Newform orbit 3920.1.j.d

• Label: 3920.1.j.d
• Level: $3920$
• Weight: $1$
• Character orbit: 3920.j
• Self dual: yes
• Analytic conductor: $1.956$
• Analytic rank: $0$
• Dimension: $2$
• Projective image: $D_{6}$
• CM discriminant: -20
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 3920 = 2^{4} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3920.j (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	yes
Analytic conductor:	\(1.95633484952\)
Analytic rank:	\(0\)
Dimension:	\(2\)
Coefficient field:	\(\Q(\sqrt{3}) \)
Defining polynomial:	\( x^{2} - 3 \)
Coefficient ring:	\(\Z[a_1, a_2, a_3]\)
Coefficient ring index:	\( 1 \)
Twist minimal:	no (minimal twist has level 560)
Projective image:	\(D_{6}\)
Projective field:	Galois closure of 6.0.3841600.1

$q$-expansion

Coefficients of the \(q\)-expansion are expressed in terms of \(\beta = \sqrt{3}\). We also show the integral \(q\)-expansion of the trace form.

\(f(q)\)	\(=\)	q - b * q^3 + q^5 + 2 * q^9 - b * q^15 + b * q^23 + q^25 - b * q^27 - q^29 - q^41 + b * q^43 + 2 * q^45 - q^61 - b * q^67 - 3 * q^69 - b * q^75 + q^81 + b * q^83 + b * q^87 + q^89
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{5} + 4 q^{9} + 2 q^{25} - 2 q^{29} - 2 q^{41} + 4 q^{45} - 2 q^{61} - 6 q^{69} + 2 q^{81} + 2 q^{89}+O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3920\mathbb{Z}\right)^\times\).

\(n\)	\(981\)	\(1471\)	\(3041\)	\(3137\)
\(\chi(n)\)	\(1\)	\(-1\)	\(1\)	\(-1\)

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  

\(\iota_m(\nu)\)

\( a_{2} \)

\( a_{3} \)

\( a_{4} \)

\( a_{5} \)

\( a_{6} \)

\( a_{7} \)

\( a_{8} \)

\( a_{9} \)

\( a_{10} \)

3039.1

1.73205
−1.73205

0

−1.73205

0

1.00000

0

0

0

2.00000

0

3039.2

0

1.73205

0

1.00000

0

0

0

2.00000

0

Inner twists

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

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	3920.1.j.d		2
4.b	odd	2	1	inner	3920.1.j.d		2
5.b	even	2	1	inner	3920.1.j.d		2
7.b	odd	2	1		3920.1.j.b		2
7.c	even	3	2		3920.1.bt.c		4
7.d	odd	6	2		560.1.bt.a	✓	4
20.d	odd	2	1	CM	3920.1.j.d		2
28.d	even	2	1		3920.1.j.b		2
28.f	even	6	2		560.1.bt.a	✓	4
28.g	odd	6	2		3920.1.bt.c		4
35.c	odd	2	1		3920.1.j.b		2
35.i	odd	6	2		560.1.bt.a	✓	4
35.j	even	6	2		3920.1.bt.c		4
35.k	even	12	2		2800.1.ce.a		2
35.k	even	12	2		2800.1.ce.b		2
56.j	odd	6	2		2240.1.bt.c		4
56.m	even	6	2		2240.1.bt.c		4
140.c	even	2	1		3920.1.j.b		2
140.p	odd	6	2		3920.1.bt.c		4
140.s	even	6	2		560.1.bt.a	✓	4
140.x	odd	12	2		2800.1.ce.a		2
140.x	odd	12	2		2800.1.ce.b		2
280.ba	even	6	2		2240.1.bt.c		4
280.bk	odd	6	2		2240.1.bt.c		4

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
560.1.bt.a	✓	4	7.d	odd	6	2
560.1.bt.a	✓	4	28.f	even	6	2
560.1.bt.a	✓	4	35.i	odd	6	2
560.1.bt.a	✓	4	140.s	even	6	2
2240.1.bt.c		4	56.j	odd	6	2
2240.1.bt.c		4	56.m	even	6	2
2240.1.bt.c		4	280.ba	even	6	2
2240.1.bt.c		4	280.bk	odd	6	2
2800.1.ce.a		2	35.k	even	12	2
2800.1.ce.a		2	140.x	odd	12	2
2800.1.ce.b		2	35.k	even	12	2
2800.1.ce.b		2	140.x	odd	12	2
3920.1.j.b		2	7.b	odd	2	1
3920.1.j.b		2	28.d	even	2	1
3920.1.j.b		2	35.c	odd	2	1
3920.1.j.b		2	140.c	even	2	1
3920.1.j.d		2	1.a	even	1	1	trivial
3920.1.j.d		2	4.b	odd	2	1	inner
3920.1.j.d		2	5.b	even	2	1	inner
3920.1.j.d		2	20.d	odd	2	1	CM
3920.1.bt.c		4	7.c	even	3	2
3920.1.bt.c		4	28.g	odd	6	2
3920.1.bt.c		4	35.j	even	6	2
3920.1.bt.c		4	140.p	odd	6	2

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{1}^{\mathrm{new}}(3920, [\chi])\):

\( T_{3}^{2} - 3 \)

\( T_{11} \)

\( T_{13} \)

\( T_{41} + 1 \)

Hecke characteristic polynomials

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