Newform orbit 2240.2.a.v

• Label: 2240.2.a.v
• Level: $2240$
• Weight: $2$
• Character orbit: 2240.a
• Self dual: yes
• Analytic conductor: $17.886$
• Analytic rank: $0$
• Dimension: $1$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	\( N \)	\(=\)	\( 2240 = 2^{6} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2240.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	\(17.8864900528\)
Analytic rank:	\(0\)
Dimension:	\(1\)
Coefficient field:	\(\mathbb{Q}\)
Coefficient ring:	\(\mathbb{Z}\)
Coefficient ring index:	\( 1 \)
Twist minimal:	no (minimal twist has level 280)
Fricke sign:	\(-1\)
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

\(f(q)\)

\(=\)

\( q + q^{3} + q^{5} - q^{7} - 2 q^{9}+O(q^{10}) \)

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

0

1.00000

0

1.00000

0

−1.00000

0

−2.00000

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	2240.2.a.v		1
4.b	odd	2	1		2240.2.a.j		1
8.b	even	2	1		280.2.a.b	✓	1
8.d	odd	2	1		560.2.a.e		1
24.f	even	2	1		5040.2.a.be		1
24.h	odd	2	1		2520.2.a.p		1
40.e	odd	2	1		2800.2.a.i		1
40.f	even	2	1		1400.2.a.k		1
40.i	odd	4	2		1400.2.g.e		2
40.k	even	4	2		2800.2.g.m		2
56.e	even	2	1		3920.2.a.r		1
56.h	odd	2	1		1960.2.a.k		1
56.j	odd	6	2		1960.2.q.e		2
56.p	even	6	2		1960.2.q.m		2
280.c	odd	2	1		9800.2.a.n		1

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
280.2.a.b	✓	1	8.b	even	2	1
560.2.a.e		1	8.d	odd	2	1
1400.2.a.k		1	40.f	even	2	1
1400.2.g.e		2	40.i	odd	4	2
1960.2.a.k		1	56.h	odd	2	1
1960.2.q.e		2	56.j	odd	6	2
1960.2.q.m		2	56.p	even	6	2
2240.2.a.j		1	4.b	odd	2	1
2240.2.a.v		1	1.a	even	1	1	trivial
2520.2.a.p		1	24.h	odd	2	1
2800.2.a.i		1	40.e	odd	2	1
2800.2.g.m		2	40.k	even	4	2
3920.2.a.r		1	56.e	even	2	1
5040.2.a.be		1	24.f	even	2	1
9800.2.a.n		1	280.c	odd	2	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(2240))\):

\( T_{3} - 1 \)

\( T_{11} - 5 \)

\( T_{13} + 1 \)

\( T_{19} - 6 \)

Hecke characteristic polynomials

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