Newform orbit 2592.1.n.b

• Label: 2592.1.n.b
• Level: $2592$
• Weight: $1$
• Character orbit: 2592.n
• Analytic conductor: $1.294$
• Analytic rank: $0$
• Dimension: $2$
• Projective image: $D_{3}$
• CM discriminant: -24
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 2592 = 2^{5} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2592.n (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(1.29357651274\)
Analytic rank:	\(0\)
Dimension:	\(2\)
Coefficient field:	\(\Q(\zeta_{6})\)
Defining polynomial:	\( x^{2} - x + 1 \)
Coefficient ring:	\(\Z[a_1, \ldots, a_{5}]\)
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:	$C_6\times S_3$
Artin field:	Galois closure of 12.0.6499837226778624.40

$q$-expansion

The \(q\)-expansion and trace form are shown below.

\(f(q)\)	\(=\)	\( q - \zeta_{6}^{2} q^{5} - \zeta_{6} q^{7} +O(q^{10}) \)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{5} - q^{7}+O(q^{10}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2592\mathbb{Z}\right)^\times\).

\(n\)	\(325\)	\(1217\)	\(2431\)
\(\chi(n)\)	\(-1\)	\(-\zeta_{6}^{2}\)	\(1\)

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

0.500000	−	0.866025i
0.500000	+	0.866025i

0

0

0

0.500000

+

0.866025i

0

−0.500000

+

0.866025i

0

0

0

2321.1

0

0

0

0.500000

−

0.866025i

0

−0.500000

−

0.866025i

0

0

0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
24.h	odd	2	1	CM by \(\Q(\sqrt{-6}) \)
9.c	even	3	1	inner
72.j	odd	6	1	inner

Twists

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

    

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

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{5}^{2} - T_{5} + 1 \) acting on \(S_{1}^{\mathrm{new}}(2592, [\chi])\).

Hecke characteristic polynomials

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