Newform orbit 6300.2.a.t

• Label: 6300.2.a.t
• Level: $6300$
• Weight: $2$
• Character orbit: 6300.a
• Self dual: yes
• Analytic conductor: $50.306$
• Analytic rank: $1$
• Dimension: $1$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	\( N \)	\(=\)	\( 6300 = 2^{2} \cdot 3^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6300.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	\(50.3057532734\)
Analytic rank:	\(1\)
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

\(f(q)\)

\(=\)

\( q + q^{7}+O(q^{10}) \)

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

0

0

0

0

1.00000

0

0

0

Atkin-Lehner signs

\( p \)	Sign
\(2\)	\( -1 \)
\(3\)	\( -1 \)
\(5\)	\( -1 \)
\(7\)	\( -1 \)

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	6300.2.a.t		1
3.b	odd	2	1		700.2.a.j		1
5.b	even	2	1		6300.2.a.c		1
5.c	odd	4	2		1260.2.k.c		2
12.b	even	2	1		2800.2.a.a		1
15.d	odd	2	1		700.2.a.a		1
15.e	even	4	2		140.2.e.a	✓	2
20.e	even	4	2		5040.2.t.s		2
21.c	even	2	1		4900.2.a.b		1
60.h	even	2	1		2800.2.a.bf		1
60.l	odd	4	2		560.2.g.a		2
105.g	even	2	1		4900.2.a.w		1
105.k	odd	4	2		980.2.e.b		2
105.w	odd	12	4		980.2.q.c		4
105.x	even	12	4		980.2.q.f		4
120.q	odd	4	2		2240.2.g.f		2
120.w	even	4	2		2240.2.g.e		2

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
140.2.e.a	✓	2	15.e	even	4	2
560.2.g.a		2	60.l	odd	4	2
700.2.a.a		1	15.d	odd	2	1
700.2.a.j		1	3.b	odd	2	1
980.2.e.b		2	105.k	odd	4	2
980.2.q.c		4	105.w	odd	12	4
980.2.q.f		4	105.x	even	12	4
1260.2.k.c		2	5.c	odd	4	2
2240.2.g.e		2	120.w	even	4	2
2240.2.g.f		2	120.q	odd	4	2
2800.2.a.a		1	12.b	even	2	1
2800.2.a.bf		1	60.h	even	2	1
4900.2.a.b		1	21.c	even	2	1
4900.2.a.w		1	105.g	even	2	1
5040.2.t.s		2	20.e	even	4	2
6300.2.a.c		1	5.b	even	2	1
6300.2.a.t		1	1.a	even	1	1	trivial

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(6300))\):

\( T_{11} + 3 \)

\( T_{13} - 1 \)

\( T_{17} - 5 \)

\( T_{37} - 10 \)

Hecke characteristic polynomials

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