Newform orbit 560.3.p.b

• Label: 560.3.p.b
• Level: $560$
• Weight: $3$
• Character orbit: 560.p
• Self dual: yes
• Analytic conductor: $15.259$
• Analytic rank: $0$
• Dimension: $1$
• CM discriminant: -35
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	560.p (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual:	yes
Analytic conductor:	\(15.2588948042\)
Analytic rank:	\(0\)
Dimension:	\(1\)
Coefficient field:	\(\mathbb{Q}\)
Coefficient ring:	\(\mathbb{Z}\)
Coefficient ring index:	\( 1 \)
Twist minimal:	no (minimal twist has level 35)
Sato-Tate group:	$\mathrm{U}(1)[D_{2}]$

$q$-expansion

\(f(q)\)

\(=\)

\( q + q^{3} + 5 q^{5} + 7 q^{7} - 8 q^{9}+O(q^{10}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/560\mathbb{Z}\right)^\times\).

\(n\)	\(241\)	\(337\)	\(351\)	\(421\)
\(\chi(n)\)	\(-1\)	\(-1\)	\(1\)	\(1\)

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  

\(\iota_m(\nu)\)

\( a_{2} \)

\( a_{3} \)

\( a_{4} \)

\( a_{5} \)

\( a_{6} \)

\( a_{7} \)

\( a_{8} \)

\( a_{9} \)

\( a_{10} \)

209.1

0

0

1.00000

0

5.00000

0

7.00000

0

−8.00000

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	560.3.p.b		1
4.b	odd	2	1		35.3.c.a	✓	1
5.b	even	2	1		560.3.p.a		1
7.b	odd	2	1		560.3.p.a		1
12.b	even	2	1		315.3.e.a		1
20.d	odd	2	1		35.3.c.b	yes	1
20.e	even	4	2		175.3.d.e		2
28.d	even	2	1		35.3.c.b	yes	1
28.f	even	6	2		245.3.i.a		2
28.g	odd	6	2		245.3.i.b		2
35.c	odd	2	1	CM	560.3.p.b		1
60.h	even	2	1		315.3.e.b		1
84.h	odd	2	1		315.3.e.b		1
140.c	even	2	1		35.3.c.a	✓	1
140.j	odd	4	2		175.3.d.e		2
140.p	odd	6	2		245.3.i.a		2
140.s	even	6	2		245.3.i.b		2
420.o	odd	2	1		315.3.e.a		1

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
35.3.c.a	✓	1	4.b	odd	2	1
35.3.c.a	✓	1	140.c	even	2	1
35.3.c.b	yes	1	20.d	odd	2	1
35.3.c.b	yes	1	28.d	even	2	1
175.3.d.e		2	20.e	even	4	2
175.3.d.e		2	140.j	odd	4	2
245.3.i.a		2	28.f	even	6	2
245.3.i.a		2	140.p	odd	6	2
245.3.i.b		2	28.g	odd	6	2
245.3.i.b		2	140.s	even	6	2
315.3.e.a		1	12.b	even	2	1
315.3.e.a		1	420.o	odd	2	1
315.3.e.b		1	60.h	even	2	1
315.3.e.b		1	84.h	odd	2	1
560.3.p.a		1	5.b	even	2	1
560.3.p.a		1	7.b	odd	2	1
560.3.p.b		1	1.a	even	1	1	trivial
560.3.p.b		1	35.c	odd	2	1	CM

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3} - 1 \) acting on \(S_{3}^{\mathrm{new}}(560, [\chi])\).

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	\( T \)
$3$	\( T - 1 \)
$5$	\( T - 5 \)
$7$	\( T - 7 \)
$11$	\( T - 13 \)