Newform orbit 1176.4.a.e

• Label: 1176.4.a.e
• Level: $1176$
• Weight: $4$
• Character orbit: 1176.a
• Self dual: yes
• Analytic conductor: $69.386$
• Analytic rank: $0$
• Dimension: $1$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	$N$	$=$	$1176 = 2^{3} \cdot 3 \cdot 7^{2}$
Weight:	$k$	$=$	$4$
Character orbit:	$[\chi]$	$=$	1176.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	$69.3862461668$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 168)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

$f(q)$

$=$

q - 3 * q^3 + 2 * q^5 + 9 * q^9 + 52 * q^11 - 86 * q^13 - 6 * q^15 + 30 * q^17 + 4 * q^19 + 120 * q^23 - 121 * q^25 - 27 * q^27 + 246 * q^29 - 80 * q^31 - 156 * q^33 - 290 * q^37 + 258 * q^39 + 374 * q^41 + 164 * q^43 + 18 * q^45 - 464 * q^47 - 90 * q^51 - 162 * q^53 + 104 * q^55 - 12 * q^57 - 180 * q^59 + 666 * q^61 - 172 * q^65 - 628 * q^67 - 360 * q^69 + 296 * q^71 + 518 * q^73 + 363 * q^75 - 1184 * q^79 + 81 * q^81 - 220 * q^83 + 60 * q^85 - 738 * q^87 + 774 * q^89 + 240 * q^93 + 8 * q^95 + 1086 * q^97 + 468 * 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

−3.00000

0

2.00000

0

0

0

9.00000

0

Atkin-Lehner signs

$p$	Sign
$2$	$-1$
$3$	$+1$
$7$	$-1$

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	1176.4.a.e		1
4.b	odd	2	1		2352.4.a.bb		1
7.b	odd	2	1		168.4.a.f	✓	1
21.c	even	2	1		504.4.a.c		1
28.d	even	2	1		336.4.a.c		1
56.e	even	2	1		1344.4.a.v		1
56.h	odd	2	1		1344.4.a.g		1
84.h	odd	2	1		1008.4.a.l		1

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
168.4.a.f	✓	1	7.b	odd	2	1
336.4.a.c		1	28.d	even	2	1
504.4.a.c		1	21.c	even	2	1
1008.4.a.l		1	84.h	odd	2	1
1176.4.a.e		1	1.a	even	1	1	trivial
1344.4.a.g		1	56.h	odd	2	1
1344.4.a.v		1	56.e	even	2	1
2352.4.a.bb		1	4.b	odd	2	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{4}^{\mathrm{new}}(\Gamma_0(1176))$:

$T_{5} - 2$

$T_{11} - 52$

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$T$
$3$	$T + 3$
$5$	$T - 2$
$7$	$T$
$11$	$T - 52$