Newform orbit 576.6.a.bc

• Label: 576.6.a.bc
• Level: $576$
• Weight: $6$
• Character orbit: 576.a
• Self dual: yes
• Analytic conductor: $92.381$
• Analytic rank: $0$
• Dimension: $1$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	$N$	$=$	$576 = 2^{6} \cdot 3^{2}$
Weight:	$k$	$=$	$6$
Character orbit:	$[\chi]$	$=$	576.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	$92.3810802123$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 4)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

$f(q)$

$=$

q + 54 * q^5 - 88 * q^7 + 540 * q^11 + 418 * q^13 - 594 * q^17 - 836 * q^19 + 4104 * q^23 - 209 * q^25 - 594 * q^29 + 4256 * q^31 - 4752 * q^35 + 298 * q^37 - 17226 * q^41 + 12100 * q^43 + 1296 * q^47 - 9063 * q^49 + 19494 * q^53 + 29160 * q^55 - 7668 * q^59 + 34738 * q^61 + 22572 * q^65 - 21812 * q^67 + 46872 * q^71 + 67562 * q^73 - 47520 * q^77 - 76912 * q^79 + 67716 * q^83 - 32076 * q^85 - 29754 * q^89 - 36784 * q^91 - 45144 * q^95 - 122398 * 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

54.0000

0

−88.0000

0

0

0

Atkin-Lehner signs

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

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	576.6.a.bc		1
3.b	odd	2	1		64.6.a.f		1
4.b	odd	2	1		576.6.a.bd		1
8.b	even	2	1		36.6.a.a		1
8.d	odd	2	1		144.6.a.c		1
12.b	even	2	1		64.6.a.b		1
24.f	even	2	1		16.6.a.b		1
24.h	odd	2	1		4.6.a.a	✓	1
40.f	even	2	1		900.6.a.h		1
40.i	odd	4	2		900.6.d.a		2
48.i	odd	4	2		256.6.b.g		2
48.k	even	4	2		256.6.b.c		2
72.j	odd	6	2		324.6.e.a		2
72.n	even	6	2		324.6.e.d		2
120.i	odd	2	1		100.6.a.b		1
120.m	even	2	1		400.6.a.d		1
120.q	odd	4	2		400.6.c.f		2
120.w	even	4	2		100.6.c.b		2
168.e	odd	2	1		784.6.a.d		1
168.i	even	2	1		196.6.a.e		1
168.s	odd	6	2		196.6.e.g		2
168.ba	even	6	2		196.6.e.d		2
264.m	even	2	1		484.6.a.a		1
312.b	odd	2	1		676.6.a.a		1
312.y	even	4	2		676.6.d.a		2

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
4.6.a.a	✓	1	24.h	odd	2	1
16.6.a.b		1	24.f	even	2	1
36.6.a.a		1	8.b	even	2	1
64.6.a.b		1	12.b	even	2	1
64.6.a.f		1	3.b	odd	2	1
100.6.a.b		1	120.i	odd	2	1
100.6.c.b		2	120.w	even	4	2
144.6.a.c		1	8.d	odd	2	1
196.6.a.e		1	168.i	even	2	1
196.6.e.d		2	168.ba	even	6	2
196.6.e.g		2	168.s	odd	6	2
256.6.b.c		2	48.k	even	4	2
256.6.b.g		2	48.i	odd	4	2
324.6.e.a		2	72.j	odd	6	2
324.6.e.d		2	72.n	even	6	2
400.6.a.d		1	120.m	even	2	1
400.6.c.f		2	120.q	odd	4	2
484.6.a.a		1	264.m	even	2	1
576.6.a.bc		1	1.a	even	1	1	trivial
576.6.a.bd		1	4.b	odd	2	1
676.6.a.a		1	312.b	odd	2	1
676.6.d.a		2	312.y	even	4	2
784.6.a.d		1	168.e	odd	2	1
900.6.a.h		1	40.f	even	2	1
900.6.d.a		2	40.i	odd	4	2

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{6}^{\mathrm{new}}(\Gamma_0(576))$:

$T_{5} - 54$

$T_{7} + 88$

$T_{11} - 540$

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$T$
$3$	$T$
$5$	$T - 54$
$7$	$T + 88$
$11$	$T - 540$