Newform orbit 1920.1.i.d

• Label: 1920.1.i.d
• Level: $1920$
• Weight: $1$
• Character orbit: 1920.i
• Self dual: yes
• Analytic conductor: $0.958$
• Analytic rank: $0$
• Dimension: $1$
• Projective image: $D_{2}$
• CM/RM discs: -20, -120, 24
• Inner twists: $4$

Newspace parameters

Level:	$N$	$=$	$1920 = 2^{7} \cdot 3 \cdot 5$
Weight:	$k$	$=$	$1$
Character orbit:	$[\chi]$	$=$	1920.i (of order $2$, degree $1$, minimal)

Newform invariants

Self dual:	yes
Analytic conductor:	$0.958204824255$
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 $\Q(\sqrt{-5}, \sqrt{6})$
Artin image:	$D_4$
Artin field:	Galois closure of 4.0.38400.2
Stark unit:	Root of $x^{4} - 70900x^{3} + 69798x^{2} - 70900x + 1$

$q$-expansion

$f(q)$

$=$

$q + q^{3} + q^{5} + q^{9} + q^{15} - 2 q^{23} + q^{25} + q^{27} - 2 q^{29} - 2 q^{43} + q^{45} + 2 q^{47} + q^{49} - 2 q^{67} - 2 q^{69} + q^{75} + q^{81} - 2 q^{87}+O(q^{100})$

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1920\mathbb{Z}\right)^\times$.

$n$	$511$	$641$	$901$	$1537$
$\chi(n)$	$1$	$-1$	$-1$	$-1$

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  

$\iota_m(\nu)$

$a_{2}$

$a_{3}$

$a_{4}$

$a_{5}$

$a_{6}$

$a_{7}$

$a_{8}$

$a_{9}$

$a_{10}$

449.1

0

0

1.00000

0

1.00000

0

0

0

1.00000

0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
20.d	odd	2	1	CM by $\Q(\sqrt{-5})$
24.f	even	2	1	RM by $\Q(\sqrt{6})$
120.i	odd	2	1	CM by $\Q(\sqrt{-30})$

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1920.1.i.d	yes	1
3.b	odd	2	1		1920.1.i.c	yes	1
4.b	odd	2	1		1920.1.i.b	yes	1
5.b	even	2	1		1920.1.i.b	yes	1
8.b	even	2	1		1920.1.i.a	✓	1
8.d	odd	2	1		1920.1.i.c	yes	1
12.b	even	2	1		1920.1.i.a	✓	1
15.d	odd	2	1		1920.1.i.a	✓	1
16.e	even	4	2		3840.1.c.g		2
16.f	odd	4	2		3840.1.c.f		2
20.d	odd	2	1	CM	1920.1.i.d	yes	1
24.f	even	2	1	RM	1920.1.i.d	yes	1
24.h	odd	2	1		1920.1.i.b	yes	1
40.e	odd	2	1		1920.1.i.a	✓	1
40.f	even	2	1		1920.1.i.c	yes	1
48.i	odd	4	2		3840.1.c.f		2
48.k	even	4	2		3840.1.c.g		2
60.h	even	2	1		1920.1.i.c	yes	1
80.k	odd	4	2		3840.1.c.g		2
80.q	even	4	2		3840.1.c.f		2
120.i	odd	2	1	CM	1920.1.i.d	yes	1
120.m	even	2	1		1920.1.i.b	yes	1
240.t	even	4	2		3840.1.c.f		2
240.bm	odd	4	2		3840.1.c.g		2

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
1920.1.i.a	✓	1	8.b	even	2	1
1920.1.i.a	✓	1	12.b	even	2	1
1920.1.i.a	✓	1	15.d	odd	2	1
1920.1.i.a	✓	1	40.e	odd	2	1
1920.1.i.b	yes	1	4.b	odd	2	1
1920.1.i.b	yes	1	5.b	even	2	1
1920.1.i.b	yes	1	24.h	odd	2	1
1920.1.i.b	yes	1	120.m	even	2	1
1920.1.i.c	yes	1	3.b	odd	2	1
1920.1.i.c	yes	1	8.d	odd	2	1
1920.1.i.c	yes	1	40.f	even	2	1
1920.1.i.c	yes	1	60.h	even	2	1
1920.1.i.d	yes	1	1.a	even	1	1	trivial
1920.1.i.d	yes	1	20.d	odd	2	1	CM
1920.1.i.d	yes	1	24.f	even	2	1	RM
1920.1.i.d	yes	1	120.i	odd	2	1	CM
3840.1.c.f		2	16.f	odd	4	2
3840.1.c.f		2	48.i	odd	4	2
3840.1.c.f		2	80.q	even	4	2
3840.1.c.f		2	240.t	even	4	2
3840.1.c.g		2	16.e	even	4	2
3840.1.c.g		2	48.k	even	4	2
3840.1.c.g		2	80.k	odd	4	2
3840.1.c.g		2	240.bm	odd	4	2

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{1}^{\mathrm{new}}(1920, [\chi])$:

$T_{7}$

$T_{23} + 2$

$T_{29} + 2$

Hecke characteristic polynomials

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