Newform orbit 1035.1.d.b

• Label: 1035.1.d.b
• Level: $1035$
• Weight: $1$
• Character orbit: 1035.d
• Self dual: yes
• Analytic conductor: $0.517$
• Analytic rank: $0$
• Dimension: $1$
• Projective image: $D_{2}$
• CM/RM discs: -15, -115, 69
• Inner twists: $4$

Newspace parameters

Level:	$N$	$=$	$1035 = 3^{2} \cdot 5 \cdot 23$
Weight:	$k$	$=$	$1$
Character orbit:	$[\chi]$	$=$	1035.d (of order $2$, degree $1$, minimal)

Newform invariants

Self dual:	yes
Analytic conductor:	$0.516532288075$
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 $\Q(\sqrt{-15}, \sqrt{69})$
Artin image:	$D_4$
Artin field:	Galois closure of 4.0.15525.2
Stark unit:	Root of $x^{4} - 1060x^{3} - 1722x^{2} - 1060x + 1$

$q$-expansion

$f(q)$

$=$

$q + q^{4} + q^{5} + q^{16} - 2 q^{17} + q^{20} - q^{23} + q^{25} - 2 q^{31} - q^{49} + 2 q^{53} + q^{64} - 2 q^{68} + q^{80} + 2 q^{83} - 2 q^{85} - q^{92}+O(q^{100})$

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1035\mathbb{Z}\right)^\times$.

$n$	$461$	$622$	$856$
$\chi(n)$	$1$	$-1$	$-1$

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  

$\iota_m(\nu)$

$a_{2}$

$a_{3}$

$a_{4}$

$a_{5}$

$a_{6}$

$a_{7}$

$a_{8}$

$a_{9}$

$a_{10}$

919.1

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
15.d	odd	2	1	CM by $\Q(\sqrt{-15})$
69.c	even	2	1	RM by $\Q(\sqrt{69})$
115.c	odd	2	1	CM by $\Q(\sqrt{-115})$

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1035.1.d.b	yes	1
3.b	odd	2	1		1035.1.d.a	✓	1
5.b	even	2	1		1035.1.d.a	✓	1
15.d	odd	2	1	CM	1035.1.d.b	yes	1
23.b	odd	2	1		1035.1.d.a	✓	1
69.c	even	2	1	RM	1035.1.d.b	yes	1
115.c	odd	2	1	CM	1035.1.d.b	yes	1
345.h	even	2	1		1035.1.d.a	✓	1

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
1035.1.d.a	✓	1	3.b	odd	2	1
1035.1.d.a	✓	1	5.b	even	2	1
1035.1.d.a	✓	1	23.b	odd	2	1
1035.1.d.a	✓	1	345.h	even	2	1
1035.1.d.b	yes	1	1.a	even	1	1	trivial
1035.1.d.b	yes	1	15.d	odd	2	1	CM
1035.1.d.b	yes	1	69.c	even	2	1	RM
1035.1.d.b	yes	1	115.c	odd	2	1	CM

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator $T_{17} + 2$ acting on $S_{1}^{\mathrm{new}}(1035, [\chi])$.

Hecke characteristic polynomials

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