Newform orbit 864.1.h.b

• Label: 864.1.h.b
• Level: $864$
• Weight: $1$
• Character orbit: 864.h
• Self dual: yes
• Analytic conductor: $0.431$
• Analytic rank: $0$
• Dimension: $1$
• Projective image: $D_{3}$
• CM discriminant: -24
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	864.h (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual:	yes
Analytic conductor:	\(0.431192170915\)
Analytic rank:	\(0\)
Dimension:	\(1\)
Coefficient field:	\(\mathbb{Q}\)
Coefficient ring:	\(\mathbb{Z}\)
Coefficient ring index:	\( 1 \)
Twist minimal:	no (minimal twist has level 216)
Projective image:	\(D_{3}\)
Projective field:	Galois closure of 3.1.216.1
Artin image:	$D_6$
Artin field:	Galois closure of 6.0.1492992.6

$q$-expansion

\(f(q)\)

\(=\)

\( q + q^{5} + q^{7}+O(q^{10}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/864\mathbb{Z}\right)^\times\).

\(n\)	\(325\)	\(353\)	\(703\)
\(\chi(n)\)	\(-1\)	\(-1\)	\(1\)

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  

\(\iota_m(\nu)\)

\( a_{2} \)

\( a_{3} \)

\( a_{4} \)

\( a_{5} \)

\( a_{6} \)

\( a_{7} \)

\( a_{8} \)

\( a_{9} \)

\( a_{10} \)

593.1

0

0

0

0

1.00000

0

1.00000

0

0

0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
24.h	odd	2	1	CM by \(\Q(\sqrt{-6}) \)

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	864.1.h.b		1
3.b	odd	2	1		864.1.h.a		1
4.b	odd	2	1		216.1.h.a	✓	1
8.b	even	2	1		864.1.h.a		1
8.d	odd	2	1		216.1.h.b	yes	1
9.c	even	3	2		2592.1.n.a		2
9.d	odd	6	2		2592.1.n.b		2
12.b	even	2	1		216.1.h.b	yes	1
24.f	even	2	1		216.1.h.a	✓	1
24.h	odd	2	1	CM	864.1.h.b		1
36.f	odd	6	2		648.1.j.b		2
36.h	even	6	2		648.1.j.a		2
72.j	odd	6	2		2592.1.n.a		2
72.l	even	6	2		648.1.j.b		2
72.n	even	6	2		2592.1.n.b		2
72.p	odd	6	2		648.1.j.a		2

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
216.1.h.a	✓	1	4.b	odd	2	1
216.1.h.a	✓	1	24.f	even	2	1
216.1.h.b	yes	1	8.d	odd	2	1
216.1.h.b	yes	1	12.b	even	2	1
648.1.j.a		2	36.h	even	6	2
648.1.j.a		2	72.p	odd	6	2
648.1.j.b		2	36.f	odd	6	2
648.1.j.b		2	72.l	even	6	2
864.1.h.a		1	3.b	odd	2	1
864.1.h.a		1	8.b	even	2	1
864.1.h.b		1	1.a	even	1	1	trivial
864.1.h.b		1	24.h	odd	2	1	CM
2592.1.n.a		2	9.c	even	3	2
2592.1.n.a		2	72.j	odd	6	2
2592.1.n.b		2	9.d	odd	6	2
2592.1.n.b		2	72.n	even	6	2

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{5} - 1 \) acting on \(S_{1}^{\mathrm{new}}(864, [\chi])\).

Hecke characteristic polynomials

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