Newform orbit 3920.2.a.be

• Label: 3920.2.a.be
• Level: $3920$
• Weight: $2$
• Character orbit: 3920.a
• Self dual: yes
• Analytic conductor: $31.301$
• Analytic rank: $0$
• Dimension: $1$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	$N$	$=$	$3920 = 2^{4} \cdot 5 \cdot 7^{2}$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	3920.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	$31.3013575923$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 70)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

$f(q)$

$=$

q + 2 * q^3 - q^5 + q^9 - 3 * q^11 + 5 * q^13 - 2 * q^15 + 6 * q^17 + q^19 - 3 * q^23 + q^25 - 4 * q^27 - 6 * q^29 + 4 * q^31 - 6 * q^33 + 11 * q^37 + 10 * q^39 + 3 * q^41 + 10 * q^43 - q^45 - 3 * q^47 + 12 * q^51 + 3 * q^53 + 3 * q^55 + 2 * q^57 - 4 * q^61 - 5 * q^65 + 4 * q^67 - 6 * q^69 - 12 * q^71 - 4 * q^73 + 2 * q^75 + 10 * q^79 - 11 * q^81 + 12 * q^83 - 6 * q^85 - 12 * q^87 + 6 * q^89 + 8 * q^93 - q^95 + 14 * q^97 - 3 * q^99

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  

$\iota_m(\nu)$

$a_{2}$

$a_{3}$

$a_{4}$

$a_{5}$

$a_{6}$

$a_{7}$

$a_{8}$

$a_{9}$

$a_{10}$

1.1

0

0

2.00000

0

−1.00000

0

0

0

1.00000

0

Atkin-Lehner signs

$p$	Sign
$2$	$-1$
$5$	$+1$
$7$	$+1$

Inner twists

This newform does not admit any (nontrivial) inner twists.

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	3920.2.a.be		1
4.b	odd	2	1		490.2.a.g		1
7.b	odd	2	1		3920.2.a.g		1
7.c	even	3	2		560.2.q.d		2
12.b	even	2	1		4410.2.a.m		1
20.d	odd	2	1		2450.2.a.p		1
20.e	even	4	2		2450.2.c.f		2
28.d	even	2	1		490.2.a.j		1
28.f	even	6	2		490.2.e.a		2
28.g	odd	6	2		70.2.e.b	✓	2
84.h	odd	2	1		4410.2.a.c		1
84.n	even	6	2		630.2.k.e		2
140.c	even	2	1		2450.2.a.f		1
140.j	odd	4	2		2450.2.c.p		2
140.p	odd	6	2		350.2.e.h		2
140.w	even	12	4		350.2.j.a		4

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
70.2.e.b	✓	2	28.g	odd	6	2
350.2.e.h		2	140.p	odd	6	2
350.2.j.a		4	140.w	even	12	4
490.2.a.g		1	4.b	odd	2	1
490.2.a.j		1	28.d	even	2	1
490.2.e.a		2	28.f	even	6	2
560.2.q.d		2	7.c	even	3	2
630.2.k.e		2	84.n	even	6	2
2450.2.a.f		1	140.c	even	2	1
2450.2.a.p		1	20.d	odd	2	1
2450.2.c.f		2	20.e	even	4	2
2450.2.c.p		2	140.j	odd	4	2
3920.2.a.g		1	7.b	odd	2	1
3920.2.a.be		1	1.a	even	1	1	trivial
4410.2.a.c		1	84.h	odd	2	1
4410.2.a.m		1	12.b	even	2	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{2}^{\mathrm{new}}(\Gamma_0(3920))$:

$T_{3} - 2$

$T_{11} + 3$

$T_{13} - 5$

$T_{17} - 6$

Hecke characteristic polynomials

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