Newform orbit 931.1.b.b

• Label: 931.1.b.b
• Level: $931$
• Weight: $1$
• Character orbit: 931.b
• Self dual: yes
• Analytic conductor: $0.465$
• Analytic rank: $0$
• Dimension: $1$
• Projective image: $D_{3}$
• CM discriminant: -19
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 931 = 7^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	931.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	yes
Analytic conductor:	\(0.464629526761\)
Analytic rank:	\(0\)
Dimension:	\(1\)
Coefficient field:	\(\mathbb{Q}\)
Coefficient ring:	\(\mathbb{Z}\)
Coefficient ring index:	\( 1 \)
Twist minimal:	no (minimal twist has level 133)
Projective image:	\(D_{3}\)
Projective field:	Galois closure of 3.1.931.1
Artin image:	$D_6$
Artin field:	Galois closure of 6.0.6067327.1

$q$-expansion

\(f(q)\)

\(=\)

\( q + q^{4} + q^{5} + q^{9}+O(q^{10}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/931\mathbb{Z}\right)^\times\).

\(n\)	\(248\)	\(344\)
\(\chi(n)\)	\(1\)	\(-1\)

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  

\(\iota_m(\nu)\)

\( a_{2} \)

\( a_{3} \)

\( a_{4} \)

\( a_{5} \)

\( a_{6} \)

\( a_{7} \)

\( a_{8} \)

\( a_{9} \)

\( a_{10} \)

246.1

0

0

0

1.00000

1.00000

0

0

0

1.00000

0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
19.b	odd	2	1	CM by \(\Q(\sqrt{-19}) \)

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	931.1.b.b		1
7.b	odd	2	1		931.1.b.a		1
7.c	even	3	2		931.1.r.a		2
7.d	odd	6	2		133.1.r.a	✓	2
19.b	odd	2	1	CM	931.1.b.b		1
21.g	even	6	2		1197.1.cz.a		2
28.f	even	6	2		2128.1.cl.c		2
35.i	odd	6	2		3325.1.bm.a		2
35.k	even	12	4		3325.1.y.a		4
133.c	even	2	1		931.1.b.a		1
133.i	even	6	2		2527.1.j.a		2
133.k	odd	6	2		2527.1.n.a		2
133.o	even	6	2		133.1.r.a	✓	2
133.r	odd	6	2		931.1.r.a		2
133.s	even	6	2		2527.1.n.a		2
133.t	odd	6	2		2527.1.j.a		2
133.x	odd	18	6		2527.1.bd.a		6
133.z	odd	18	6		2527.1.be.a		6
133.bb	even	18	6		2527.1.bd.a		6
133.bf	even	18	6		2527.1.be.a		6
399.s	odd	6	2		1197.1.cz.a		2
532.bh	odd	6	2		2128.1.cl.c		2
665.y	even	6	2		3325.1.bm.a		2
665.ca	odd	12	4		3325.1.y.a		4

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
133.1.r.a	✓	2	7.d	odd	6	2
133.1.r.a	✓	2	133.o	even	6	2
931.1.b.a		1	7.b	odd	2	1
931.1.b.a		1	133.c	even	2	1
931.1.b.b		1	1.a	even	1	1	trivial
931.1.b.b		1	19.b	odd	2	1	CM
931.1.r.a		2	7.c	even	3	2
931.1.r.a		2	133.r	odd	6	2
1197.1.cz.a		2	21.g	even	6	2
1197.1.cz.a		2	399.s	odd	6	2
2128.1.cl.c		2	28.f	even	6	2
2128.1.cl.c		2	532.bh	odd	6	2
2527.1.j.a		2	133.i	even	6	2
2527.1.j.a		2	133.t	odd	6	2
2527.1.n.a		2	133.k	odd	6	2
2527.1.n.a		2	133.s	even	6	2
2527.1.bd.a		6	133.x	odd	18	6
2527.1.bd.a		6	133.bb	even	18	6
2527.1.be.a		6	133.z	odd	18	6
2527.1.be.a		6	133.bf	even	18	6
3325.1.y.a		4	35.k	even	12	4
3325.1.y.a		4	665.ca	odd	12	4
3325.1.bm.a		2	35.i	odd	6	2
3325.1.bm.a		2	665.y	even	6	2

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{5} - 1 \) acting on \(S_{1}^{\mathrm{new}}(931, [\chi])\).

Hecke characteristic polynomials

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