Newform orbit 175.2.a.a

• Label: 175.2.a.a
• Level: $175$
• Weight: $2$
• Character orbit: 175.a
• Self dual: yes
• Analytic conductor: $1.397$
• Analytic rank: $1$
• Dimension: $1$
• CM: no
• Inner twists: $1$

Newspace parameters

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

Newform invariants

Self dual:	yes
Analytic conductor:	\(1.39738203537\)
Analytic rank:	\(1\)
Dimension:	\(1\)
Coefficient field:	\(\mathbb{Q}\)
Coefficient ring:	\(\mathbb{Z}\)
Coefficient ring index:	\( 1 \)
Twist minimal:	no (minimal twist has level 35)
Fricke sign:	\(1\)
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

\(f(q)\)

\(=\)

\( q - 2 q^{2} - q^{3} + 2 q^{4} + 2 q^{6} + q^{7} - 2 q^{9}+O(q^{10}) \)

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

−2.00000

−1.00000

2.00000

0

2.00000

1.00000

0

−2.00000

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	175.2.a.a		1
3.b	odd	2	1		1575.2.a.k		1
4.b	odd	2	1		2800.2.a.w		1
5.b	even	2	1		175.2.a.c		1
5.c	odd	4	2		35.2.b.a	✓	2
7.b	odd	2	1		1225.2.a.a		1
15.d	odd	2	1		1575.2.a.a		1
15.e	even	4	2		315.2.d.a		2
20.d	odd	2	1		2800.2.a.l		1
20.e	even	4	2		560.2.g.b		2
35.c	odd	2	1		1225.2.a.i		1
35.f	even	4	2		245.2.b.a		2
35.k	even	12	4		245.2.j.d		4
35.l	odd	12	4		245.2.j.e		4
40.i	odd	4	2		2240.2.g.h		2
40.k	even	4	2		2240.2.g.g		2
60.l	odd	4	2		5040.2.t.p		2
105.k	odd	4	2		2205.2.d.b		2

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
35.2.b.a	✓	2	5.c	odd	4	2
175.2.a.a		1	1.a	even	1	1	trivial
175.2.a.c		1	5.b	even	2	1
245.2.b.a		2	35.f	even	4	2
245.2.j.d		4	35.k	even	12	4
245.2.j.e		4	35.l	odd	12	4
315.2.d.a		2	15.e	even	4	2
560.2.g.b		2	20.e	even	4	2
1225.2.a.a		1	7.b	odd	2	1
1225.2.a.i		1	35.c	odd	2	1
1575.2.a.a		1	15.d	odd	2	1
1575.2.a.k		1	3.b	odd	2	1
2205.2.d.b		2	105.k	odd	4	2
2240.2.g.g		2	40.k	even	4	2
2240.2.g.h		2	40.i	odd	4	2
2800.2.a.l		1	20.d	odd	2	1
2800.2.a.w		1	4.b	odd	2	1
5040.2.t.p		2	60.l	odd	4	2

Hecke kernels

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

Hecke characteristic polynomials

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