Newform orbit 630.2.a.h

• Label: 630.2.a.h
• Level: $630$
• Weight: $2$
• Character orbit: 630.a
• Self dual: yes
• Analytic conductor: $5.031$
• Analytic rank: $0$
• Dimension: $1$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	$N$	$=$	$630 = 2 \cdot 3^{2} \cdot 5 \cdot 7$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	630.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 210)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

$f(q)$

$=$

q + q^2 + q^4 - q^5 + q^7 + q^8 - q^10 + 2 * q^13 + q^14 + q^16 + 6 * q^17 + 8 * q^19 - q^20 + q^25 + 2 * q^26 + q^28 - 6 * q^29 - 4 * q^31 + q^32 + 6 * q^34 - q^35 - 10 * q^37 + 8 * q^38 - q^40 + 6 * q^41 - 4 * q^43 + q^49 + q^50 + 2 * q^52 + 6 * q^53 + q^56 - 6 * q^58 + 12 * q^59 - 10 * q^61 - 4 * q^62 + q^64 - 2 * q^65 - 4 * q^67 + 6 * q^68 - q^70 - 12 * q^71 - 10 * q^73 - 10 * q^74 + 8 * q^76 + 8 * q^79 - q^80 + 6 * q^82 - 12 * q^83 - 6 * q^85 - 4 * q^86 + 6 * q^89 + 2 * q^91 - 8 * q^95 - 10 * q^97 + q^98

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

1.00000

0

1.00000

−1.00000

0

1.00000

1.00000

0

−1.00000

Atkin-Lehner signs

$p$	Sign
$2$	$-1$
$3$	$-1$
$5$	$+1$
$7$	$-1$

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	630.2.a.h		1
3.b	odd	2	1		210.2.a.b	✓	1
4.b	odd	2	1		5040.2.a.g		1
5.b	even	2	1		3150.2.a.f		1
5.c	odd	4	2		3150.2.g.i		2
7.b	odd	2	1		4410.2.a.bi		1
12.b	even	2	1		1680.2.a.g		1
15.d	odd	2	1		1050.2.a.k		1
15.e	even	4	2		1050.2.g.c		2
21.c	even	2	1		1470.2.a.b		1
21.g	even	6	2		1470.2.i.s		2
21.h	odd	6	2		1470.2.i.l		2
24.f	even	2	1		6720.2.a.bi		1
24.h	odd	2	1		6720.2.a.n		1
60.h	even	2	1		8400.2.a.cm		1
105.g	even	2	1		7350.2.a.cs		1

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
210.2.a.b	✓	1	3.b	odd	2	1
630.2.a.h		1	1.a	even	1	1	trivial
1050.2.a.k		1	15.d	odd	2	1
1050.2.g.c		2	15.e	even	4	2
1470.2.a.b		1	21.c	even	2	1
1470.2.i.l		2	21.h	odd	6	2
1470.2.i.s		2	21.g	even	6	2
1680.2.a.g		1	12.b	even	2	1
3150.2.a.f		1	5.b	even	2	1
3150.2.g.i		2	5.c	odd	4	2
4410.2.a.bi		1	7.b	odd	2	1
5040.2.a.g		1	4.b	odd	2	1
6720.2.a.n		1	24.h	odd	2	1
6720.2.a.bi		1	24.f	even	2	1
7350.2.a.cs		1	105.g	even	2	1
8400.2.a.cm		1	60.h	even	2	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{2}^{\mathrm{new}}(\Gamma_0(630))$:

$T_{11}$

$T_{13} - 2$

$T_{17} - 6$

$T_{19} - 8$

$T_{29} + 6$

Hecke characteristic polynomials

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