Newform orbit 192.8.a.h

• Label: 192.8.a.h
• Level: $192$
• Weight: $8$
• Character orbit: 192.a
• Self dual: yes
• Analytic conductor: $59.978$
• Analytic rank: $0$
• Dimension: $1$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	$N$	$=$	$192 = 2^{6} \cdot 3$
Weight:	$k$	$=$	$8$
Character orbit:	$[\chi]$	$=$	192.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	$59.9779248930$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 24)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

$f(q)$

$=$

q - 27 * q^3 + 530 * q^5 + 120 * q^7 + 729 * q^9 + 7196 * q^11 + 9626 * q^13 - 14310 * q^15 + 18674 * q^17 - 7004 * q^19 - 3240 * q^21 - 63704 * q^23 + 202775 * q^25 - 19683 * q^27 - 29334 * q^29 + 87968 * q^31 - 194292 * q^33 + 63600 * q^35 - 227982 * q^37 - 259902 * q^39 - 160806 * q^41 - 136132 * q^43 + 386370 * q^45 - 1206960 * q^47 - 809143 * q^49 - 504198 * q^51 + 398786 * q^53 + 3813880 * q^55 + 189108 * q^57 - 1152436 * q^59 + 2070602 * q^61 + 87480 * q^63 + 5101780 * q^65 + 4073428 * q^67 + 1720008 * q^69 - 383752 * q^71 + 3006010 * q^73 - 5474925 * q^75 + 863520 * q^77 - 4948112 * q^79 + 531441 * q^81 + 9163492 * q^83 + 9897220 * q^85 + 792018 * q^87 + 7304106 * q^89 + 1155120 * q^91 - 2375136 * q^93 - 3712120 * q^95 - 690526 * q^97 + 5245884 * 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

−27.0000

0

530.000

0

120.000

0

729.000

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	192.8.a.h		1
3.b	odd	2	1		576.8.a.c		1
4.b	odd	2	1		192.8.a.p		1
8.b	even	2	1		24.8.a.b	✓	1
8.d	odd	2	1		48.8.a.a		1
12.b	even	2	1		576.8.a.b		1
24.f	even	2	1		144.8.a.k		1
24.h	odd	2	1		72.8.a.e		1
40.f	even	2	1		600.8.a.b		1
40.i	odd	4	2		600.8.f.a		2

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
24.8.a.b	✓	1	8.b	even	2	1
48.8.a.a		1	8.d	odd	2	1
72.8.a.e		1	24.h	odd	2	1
144.8.a.k		1	24.f	even	2	1
192.8.a.h		1	1.a	even	1	1	trivial
192.8.a.p		1	4.b	odd	2	1
576.8.a.b		1	12.b	even	2	1
576.8.a.c		1	3.b	odd	2	1
600.8.a.b		1	40.f	even	2	1
600.8.f.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 $S_{8}^{\mathrm{new}}(\Gamma_0(192))$:

$T_{5} - 530$

$T_{7} - 120$

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$T$
$3$	$T + 27$
$5$	$T - 530$
$7$	$T - 120$
$11$	$T - 7196$