Newform orbit 1080.1.i.b

• Label: 1080.1.i.b
• Level: $1080$
• Weight: $1$
• Character orbit: 1080.i
• Self dual: yes
• Analytic conductor: $0.539$
• Analytic rank: $0$
• Dimension: $1$
• Projective image: $D_{3}$
• CM discriminant: -120
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1080 = 2^{3} \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1080.i (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	yes
Analytic conductor:	\(0.538990213644\)
Analytic rank:	\(0\)
Dimension:	\(1\)
Coefficient field:	\(\mathbb{Q}\)
Coefficient ring:	\(\mathbb{Z}\)
Coefficient ring index:	\( 1 \)
Twist minimal:	yes
Projective image:	\(D_{3}\)
Projective field:	Galois closure of 3.1.1080.1
Artin image:	$D_6$
Artin field:	Galois closure of 6.2.5832000.1
Stark unit:	Root of $x^{6} - 87x^{5} + 1068x^{4} - 5609x^{3} + 1068x^{2} - 87x + 1$

$q$-expansion

\(f(q)\)

\(=\)

q - q^2 + q^4 + q^5 - q^8 - q^10 - q^11 + q^13 + q^16 + q^17 + q^20 + q^22 + q^23 + q^25 - q^26 - q^29 - q^31 - q^32 - q^34 - 2 * q^37 - q^40 + q^43 - q^44 - q^46 + q^47 + q^49 - q^50 + q^52 - q^55 + q^58 + 2 * q^59 + q^62 + q^64 + q^65 - 2 * q^67 + q^68 + 2 * q^74 - q^79 + q^80 + q^85 - q^86 + q^88 + q^92 - q^94 - q^98

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1080\mathbb{Z}\right)^\times\).

\(n\)	\(217\)	\(271\)	\(541\)	\(1001\)
\(\chi(n)\)	\(1\)	\(0\)	\(1\)	\(1\)

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  

\(\iota_m(\nu)\)

\( a_{2} \)

\( a_{3} \)

\( a_{4} \)

\( a_{5} \)

\( a_{6} \)

\( a_{7} \)

\( a_{8} \)

\( a_{9} \)

\( a_{10} \)

269.1

0

−1.00000

0

1.00000

1.00000

0

0

−1.00000

0

−1.00000

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
120.i	odd	2	1	CM by \(\Q(\sqrt{-30}) \)

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1080.1.i.b	yes	1
3.b	odd	2	1		1080.1.i.c	yes	1
5.b	even	2	1		1080.1.i.d	yes	1
8.b	even	2	1		1080.1.i.a	✓	1
9.c	even	3	2		3240.1.bh.c		2
9.d	odd	6	2		3240.1.bh.b		2
15.d	odd	2	1		1080.1.i.a	✓	1
24.h	odd	2	1		1080.1.i.d	yes	1
40.f	even	2	1		1080.1.i.c	yes	1
45.h	odd	6	2		3240.1.bh.d		2
45.j	even	6	2		3240.1.bh.a		2
72.j	odd	6	2		3240.1.bh.a		2
72.n	even	6	2		3240.1.bh.d		2
120.i	odd	2	1	CM	1080.1.i.b	yes	1
360.bh	odd	6	2		3240.1.bh.c		2
360.bk	even	6	2		3240.1.bh.b		2

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
1080.1.i.a	✓	1	8.b	even	2	1
1080.1.i.a	✓	1	15.d	odd	2	1
1080.1.i.b	yes	1	1.a	even	1	1	trivial
1080.1.i.b	yes	1	120.i	odd	2	1	CM
1080.1.i.c	yes	1	3.b	odd	2	1
1080.1.i.c	yes	1	40.f	even	2	1
1080.1.i.d	yes	1	5.b	even	2	1
1080.1.i.d	yes	1	24.h	odd	2	1
3240.1.bh.a		2	45.j	even	6	2
3240.1.bh.a		2	72.j	odd	6	2
3240.1.bh.b		2	9.d	odd	6	2
3240.1.bh.b		2	360.bk	even	6	2
3240.1.bh.c		2	9.c	even	3	2
3240.1.bh.c		2	360.bh	odd	6	2
3240.1.bh.d		2	45.h	odd	6	2
3240.1.bh.d		2	72.n	even	6	2

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{1}^{\mathrm{new}}(1080, [\chi])\):

\( T_{7} \)

\( T_{11} + 1 \)

\( T_{13} - 1 \)

Hecke characteristic polynomials

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