Newform orbit 35.5.c.a

• Label: 35.5.c.a
• Level: $35$
• Weight: $5$
• Character orbit: 35.c
• Self dual: yes
• Analytic conductor: $3.618$
• Analytic rank: $0$
• Dimension: $1$
• CM discriminant: -35
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 35 = 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	35.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	yes
Analytic conductor:	\(3.61794870793\)
Analytic rank:	\(0\)
Dimension:	\(1\)
Coefficient field:	\(\mathbb{Q}\)
Coefficient ring:	\(\mathbb{Z}\)
Coefficient ring index:	\( 1 \)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{2}]$

$q$-expansion

\(f(q)\)

\(=\)

\( q - 17 q^{3} + 16 q^{4} + 25 q^{5} + 49 q^{7} + 208 q^{9}+O(q^{10}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/35\mathbb{Z}\right)^\times\).

\(n\)	\(22\)	\(31\)
\(\chi(n)\)	\(-1\)	\(-1\)

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  

\(\iota_m(\nu)\)

\( a_{2} \)

\( a_{3} \)

\( a_{4} \)

\( a_{5} \)

\( a_{6} \)

\( a_{7} \)

\( a_{8} \)

\( a_{9} \)

\( a_{10} \)

34.1

0

0

−17.0000

16.0000

25.0000

0

49.0000

0

208.000

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	35.5.c.a	✓	1
3.b	odd	2	1		315.5.e.a		1
4.b	odd	2	1		560.5.p.b		1
5.b	even	2	1		35.5.c.b	yes	1
5.c	odd	4	2		175.5.d.c		2
7.b	odd	2	1		35.5.c.b	yes	1
15.d	odd	2	1		315.5.e.b		1
20.d	odd	2	1		560.5.p.a		1
21.c	even	2	1		315.5.e.b		1
28.d	even	2	1		560.5.p.a		1
35.c	odd	2	1	CM	35.5.c.a	✓	1
35.f	even	4	2		175.5.d.c		2
105.g	even	2	1		315.5.e.a		1
140.c	even	2	1		560.5.p.b		1

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
35.5.c.a	✓	1	1.a	even	1	1	trivial
35.5.c.a	✓	1	35.c	odd	2	1	CM
35.5.c.b	yes	1	5.b	even	2	1
35.5.c.b	yes	1	7.b	odd	2	1
175.5.d.c		2	5.c	odd	4	2
175.5.d.c		2	35.f	even	4	2
315.5.e.a		1	3.b	odd	2	1
315.5.e.a		1	105.g	even	2	1
315.5.e.b		1	15.d	odd	2	1
315.5.e.b		1	21.c	even	2	1
560.5.p.a		1	20.d	odd	2	1
560.5.p.a		1	28.d	even	2	1
560.5.p.b		1	4.b	odd	2	1
560.5.p.b		1	140.c	even	2	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{5}^{\mathrm{new}}(35, [\chi])\):

\( T_{2} \)

\( T_{3} + 17 \)

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	\( T \)
$3$	\( T + 17 \)
$5$	\( T - 25 \)
$7$	\( T - 49 \)
$11$	\( T + 73 \)