Newform orbit 980.2.a.a

• Label: 980.2.a.a
• Level: $980$
• Weight: $2$
• Character orbit: 980.a
• Self dual: yes
• Analytic conductor: $7.825$
• Analytic rank: $0$
• Dimension: $1$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	\( N \)	\(=\)	\( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	980.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	\(7.82533939809\)
Analytic rank:	\(0\)
Dimension:	\(1\)
Coefficient field:	\(\mathbb{Q}\)
Coefficient ring:	\(\mathbb{Z}\)
Coefficient ring index:	\( 1 \)
Twist minimal:	no (minimal twist has level 140)
Fricke sign:	\(-1\)
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

\(f(q)\)

\(=\)

\( q - 3 q^{3} - q^{5} + 6 q^{9}+O(q^{10}) \)

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

0

−3.00000

0

−1.00000

0

0

0

6.00000

0

Atkin-Lehner signs

\( p \)	Sign
\(2\)	\( -1 \)
\(5\)	\( +1 \)
\(7\)	\( +1 \)

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	980.2.a.a		1
3.b	odd	2	1		8820.2.a.w		1
4.b	odd	2	1		3920.2.a.bi		1
5.b	even	2	1		4900.2.a.v		1
5.c	odd	4	2		4900.2.e.c		2
7.b	odd	2	1		980.2.a.i		1
7.c	even	3	2		140.2.i.b	✓	2
7.d	odd	6	2		980.2.i.a		2
21.c	even	2	1		8820.2.a.k		1
21.h	odd	6	2		1260.2.s.b		2
28.d	even	2	1		3920.2.a.d		1
28.g	odd	6	2		560.2.q.a		2
35.c	odd	2	1		4900.2.a.a		1
35.f	even	4	2		4900.2.e.b		2
35.j	even	6	2		700.2.i.a		2
35.l	odd	12	4		700.2.r.c		4

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
140.2.i.b	✓	2	7.c	even	3	2
560.2.q.a		2	28.g	odd	6	2
700.2.i.a		2	35.j	even	6	2
700.2.r.c		4	35.l	odd	12	4
980.2.a.a		1	1.a	even	1	1	trivial
980.2.a.i		1	7.b	odd	2	1
980.2.i.a		2	7.d	odd	6	2
1260.2.s.b		2	21.h	odd	6	2
3920.2.a.d		1	28.d	even	2	1
3920.2.a.bi		1	4.b	odd	2	1
4900.2.a.a		1	35.c	odd	2	1
4900.2.a.v		1	5.b	even	2	1
4900.2.e.b		2	35.f	even	4	2
4900.2.e.c		2	5.c	odd	4	2
8820.2.a.k		1	21.c	even	2	1
8820.2.a.w		1	3.b	odd	2	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(980))\):

\( T_{3} + 3 \)

\( T_{11} + 2 \)

Hecke characteristic polynomials

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