Newform orbit 2548.2.a.e

• Label: 2548.2.a.e
• Level: $2548$
• Weight: $2$
• Character orbit: 2548.a
• Self dual: yes
• Analytic conductor: $20.346$
• Analytic rank: $0$
• Dimension: $1$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	$N$	$=$	$2548 = 2^{2} \cdot 7^{2} \cdot 13$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	2548.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	$20.3458824350$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 52)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

$f(q)$

$=$

q - 2 * q^5 - 3 * q^9 - 2 * q^11 + q^13 - 6 * q^17 + 6 * q^19 + 8 * q^23 - q^25 + 2 * q^29 - 10 * q^31 - 6 * q^37 + 6 * q^41 + 4 * q^43 + 6 * q^45 + 2 * q^47 + 6 * q^53 + 4 * q^55 + 10 * q^59 + 2 * q^61 - 2 * q^65 + 10 * q^67 + 10 * q^71 - 2 * q^73 - 4 * q^79 + 9 * q^81 + 6 * q^83 + 12 * q^85 + 6 * q^89 - 12 * q^95 - 2 * q^97 + 6 * 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

0

0

−2.00000

0

0

0

−3.00000

0

Atkin-Lehner signs

$p$	Sign
$2$	$-1$
$7$	$-1$
$13$	$-1$

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	2548.2.a.e		1
7.b	odd	2	1		52.2.a.a	✓	1
7.c	even	3	2		2548.2.j.f		2
7.d	odd	6	2		2548.2.j.e		2
21.c	even	2	1		468.2.a.b		1
28.d	even	2	1		208.2.a.c		1
35.c	odd	2	1		1300.2.a.d		1
35.f	even	4	2		1300.2.c.c		2
56.e	even	2	1		832.2.a.f		1
56.h	odd	2	1		832.2.a.e		1
63.l	odd	6	2		4212.2.i.d		2
63.o	even	6	2		4212.2.i.i		2
77.b	even	2	1		6292.2.a.g		1
84.h	odd	2	1		1872.2.a.f		1
91.b	odd	2	1		676.2.a.c		1
91.i	even	4	2		676.2.d.c		2
91.n	odd	6	2		676.2.e.c		2
91.t	odd	6	2		676.2.e.b		2
91.bc	even	12	4		676.2.h.c		4
112.j	even	4	2		3328.2.b.e		2
112.l	odd	4	2		3328.2.b.q		2
140.c	even	2	1		5200.2.a.q		1
168.e	odd	2	1		7488.2.a.bw		1
168.i	even	2	1		7488.2.a.bn		1
273.g	even	2	1		6084.2.a.m		1
273.o	odd	4	2		6084.2.b.m		2
364.h	even	2	1		2704.2.a.g		1
364.p	odd	4	2		2704.2.f.f		2

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
52.2.a.a	✓	1	7.b	odd	2	1
208.2.a.c		1	28.d	even	2	1
468.2.a.b		1	21.c	even	2	1
676.2.a.c		1	91.b	odd	2	1
676.2.d.c		2	91.i	even	4	2
676.2.e.b		2	91.t	odd	6	2
676.2.e.c		2	91.n	odd	6	2
676.2.h.c		4	91.bc	even	12	4
832.2.a.e		1	56.h	odd	2	1
832.2.a.f		1	56.e	even	2	1
1300.2.a.d		1	35.c	odd	2	1
1300.2.c.c		2	35.f	even	4	2
1872.2.a.f		1	84.h	odd	2	1
2548.2.a.e		1	1.a	even	1	1	trivial
2548.2.j.e		2	7.d	odd	6	2
2548.2.j.f		2	7.c	even	3	2
2704.2.a.g		1	364.h	even	2	1
2704.2.f.f		2	364.p	odd	4	2
3328.2.b.e		2	112.j	even	4	2
3328.2.b.q		2	112.l	odd	4	2
4212.2.i.d		2	63.l	odd	6	2
4212.2.i.i		2	63.o	even	6	2
5200.2.a.q		1	140.c	even	2	1
6084.2.a.m		1	273.g	even	2	1
6084.2.b.m		2	273.o	odd	4	2
6292.2.a.g		1	77.b	even	2	1
7488.2.a.bn		1	168.i	even	2	1
7488.2.a.bw		1	168.e	odd	2	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{2}^{\mathrm{new}}(\Gamma_0(2548))$:

$T_{3}$

$T_{5} + 2$

Hecke characteristic polynomials

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