Newform orbit 6498.2.a.e

• Label: 6498.2.a.e
• Level: $6498$
• Weight: $2$
• Character orbit: 6498.a
• Self dual: yes
• Analytic conductor: $51.887$
• Analytic rank: $1$
• Dimension: $1$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	\( N \)	\(=\)	\( 6498 = 2 \cdot 3^{2} \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6498.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	\(51.8867912334\)
Analytic rank:	\(1\)
Dimension:	\(1\)
Coefficient field:	\(\mathbb{Q}\)
Coefficient ring:	\(\mathbb{Z}\)
Coefficient ring index:	\( 1 \)
Twist minimal:	no (minimal twist has level 38)
Fricke sign:	\(+1\)
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

\(f(q)\)

\(=\)

\( q - q^{2} + q^{4} - 4 q^{7} - q^{8}+O(q^{10}) \)

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

−1.00000

0

1.00000

0

0

−4.00000

−1.00000

0

0

Atkin-Lehner signs

\( p \)	Sign
\(2\)	\( +1 \)
\(3\)	\( -1 \)
\(19\)	\( -1 \)

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	6498.2.a.e		1
3.b	odd	2	1		722.2.a.d		1
12.b	even	2	1		5776.2.a.n		1
19.b	odd	2	1		6498.2.a.s		1
19.d	odd	6	2		342.2.g.b		2
57.d	even	2	1		722.2.a.c		1
57.f	even	6	2		38.2.c.a	✓	2
57.h	odd	6	2		722.2.c.b		2
57.j	even	18	6		722.2.e.j		6
57.l	odd	18	6		722.2.e.i		6
76.f	even	6	2		2736.2.s.m		2
228.b	odd	2	1		5776.2.a.g		1
228.n	odd	6	2		304.2.i.c		2
285.q	even	6	2		950.2.e.d		2
285.w	odd	12	4		950.2.j.e		4
456.s	odd	6	2		1216.2.i.d		2
456.v	even	6	2		1216.2.i.h		2

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
38.2.c.a	✓	2	57.f	even	6	2
304.2.i.c		2	228.n	odd	6	2
342.2.g.b		2	19.d	odd	6	2
722.2.a.c		1	57.d	even	2	1
722.2.a.d		1	3.b	odd	2	1
722.2.c.b		2	57.h	odd	6	2
722.2.e.i		6	57.l	odd	18	6
722.2.e.j		6	57.j	even	18	6
950.2.e.d		2	285.q	even	6	2
950.2.j.e		4	285.w	odd	12	4
1216.2.i.d		2	456.s	odd	6	2
1216.2.i.h		2	456.v	even	6	2
2736.2.s.m		2	76.f	even	6	2
5776.2.a.g		1	228.b	odd	2	1
5776.2.a.n		1	12.b	even	2	1
6498.2.a.e		1	1.a	even	1	1	trivial
6498.2.a.s		1	19.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 \(S_{2}^{\mathrm{new}}(\Gamma_0(6498))\):

\( T_{5} \)

\( T_{7} + 4 \)

\( T_{11} + 3 \)

\( T_{13} + 2 \)

\( T_{29} \)

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	\( T + 1 \)
$3$	\( T \)
$5$	\( T \)
$7$	\( T + 4 \)
$11$	\( T + 3 \)