Newform orbit 175.6.a.b

• Label: 175.6.a.b
• Level: $175$
• Weight: $6$
• Character orbit: 175.a
• Self dual: yes
• Analytic conductor: $28.067$
• Analytic rank: $0$
• Dimension: $1$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	175.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	\(28.0671684673\)
Analytic rank:	\(0\)
Dimension:	\(1\)
Coefficient field:	\(\mathbb{Q}\)
Coefficient ring:	\(\mathbb{Z}\)
Coefficient ring index:	\( 1 \)
Twist minimal:	no (minimal twist has level 7)
Fricke sign:	\(-1\)
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

\(f(q)\)

\(=\)

\( q + 10 q^{2} + 14 q^{3} + 68 q^{4} + 140 q^{6} + 49 q^{7} + 360 q^{8} - 47 q^{9}+O(q^{10}) \)

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

\(\iota_m(\nu)\)

\( a_{2} \)

\( a_{3} \)

\( a_{4} \)

\( a_{5} \)

\( a_{6} \)

\( a_{7} \)

\( a_{8} \)

\( a_{9} \)

\( a_{10} \)

1.1

0

10.0000

14.0000

68.0000

0

140.000

49.0000

360.000

−47.0000

0

Atkin-Lehner signs

\( p \)	Sign
\(5\)	\(1\)
\(7\)	\(-1\)

Inner twists

This newform does not admit any (nontrivial) inner twists.

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	175.6.a.b		1
5.b	even	2	1		7.6.a.a	✓	1
5.c	odd	4	2		175.6.b.a		2
15.d	odd	2	1		63.6.a.e		1
20.d	odd	2	1		112.6.a.g		1
35.c	odd	2	1		49.6.a.a		1
35.i	odd	6	2		49.6.c.b		2
35.j	even	6	2		49.6.c.c		2
40.e	odd	2	1		448.6.a.c		1
40.f	even	2	1		448.6.a.m		1
55.d	odd	2	1		847.6.a.b		1
60.h	even	2	1		1008.6.a.y		1
105.g	even	2	1		441.6.a.k		1
140.c	even	2	1		784.6.a.c		1

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
7.6.a.a	✓	1	5.b	even	2	1
49.6.a.a		1	35.c	odd	2	1
49.6.c.b		2	35.i	odd	6	2
49.6.c.c		2	35.j	even	6	2
63.6.a.e		1	15.d	odd	2	1
112.6.a.g		1	20.d	odd	2	1
175.6.a.b		1	1.a	even	1	1	trivial
175.6.b.a		2	5.c	odd	4	2
441.6.a.k		1	105.g	even	2	1
448.6.a.c		1	40.e	odd	2	1
448.6.a.m		1	40.f	even	2	1
784.6.a.c		1	140.c	even	2	1
847.6.a.b		1	55.d	odd	2	1
1008.6.a.y		1	60.h	even	2	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2} - 10 \) acting on \(S_{6}^{\mathrm{new}}(\Gamma_0(175))\).

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	\( T - 10 \)
$3$	\( T - 14 \)
$5$	\( T \)
$7$	\( T - 49 \)
$11$	\( T - 232 \)