Newform orbit 1620.1.f.c

• Label: 1620.1.f.c
• Level: $1620$
• Weight: $1$
• Character orbit: 1620.f
• Self dual: yes
• Analytic conductor: $0.808$
• Analytic rank: $0$
• Dimension: $1$
• Projective image: $D_{3}$
• CM discriminant: -20
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1620.f (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	yes
Analytic conductor:	\(0.808485320465\)
Analytic rank:	\(0\)
Dimension:	\(1\)
Coefficient field:	\(\mathbb{Q}\)
Coefficient ring:	\(\mathbb{Z}\)
Coefficient ring index:	\( 1 \)
Twist minimal:	no (minimal twist has level 180)
Projective image:	\(D_{3}\)
Projective field:	Galois closure of 3.1.1620.1
Artin image:	$D_6$
Artin field:	Galois closure of 6.2.31492800.1
Stark unit:	Root of $x^{6} - 79926x^{5} + 24440847x^{4} - 6339443636x^{3} + 24440847x^{2} - 79926x + 1$

$q$-expansion

\(f(q)\)

\(=\)

q + q^2 + q^4 - q^5 + q^7 + q^8 - q^10 + q^14 + q^16 - q^20 - q^23 + q^25 + q^28 + q^29 + q^32 - q^35 - q^40 + q^41 - 2 * q^43 - q^46 - q^47 + q^50 + q^56 + q^58 - q^61 + q^64 + q^67 - q^70 - q^80 + q^82 - q^83 - 2 * q^86 + q^89 - q^92 - q^94

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1620\mathbb{Z}\right)^\times\).

\(n\)	\(811\)	\(1297\)	\(1541\)
\(\chi(n)\)	\(1\)	\(1\)	\(0\)

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  

\(\iota_m(\nu)\)

\( a_{2} \)

\( a_{3} \)

\( a_{4} \)

\( a_{5} \)

\( a_{6} \)

\( a_{7} \)

\( a_{8} \)

\( a_{9} \)

\( a_{10} \)

1459.1

0

1.00000

0

1.00000

−1.00000

0

1.00000

1.00000

0

−1.00000

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
20.d	odd	2	1	CM by \(\Q(\sqrt{-5}) \)

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1620.1.f.c		1
3.b	odd	2	1		1620.1.f.b		1
4.b	odd	2	1		1620.1.f.a		1
5.b	even	2	1		1620.1.f.a		1
9.c	even	3	2		540.1.p.a		2
9.d	odd	6	2		180.1.p.b	yes	2
12.b	even	2	1		1620.1.f.d		1
15.d	odd	2	1		1620.1.f.d		1
20.d	odd	2	1	CM	1620.1.f.c		1
36.f	odd	6	2		540.1.p.b		2
36.h	even	6	2		180.1.p.a	✓	2
45.h	odd	6	2		180.1.p.a	✓	2
45.j	even	6	2		540.1.p.b		2
45.k	odd	12	4		2700.1.t.a		4
45.l	even	12	4		900.1.t.a		4
60.h	even	2	1		1620.1.f.b		1
72.j	odd	6	2		2880.1.bu.a		2
72.l	even	6	2		2880.1.bu.b		2
180.n	even	6	2		180.1.p.b	yes	2
180.p	odd	6	2		540.1.p.a		2
180.v	odd	12	4		900.1.t.a		4
180.x	even	12	4		2700.1.t.a		4
360.bd	even	6	2		2880.1.bu.a		2
360.bh	odd	6	2		2880.1.bu.b		2

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
180.1.p.a	✓	2	36.h	even	6	2
180.1.p.a	✓	2	45.h	odd	6	2
180.1.p.b	yes	2	9.d	odd	6	2
180.1.p.b	yes	2	180.n	even	6	2
540.1.p.a		2	9.c	even	3	2
540.1.p.a		2	180.p	odd	6	2
540.1.p.b		2	36.f	odd	6	2
540.1.p.b		2	45.j	even	6	2
900.1.t.a		4	45.l	even	12	4
900.1.t.a		4	180.v	odd	12	4
1620.1.f.a		1	4.b	odd	2	1
1620.1.f.a		1	5.b	even	2	1
1620.1.f.b		1	3.b	odd	2	1
1620.1.f.b		1	60.h	even	2	1
1620.1.f.c		1	1.a	even	1	1	trivial
1620.1.f.c		1	20.d	odd	2	1	CM
1620.1.f.d		1	12.b	even	2	1
1620.1.f.d		1	15.d	odd	2	1
2700.1.t.a		4	45.k	odd	12	4
2700.1.t.a		4	180.x	even	12	4
2880.1.bu.a		2	72.j	odd	6	2
2880.1.bu.a		2	360.bd	even	6	2
2880.1.bu.b		2	72.l	even	6	2
2880.1.bu.b		2	360.bh	odd	6	2

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{1}^{\mathrm{new}}(1620, [\chi])\):

\( T_{7} - 1 \)

\( T_{23} + 1 \)

Hecke characteristic polynomials

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