Newform orbit 1152.1.b.a

• Label: 1152.1.b.a
• Level: $1152$
• Weight: $1$
• Character orbit: 1152.b
• Self dual: yes
• Analytic conductor: $0.575$
• Analytic rank: $0$
• Dimension: $1$
• Projective image: $D_{2}$
• CM/RM discs: -4, -8, 8
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1152 = 2^{7} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1152.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	yes
Analytic conductor:	\(0.574922894553\)
Analytic rank:	\(0\)
Dimension:	\(1\)
Coefficient field:	\(\mathbb{Q}\)
Coefficient ring:	\(\mathbb{Z}\)
Coefficient ring index:	\( 1 \)
Twist minimal:	no (minimal twist has level 128)
Projective image:	\(D_{2}\)
Projective field:	Galois closure of \(\Q(\zeta_{8})\)
Artin image:	$D_4$
Artin field:	Galois closure of 4.0.4608.1

$q$-expansion

\(f(q)\)

\(=\)

\( q+O(q^{10}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times\).

\(n\)	\(127\)	\(641\)	\(901\)
\(\chi(n)\)	\(-1\)	\(1\)	\(-1\)

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  

\(\iota_m(\nu)\)

\( a_{2} \)

\( a_{3} \)

\( a_{4} \)

\( a_{5} \)

\( a_{6} \)

\( a_{7} \)

\( a_{8} \)

\( a_{9} \)

\( a_{10} \)

703.1

0

0

0

0

0

0

0

0

0

0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
4.b	odd	2	1	CM by \(\Q(\sqrt{-1}) \)
8.b	even	2	1	RM by \(\Q(\sqrt{2}) \)
8.d	odd	2	1	CM by \(\Q(\sqrt{-2}) \)

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1152.1.b.a		1
3.b	odd	2	1		128.1.d.a	✓	1
4.b	odd	2	1	CM	1152.1.b.a		1
8.b	even	2	1	RM	1152.1.b.a		1
8.d	odd	2	1	CM	1152.1.b.a		1
12.b	even	2	1		128.1.d.a	✓	1
15.d	odd	2	1		3200.1.g.a		1
15.e	even	4	2		3200.1.e.a		2
16.e	even	4	2		2304.1.g.b		1
16.f	odd	4	2		2304.1.g.b		1
24.f	even	2	1		128.1.d.a	✓	1
24.h	odd	2	1		128.1.d.a	✓	1
48.i	odd	4	2		256.1.c.a		1
48.k	even	4	2		256.1.c.a		1
60.h	even	2	1		3200.1.g.a		1
60.l	odd	4	2		3200.1.e.a		2
96.o	even	8	4		1024.1.f.b		2
96.p	odd	8	4		1024.1.f.b		2
120.i	odd	2	1		3200.1.g.a		1
120.m	even	2	1		3200.1.g.a		1
120.q	odd	4	2		3200.1.e.a		2
120.w	even	4	2		3200.1.e.a		2

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
128.1.d.a	✓	1	3.b	odd	2	1
128.1.d.a	✓	1	12.b	even	2	1
128.1.d.a	✓	1	24.f	even	2	1
128.1.d.a	✓	1	24.h	odd	2	1
256.1.c.a		1	48.i	odd	4	2
256.1.c.a		1	48.k	even	4	2
1024.1.f.b		2	96.o	even	8	4
1024.1.f.b		2	96.p	odd	8	4
1152.1.b.a		1	1.a	even	1	1	trivial
1152.1.b.a		1	4.b	odd	2	1	CM
1152.1.b.a		1	8.b	even	2	1	RM
1152.1.b.a		1	8.d	odd	2	1	CM
2304.1.g.b		1	16.e	even	4	2
2304.1.g.b		1	16.f	odd	4	2
3200.1.e.a		2	15.e	even	4	2
3200.1.e.a		2	60.l	odd	4	2
3200.1.e.a		2	120.q	odd	4	2
3200.1.e.a		2	120.w	even	4	2
3200.1.g.a		1	15.d	odd	2	1
3200.1.g.a		1	60.h	even	2	1
3200.1.g.a		1	120.i	odd	2	1
3200.1.g.a		1	120.m	even	2	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{5} \) acting on \(S_{1}^{\mathrm{new}}(1152, [\chi])\).

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	\( T \)
$3$	\( T \)
$5$	\( T \)
$7$	\( T \)
$11$	\( T \)