Newform orbit 64.9.c.a

• Label: 64.9.c.a
• Level: $64$
• Weight: $9$
• Character orbit: 64.c
• Self dual: yes
• Analytic conductor: $26.072$
• Analytic rank: $0$
• Dimension: $1$
• CM discriminant: -4
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 64 = 2^{6} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	64.c (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual:	yes
Analytic conductor:	\(26.0722310439\)
Analytic rank:	\(0\)
Dimension:	\(1\)
Coefficient field:	\(\mathbb{Q}\)
Coefficient ring:	\(\mathbb{Z}\)
Coefficient ring index:	\( 1 \)
Twist minimal:	no (minimal twist has level 4)
Sato-Tate group:	$\mathrm{U}(1)[D_{2}]$

$q$-expansion

\(f(q)\)

\(=\)

\( q + 1054 q^{5} + 6561 q^{9}+O(q^{10}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/64\mathbb{Z}\right)^\times\).

\(n\)	\(5\)	\(63\)
\(\chi(n)\)	\(1\)	\(-1\)

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  

\(\iota_m(\nu)\)

\( a_{2} \)

\( a_{3} \)

\( a_{4} \)

\( a_{5} \)

\( a_{6} \)

\( a_{7} \)

\( a_{8} \)

\( a_{9} \)

\( a_{10} \)

63.1

0

0

0

0

1054.00

0

0

0

6561.00

0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
4.b	odd	2	1	CM by \(\Q(\sqrt{-1}) \)

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	64.9.c.a		1
4.b	odd	2	1	CM	64.9.c.a		1
8.b	even	2	1		4.9.b.a	✓	1
8.d	odd	2	1		4.9.b.a	✓	1
16.e	even	4	2		256.9.d.a		2
16.f	odd	4	2		256.9.d.a		2
24.f	even	2	1		36.9.d.a		1
24.h	odd	2	1		36.9.d.a		1
40.e	odd	2	1		100.9.b.a		1
40.f	even	2	1		100.9.b.a		1
40.i	odd	4	2		100.9.d.a		2
40.k	even	4	2		100.9.d.a		2

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
4.9.b.a	✓	1	8.b	even	2	1
4.9.b.a	✓	1	8.d	odd	2	1
36.9.d.a		1	24.f	even	2	1
36.9.d.a		1	24.h	odd	2	1
64.9.c.a		1	1.a	even	1	1	trivial
64.9.c.a		1	4.b	odd	2	1	CM
100.9.b.a		1	40.e	odd	2	1
100.9.b.a		1	40.f	even	2	1
100.9.d.a		2	40.i	odd	4	2
100.9.d.a		2	40.k	even	4	2
256.9.d.a		2	16.e	even	4	2
256.9.d.a		2	16.f	odd	4	2

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3} \) acting on \(S_{9}^{\mathrm{new}}(64, [\chi])\).

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	\( T \)
$3$	\( T \)
$5$	\( T - 1054 \)
$7$	\( T \)
$11$	\( T \)