Newform orbit 1400.2.a.a

• Label: 1400.2.a.a
• Level: $1400$
• Weight: $2$
• Character orbit: 1400.a
• Self dual: yes
• Analytic conductor: $11.179$
• Analytic rank: $0$
• Dimension: $1$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1400 = 2^{3} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1400.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	\(11.1790562830\)
Analytic rank:	\(0\)
Dimension:	\(1\)
Coefficient field:	\(\mathbb{Q}\)
Coefficient ring:	\(\mathbb{Z}\)
Coefficient ring index:	\( 1 \)
Twist minimal:	no (minimal twist has level 56)
Fricke sign:	\(-1\)
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

\(f(q)\)

\(=\)

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

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

−2.00000

0

0

0

−1.00000

0

1.00000

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	1400.2.a.a		1
4.b	odd	2	1		2800.2.a.bd		1
5.b	even	2	1		56.2.a.b	✓	1
5.c	odd	4	2		1400.2.g.b		2
7.b	odd	2	1		9800.2.a.bj		1
15.d	odd	2	1		504.2.a.h		1
20.d	odd	2	1		112.2.a.a		1
20.e	even	4	2		2800.2.g.g		2
35.c	odd	2	1		392.2.a.b		1
35.i	odd	6	2		392.2.i.e		2
35.j	even	6	2		392.2.i.a		2
40.e	odd	2	1		448.2.a.h		1
40.f	even	2	1		448.2.a.c		1
55.d	odd	2	1		6776.2.a.h		1
60.h	even	2	1		1008.2.a.m		1
65.d	even	2	1		9464.2.a.h		1
80.k	odd	4	2		1792.2.b.h		2
80.q	even	4	2		1792.2.b.a		2
105.g	even	2	1		3528.2.a.b		1
105.o	odd	6	2		3528.2.s.a		2
105.p	even	6	2		3528.2.s.ba		2
120.i	odd	2	1		4032.2.a.d		1
120.m	even	2	1		4032.2.a.a		1
140.c	even	2	1		784.2.a.i		1
140.p	odd	6	2		784.2.i.j		2
140.s	even	6	2		784.2.i.b		2
280.c	odd	2	1		3136.2.a.w		1
280.n	even	2	1		3136.2.a.c		1
420.o	odd	2	1		7056.2.a.c		1

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
56.2.a.b	✓	1	5.b	even	2	1
112.2.a.a		1	20.d	odd	2	1
392.2.a.b		1	35.c	odd	2	1
392.2.i.a		2	35.j	even	6	2
392.2.i.e		2	35.i	odd	6	2
448.2.a.c		1	40.f	even	2	1
448.2.a.h		1	40.e	odd	2	1
504.2.a.h		1	15.d	odd	2	1
784.2.a.i		1	140.c	even	2	1
784.2.i.b		2	140.s	even	6	2
784.2.i.j		2	140.p	odd	6	2
1008.2.a.m		1	60.h	even	2	1
1400.2.a.a		1	1.a	even	1	1	trivial
1400.2.g.b		2	5.c	odd	4	2
1792.2.b.a		2	80.q	even	4	2
1792.2.b.h		2	80.k	odd	4	2
2800.2.a.bd		1	4.b	odd	2	1
2800.2.g.g		2	20.e	even	4	2
3136.2.a.c		1	280.n	even	2	1
3136.2.a.w		1	280.c	odd	2	1
3528.2.a.b		1	105.g	even	2	1
3528.2.s.a		2	105.o	odd	6	2
3528.2.s.ba		2	105.p	even	6	2
4032.2.a.a		1	120.m	even	2	1
4032.2.a.d		1	120.i	odd	2	1
6776.2.a.h		1	55.d	odd	2	1
7056.2.a.c		1	420.o	odd	2	1
9464.2.a.h		1	65.d	even	2	1
9800.2.a.bj		1	7.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 \(S_{2}^{\mathrm{new}}(\Gamma_0(1400))\):

\( T_{3} + 2 \)

\( T_{11} \)

\( T_{13} \)

Hecke characteristic polynomials

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