Newform orbit 64.10.a.a

• Label: 64.10.a.a
• Level: $64$
• Weight: $10$
• Character orbit: 64.a
• Self dual: yes
• Analytic conductor: $32.962$
• Analytic rank: $1$
• Dimension: $1$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	\( N \)	\(=\)	\( 64 = 2^{6} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	64.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	\(32.9622935145\)
Analytic rank:	\(1\)
Dimension:	\(1\)
Coefficient field:	\(\mathbb{Q}\)
Coefficient ring:	\(\mathbb{Z}\)
Coefficient ring index:	\( 1 \)
Twist minimal:	no (minimal twist has level 4)
Fricke sign:	\(1\)
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

\(f(q)\)

\(=\)

\( q - 228 q^{3} + 666 q^{5} - 6328 q^{7} + 32301 q^{9}+O(q^{10}) \)

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

−228.000

0

666.000

0

−6328.00

0

32301.0

0

Atkin-Lehner signs

\( p \)	Sign
\(2\)	\(1\)

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	64.10.a.a		1
4.b	odd	2	1		64.10.a.i		1
8.b	even	2	1		4.10.a.a	✓	1
8.d	odd	2	1		16.10.a.a		1
16.e	even	4	2		256.10.b.j		2
16.f	odd	4	2		256.10.b.b		2
24.f	even	2	1		144.10.a.j		1
24.h	odd	2	1		36.10.a.b		1
40.e	odd	2	1		400.10.a.k		1
40.f	even	2	1		100.10.a.a		1
40.i	odd	4	2		100.10.c.a		2
40.k	even	4	2		400.10.c.a		2
56.h	odd	2	1		196.10.a.a		1
56.j	odd	6	2		196.10.e.b		2
56.p	even	6	2		196.10.e.a		2
72.j	odd	6	2		324.10.e.b		2
72.n	even	6	2		324.10.e.e		2

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
4.10.a.a	✓	1	8.b	even	2	1
16.10.a.a		1	8.d	odd	2	1
36.10.a.b		1	24.h	odd	2	1
64.10.a.a		1	1.a	even	1	1	trivial
64.10.a.i		1	4.b	odd	2	1
100.10.a.a		1	40.f	even	2	1
100.10.c.a		2	40.i	odd	4	2
144.10.a.j		1	24.f	even	2	1
196.10.a.a		1	56.h	odd	2	1
196.10.e.a		2	56.p	even	6	2
196.10.e.b		2	56.j	odd	6	2
256.10.b.b		2	16.f	odd	4	2
256.10.b.j		2	16.e	even	4	2
324.10.e.b		2	72.j	odd	6	2
324.10.e.e		2	72.n	even	6	2
400.10.a.k		1	40.e	odd	2	1
400.10.c.a		2	40.k	even	4	2

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3} + 228 \) acting on \(S_{10}^{\mathrm{new}}(\Gamma_0(64))\).

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	\( T \)
$3$	\( T + 228 \)
$5$	\( T - 666 \)
$7$	\( T + 6328 \)
$11$	\( T - 30420 \)