Newform orbit 6336.2.a.l

• Label: 6336.2.a.l
• Level: $6336$
• Weight: $2$
• Character orbit: 6336.a
• Self dual: yes
• Analytic conductor: $50.593$
• Analytic rank: $0$
• Dimension: $1$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	$N$	$=$	$6336 = 2^{6} \cdot 3^{2} \cdot 11$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	6336.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	$50.5932147207$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 352)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

$f(q)$

$=$

q - 3 * q^5 + 4 * q^7 - q^11 + 2 * q^13 + 8 * q^17 + 6 * q^19 + 5 * q^23 + 4 * q^25 + 4 * q^29 - q^31 - 12 * q^35 - 3 * q^37 + 6 * q^41 - 6 * q^43 - 12 * q^47 + 9 * q^49 - 6 * q^53 + 3 * q^55 - 3 * q^59 - 6 * q^65 + 11 * q^67 - 5 * q^71 - 10 * q^73 - 4 * q^77 + 2 * q^79 + 2 * q^83 - 24 * q^85 + 5 * q^89 + 8 * q^91 - 18 * q^95 + 13 * q^97

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

−3.00000

0

4.00000

0

0

0

Atkin-Lehner signs

$p$	Sign
$2$	$+1$
$3$	$-1$
$11$	$+1$

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	6336.2.a.l		1
3.b	odd	2	1		704.2.a.j		1
4.b	odd	2	1		6336.2.a.g		1
8.b	even	2	1		3168.2.a.z		1
8.d	odd	2	1		3168.2.a.y		1
12.b	even	2	1		704.2.a.e		1
24.f	even	2	1		352.2.a.d	yes	1
24.h	odd	2	1		352.2.a.b	✓	1
33.d	even	2	1		7744.2.a.ba		1
48.i	odd	4	2		2816.2.c.b		2
48.k	even	4	2		2816.2.c.l		2
120.i	odd	2	1		8800.2.a.p		1
120.m	even	2	1		8800.2.a.m		1
132.d	odd	2	1		7744.2.a.o		1
264.m	even	2	1		3872.2.a.d		1
264.p	odd	2	1		3872.2.a.i		1

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
352.2.a.b	✓	1	24.h	odd	2	1
352.2.a.d	yes	1	24.f	even	2	1
704.2.a.e		1	12.b	even	2	1
704.2.a.j		1	3.b	odd	2	1
2816.2.c.b		2	48.i	odd	4	2
2816.2.c.l		2	48.k	even	4	2
3168.2.a.y		1	8.d	odd	2	1
3168.2.a.z		1	8.b	even	2	1
3872.2.a.d		1	264.m	even	2	1
3872.2.a.i		1	264.p	odd	2	1
6336.2.a.g		1	4.b	odd	2	1
6336.2.a.l		1	1.a	even	1	1	trivial
7744.2.a.o		1	132.d	odd	2	1
7744.2.a.ba		1	33.d	even	2	1
8800.2.a.m		1	120.m	even	2	1
8800.2.a.p		1	120.i	odd	2	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{2}^{\mathrm{new}}(\Gamma_0(6336))$:

$T_{5} + 3$

$T_{7} - 4$

$T_{13} - 2$

$T_{17} - 8$

$T_{19} - 6$

$T_{23} - 5$

$T_{47} + 12$

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$T$
$3$	$T$
$5$	$T + 3$
$7$	$T - 4$
$11$	$T + 1$