Newform orbit 1323.2.a.j

• Label: 1323.2.a.j
• Level: $1323$
• Weight: $2$
• Character orbit: 1323.a
• Self dual: yes
• Analytic conductor: $10.564$
• Analytic rank: $1$
• Dimension: $1$
• CM discriminant: -3
• Inner twists: $2$

Newspace parameters

Level:	$N$	$=$	$1323 = 3^{3} \cdot 7^{2}$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	1323.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	$10.5642081874$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 189)
Fricke sign:	$+1$
Sato-Tate group:	$N(\mathrm{U}(1))$

$q$-expansion

$f(q)$

$=$

$q - 2 q^{4} - 2 q^{13} + 4 q^{16} + 7 q^{19} - 5 q^{25} - 11 q^{31} - 10 q^{37} - 13 q^{43} + 4 q^{52} + 13 q^{61} - 8 q^{64} - 16 q^{67} + 7 q^{73} - 14 q^{76} - 4 q^{79} - 5 q^{97}+O(q^{100})$

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

0

−2.00000

0

0

0

0

0

0

Atkin-Lehner signs

$p$	Sign
$3$	$-1$
$7$	$-1$

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	CM by $\Q(\sqrt{-3})$

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1323.2.a.j		1
3.b	odd	2	1	CM	1323.2.a.j		1
7.b	odd	2	1		1323.2.a.k		1
7.d	odd	6	2		189.2.e.b	✓	2
21.c	even	2	1		1323.2.a.k		1
21.g	even	6	2		189.2.e.b	✓	2
63.i	even	6	2		567.2.h.d		2
63.k	odd	6	2		567.2.g.c		2
63.s	even	6	2		567.2.g.c		2
63.t	odd	6	2		567.2.h.d		2

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
189.2.e.b	✓	2	7.d	odd	6	2
189.2.e.b	✓	2	21.g	even	6	2
567.2.g.c		2	63.k	odd	6	2
567.2.g.c		2	63.s	even	6	2
567.2.h.d		2	63.i	even	6	2
567.2.h.d		2	63.t	odd	6	2
1323.2.a.j		1	1.a	even	1	1	trivial
1323.2.a.j		1	3.b	odd	2	1	CM
1323.2.a.k		1	7.b	odd	2	1
1323.2.a.k		1	21.c	even	2	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{2}^{\mathrm{new}}(\Gamma_0(1323))$:

$T_{2}$

$T_{5}$

$T_{13} + 2$

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$T$
$3$	$T$
$5$	$T$
$7$	$T$
$11$	$T$