Newform orbit 2592.1.b.a

• Label: 2592.1.b.a
• Level: $2592$
• Weight: $1$
• Character orbit: 2592.b
• Self dual: yes
• Analytic conductor: $1.294$
• Analytic rank: $0$
• Dimension: $1$
• Projective image: $D_{3}$
• CM discriminant: -8
• Inner twists: $2$

Newspace parameters

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

Newform invariants

Self dual:	yes
Analytic conductor:	\(1.29357651274\)
Analytic rank:	\(0\)
Dimension:	\(1\)
Coefficient field:	\(\mathbb{Q}\)
Coefficient ring:	\(\mathbb{Z}\)
Coefficient ring index:	\( 1 \)
Twist minimal:	no (minimal twist has level 72)
Projective image:	\(D_{3}\)
Projective field:	Galois closure of 3.1.648.1
Artin image:	$D_6$
Artin field:	Galois closure of 6.2.20155392.5
Stark unit:	Root of $x^{6} - 6054x^{5} + 761955x^{4} - 35139116x^{3} + 761955x^{2} - 6054x + 1$

$q$-expansion

\(f(q)\)

\(=\)

\( q - q^{11} + q^{17} + q^{19} + q^{25} + q^{41} + q^{43} + q^{49} - q^{59} + q^{67} - q^{73} + 2 q^{83} - 2 q^{89} - q^{97}+O(q^{100}) \)

Character values

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

\(n\)	\(325\)	\(1217\)	\(2431\)
\(\chi(n)\)	\(1\)	\(0\)	\(1\)

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  

\(\iota_m(\nu)\)

\( a_{2} \)

\( a_{3} \)

\( a_{4} \)

\( a_{5} \)

\( a_{6} \)

\( a_{7} \)

\( a_{8} \)

\( a_{9} \)

\( a_{10} \)

1135.1

0

0

0

0

0

0

0

0

0

0

Inner twists

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

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	2592.1.b.a		1
3.b	odd	2	1		2592.1.b.b		1
4.b	odd	2	1		648.1.b.a		1
8.b	even	2	1		648.1.b.a		1
8.d	odd	2	1	CM	2592.1.b.a		1
9.c	even	3	2		864.1.t.a		2
9.d	odd	6	2		288.1.t.a		2
12.b	even	2	1		648.1.b.b		1
24.f	even	2	1		2592.1.b.b		1
24.h	odd	2	1		648.1.b.b		1
36.f	odd	6	2		216.1.p.a		2
36.h	even	6	2		72.1.p.a	✓	2
72.j	odd	6	2		72.1.p.a	✓	2
72.l	even	6	2		288.1.t.a		2
72.n	even	6	2		216.1.p.a		2
72.p	odd	6	2		864.1.t.a		2
144.u	even	12	4		2304.1.o.c		4
144.w	odd	12	4		2304.1.o.c		4
180.n	even	6	2		1800.1.bk.d		2
180.v	odd	12	4		1800.1.ba.b		4
252.o	even	6	2		3528.1.ba.b		2
252.r	odd	6	2		3528.1.ce.b		2
252.s	odd	6	2		3528.1.cg.a		2
252.bb	even	6	2		3528.1.ce.a		2
252.bn	odd	6	2		3528.1.ba.a		2
360.bh	odd	6	2		1800.1.bk.d		2
360.br	even	12	4		1800.1.ba.b		4
504.y	even	6	2		3528.1.ba.a		2
504.bi	odd	6	2		3528.1.ce.a		2
504.ca	even	6	2		3528.1.ce.b		2
504.cc	even	6	2		3528.1.cg.a		2
504.db	odd	6	2		3528.1.ba.b		2

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
72.1.p.a	✓	2	36.h	even	6	2
72.1.p.a	✓	2	72.j	odd	6	2
216.1.p.a		2	36.f	odd	6	2
216.1.p.a		2	72.n	even	6	2
288.1.t.a		2	9.d	odd	6	2
288.1.t.a		2	72.l	even	6	2
648.1.b.a		1	4.b	odd	2	1
648.1.b.a		1	8.b	even	2	1
648.1.b.b		1	12.b	even	2	1
648.1.b.b		1	24.h	odd	2	1
864.1.t.a		2	9.c	even	3	2
864.1.t.a		2	72.p	odd	6	2
1800.1.ba.b		4	180.v	odd	12	4
1800.1.ba.b		4	360.br	even	12	4
1800.1.bk.d		2	180.n	even	6	2
1800.1.bk.d		2	360.bh	odd	6	2
2304.1.o.c		4	144.u	even	12	4
2304.1.o.c		4	144.w	odd	12	4
2592.1.b.a		1	1.a	even	1	1	trivial
2592.1.b.a		1	8.d	odd	2	1	CM
2592.1.b.b		1	3.b	odd	2	1
2592.1.b.b		1	24.f	even	2	1
3528.1.ba.a		2	252.bn	odd	6	2
3528.1.ba.a		2	504.y	even	6	2
3528.1.ba.b		2	252.o	even	6	2
3528.1.ba.b		2	504.db	odd	6	2
3528.1.ce.a		2	252.bb	even	6	2
3528.1.ce.a		2	504.bi	odd	6	2
3528.1.ce.b		2	252.r	odd	6	2
3528.1.ce.b		2	504.ca	even	6	2
3528.1.cg.a		2	252.s	odd	6	2
3528.1.cg.a		2	504.cc	even	6	2

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{11} + 1 \) acting on \(S_{1}^{\mathrm{new}}(2592, [\chi])\).

Hecke characteristic polynomials

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