Newform orbit 1176.1.n.d

• Label: 1176.1.n.d
• Level: $1176$
• Weight: $1$
• Character orbit: 1176.n
• Self dual: yes
• Analytic conductor: $0.587$
• Analytic rank: $0$
• Dimension: $1$
• Projective image: $D_{3}$
• CM discriminant: -24
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1176 = 2^{3} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1176.n (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	yes
Analytic conductor:	\(0.586900454856\)
Analytic rank:	\(0\)
Dimension:	\(1\)
Coefficient field:	\(\mathbb{Q}\)
Coefficient ring:	\(\mathbb{Z}\)
Coefficient ring index:	\( 1 \)
Twist minimal:	no (minimal twist has level 168)
Projective image:	\(D_{3}\)
Projective field:	Galois closure of 3.1.1176.1
Artin image:	$S_3$
Artin field:	Galois closure of 3.1.1176.1

$q$-expansion

\(f(q)\)

\(=\)

\( q + q^{2} + q^{3} + q^{4} - q^{5} + q^{6} + q^{8} + q^{9}+O(q^{10}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1176\mathbb{Z}\right)^\times\).

\(n\)	\(295\)	\(589\)	\(785\)	\(1081\)
\(\chi(n)\)	\(1\)	\(-1\)	\(-1\)	\(1\)

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  

\(\iota_m(\nu)\)

\( a_{2} \)

\( a_{3} \)

\( a_{4} \)

\( a_{5} \)

\( a_{6} \)

\( a_{7} \)

\( a_{8} \)

\( a_{9} \)

\( a_{10} \)

197.1

0

1.00000

1.00000

1.00000

−1.00000

1.00000

0

1.00000

1.00000

−1.00000

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
24.h	odd	2	1	CM by \(\Q(\sqrt{-6}) \)

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1176.1.n.d		1
3.b	odd	2	1		1176.1.n.a		1
7.b	odd	2	1		1176.1.n.c		1
7.c	even	3	2		168.1.s.a	✓	2
7.d	odd	6	2		1176.1.s.a		2
8.b	even	2	1		1176.1.n.a		1
21.c	even	2	1		1176.1.n.b		1
21.g	even	6	2		1176.1.s.b		2
21.h	odd	6	2		168.1.s.b	yes	2
24.h	odd	2	1	CM	1176.1.n.d		1
28.g	odd	6	2		672.1.ba.b		2
56.h	odd	2	1		1176.1.n.b		1
56.j	odd	6	2		1176.1.s.b		2
56.k	odd	6	2		672.1.ba.a		2
56.p	even	6	2		168.1.s.b	yes	2
84.n	even	6	2		672.1.ba.a		2
168.i	even	2	1		1176.1.n.c		1
168.s	odd	6	2		168.1.s.a	✓	2
168.v	even	6	2		672.1.ba.b		2
168.ba	even	6	2		1176.1.s.a		2

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
168.1.s.a	✓	2	7.c	even	3	2
168.1.s.a	✓	2	168.s	odd	6	2
168.1.s.b	yes	2	21.h	odd	6	2
168.1.s.b	yes	2	56.p	even	6	2
672.1.ba.a		2	56.k	odd	6	2
672.1.ba.a		2	84.n	even	6	2
672.1.ba.b		2	28.g	odd	6	2
672.1.ba.b		2	168.v	even	6	2
1176.1.n.a		1	3.b	odd	2	1
1176.1.n.a		1	8.b	even	2	1
1176.1.n.b		1	21.c	even	2	1
1176.1.n.b		1	56.h	odd	2	1
1176.1.n.c		1	7.b	odd	2	1
1176.1.n.c		1	168.i	even	2	1
1176.1.n.d		1	1.a	even	1	1	trivial
1176.1.n.d		1	24.h	odd	2	1	CM
1176.1.s.a		2	7.d	odd	6	2
1176.1.s.a		2	168.ba	even	6	2
1176.1.s.b		2	21.g	even	6	2
1176.1.s.b		2	56.j	odd	6	2

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{1}^{\mathrm{new}}(1176, [\chi])\):

\( T_{5} + 1 \)

\( T_{11} + 1 \)

Hecke characteristic polynomials

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