters

Level:	$N$	$=$	$459 = 3^{3} \cdot 17$
Weight:	$k$	$=$	$1$
Character orbit:	$[\chi]$	$=$	459.c (of order $2$, degree $1$, minimal)

Newform invariants

Self dual:	yes
Analytic conductor:	$0.229070840799$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$1$
Twist minimal:	yes
Projective image:	$D_{3}$
Projective field:	Galois closure of 3.1.459.1
Artin image:	$D_6$
Artin field:	Galois closure of 6.0.632043.1
Stark unit:	Root of $x^{6} - 72x^{5} + 756x^{4} - 3818x^{3} + 756x^{2} - 72x + 1$

$q$-expansion

$f(q)$

$=$

q + q^4 + q^5 - 2 * q^11 - q^13 + q^16 - q^17 - q^19 + q^20 + q^23 + q^29 + q^41 - q^43 - 2 * q^44 + q^49 - q^52 - 2 * q^55 + q^64 - q^65 - q^67 - q^68 + q^71 - q^76 + q^80 - q^85 + q^92 - q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/459\mathbb{Z}\right)^\times$.

$n$	$137$	$190$
$\chi(n)$	$-1$	$-1$

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  

$\iota_m(\nu)$

$a_{2}$

$a_{3}$

$a_{4}$

$a_{5}$

$a_{6}$

$a_{7}$

$a_{8}$

$a_{9}$

$a_{10}$

458.1

0

0

0

1.00000

1.00000

0

0

0

0

0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
51.c	odd	2	1	CM by $\Q(\sqrt{-51})$

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	459.1.c.b	yes	1
3.b	odd	2	1		459.1.c.a	✓	1
9.c	even	3	2		1377.1.i.a		2
9.d	odd	6	2		1377.1.i.b		2
17.b	even	2	1		459.1.c.a	✓	1
51.c	odd	2	1	CM	459.1.c.b	yes	1
153.h	even	6	2		1377.1.i.b		2
153.i	odd	6	2		1377.1.i.a		2

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
459.1.c.a	✓	1	3.b	odd	2	1
459.1.c.a	✓	1	17.b	even	2	1
459.1.c.b	yes	1	1.a	even	1	1	trivial
459.1.c.b	yes	1	51.c	odd	2	1	CM
1377.1.i.a		2	9.c	even	3	2
1377.1.i.a		2	153.i	odd	6	2
1377.1.i.b		2	9.d	odd	6	2
1377.1.i.b		2	153.h	even	6	2

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator $T_{5} - 1$ acting on $S_{1}^{\mathrm{new}}(459, [\chi])$.

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$T$
$3$	$T$
$5$	$T - 1$
$7$	$T$
$11$	$T + 2$