Newform orbit 140.1.h.b

• Label: 140.1.h.b
• Level: $140$
• Weight: $1$
• Character orbit: 140.h
• Self dual: yes
• Analytic conductor: $0.070$
• Analytic rank: $0$
• Dimension: $1$
• Projective image: $D_{3}$
• CM discriminant: -35
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 140 = 2^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	140.h (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	yes
Analytic conductor:	\(0.0698691017686\)
Analytic rank:	\(0\)
Dimension:	\(1\)
Coefficient field:	\(\mathbb{Q}\)
Coefficient ring:	\(\mathbb{Z}\)
Coefficient ring index:	\( 1 \)
Twist minimal:	yes
Projective image:	\(D_{3}\)
Projective field:	Galois closure of 3.1.140.1
Artin image:	$D_6$
Artin field:	Galois closure of 6.2.98000.1

$q$-expansion

\(f(q)\)

\(=\)

\( q + q^{3} - q^{5} - q^{7} + O(q^{10}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/140\mathbb{Z}\right)^\times\).

\(n\)	\(57\)	\(71\)	\(101\)
\(\chi(n)\)	\(-1\)	\(1\)	\(-1\)

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

\(\iota_m(\nu)\)

\( a_{2} \)

\( a_{3} \)

\( a_{4} \)

\( a_{5} \)

\( a_{6} \)

\( a_{7} \)

\( a_{8} \)

\( a_{9} \)

\( a_{10} \)

69.1

0

0

1.00000

0

−1.00000

0

−1.00000

0

0

0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
35.c	odd	2	1	CM by \(\Q(\sqrt{-35}) \)

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	140.1.h.b	yes	1
3.b	odd	2	1		1260.1.p.b		1
4.b	odd	2	1		560.1.p.a		1
5.b	even	2	1		140.1.h.a	✓	1
5.c	odd	4	2		700.1.d.a		2
7.b	odd	2	1		140.1.h.a	✓	1
7.c	even	3	2		980.1.n.a		2
7.d	odd	6	2		980.1.n.b		2
8.b	even	2	1		2240.1.p.b		1
8.d	odd	2	1		2240.1.p.d		1
15.d	odd	2	1		1260.1.p.a		1
20.d	odd	2	1		560.1.p.b		1
20.e	even	4	2		2800.1.f.c		2
21.c	even	2	1		1260.1.p.a		1
28.d	even	2	1		560.1.p.b		1
28.f	even	6	2		3920.1.br.a		2
28.g	odd	6	2		3920.1.br.b		2
35.c	odd	2	1	CM	140.1.h.b	yes	1
35.f	even	4	2		700.1.d.a		2
35.i	odd	6	2		980.1.n.a		2
35.j	even	6	2		980.1.n.b		2
40.e	odd	2	1		2240.1.p.a		1
40.f	even	2	1		2240.1.p.c		1
56.e	even	2	1		2240.1.p.a		1
56.h	odd	2	1		2240.1.p.c		1
105.g	even	2	1		1260.1.p.b		1
140.c	even	2	1		560.1.p.a		1
140.j	odd	4	2		2800.1.f.c		2
140.p	odd	6	2		3920.1.br.a		2
140.s	even	6	2		3920.1.br.b		2
280.c	odd	2	1		2240.1.p.b		1
280.n	even	2	1		2240.1.p.d		1

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
140.1.h.a	✓	1	5.b	even	2	1
140.1.h.a	✓	1	7.b	odd	2	1
140.1.h.b	yes	1	1.a	even	1	1	trivial
140.1.h.b	yes	1	35.c	odd	2	1	CM
560.1.p.a		1	4.b	odd	2	1
560.1.p.a		1	140.c	even	2	1
560.1.p.b		1	20.d	odd	2	1
560.1.p.b		1	28.d	even	2	1
700.1.d.a		2	5.c	odd	4	2
700.1.d.a		2	35.f	even	4	2
980.1.n.a		2	7.c	even	3	2
980.1.n.a		2	35.i	odd	6	2
980.1.n.b		2	7.d	odd	6	2
980.1.n.b		2	35.j	even	6	2
1260.1.p.a		1	15.d	odd	2	1
1260.1.p.a		1	21.c	even	2	1
1260.1.p.b		1	3.b	odd	2	1
1260.1.p.b		1	105.g	even	2	1
2240.1.p.a		1	40.e	odd	2	1
2240.1.p.a		1	56.e	even	2	1
2240.1.p.b		1	8.b	even	2	1
2240.1.p.b		1	280.c	odd	2	1
2240.1.p.c		1	40.f	even	2	1
2240.1.p.c		1	56.h	odd	2	1
2240.1.p.d		1	8.d	odd	2	1
2240.1.p.d		1	280.n	even	2	1
2800.1.f.c		2	20.e	even	4	2
2800.1.f.c		2	140.j	odd	4	2
3920.1.br.a		2	28.f	even	6	2
3920.1.br.a		2	140.p	odd	6	2
3920.1.br.b		2	28.g	odd	6	2
3920.1.br.b		2	140.s	even	6	2

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3} - 1 \) acting on \(S_{1}^{\mathrm{new}}(140, [\chi])\).

Hecke characteristic polynomials

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