Newform orbit 476.3.x.a

• Label: 476.3.x.a
• Level: $476$
• Weight: $3$
• Character orbit: 476.x
• Analytic conductor: $12.970$
• Analytic rank: $0$
• Dimension: $96$
• Inner twists: $4$

Newspace parameters

Level:	$N$	$=$	$476 = 2^{2} \cdot 7 \cdot 17$
Weight:	$k$	$=$	$3$
Character orbit:	$[\chi]$	$=$	476.x (of order $8$, degree $4$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$12.9700605836$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$24$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

$q$-expansion

The algebraic $q$-expansion of this newform has not been computed, but we have computed the trace expansion.

$\operatorname{Tr}(f)(q) =$ 96 * q - 40 * q^11 - 16 * q^15 + 72 * q^23 + 72 * q^25 + 32 * q^35 - 256 * q^37 - 88 * q^39 - 32 * q^43 - 20 * q^49 - 120 * q^51 - 80 * q^53 + 492 * q^63 - 104 * q^65 - 144 * q^67 - 64 * q^71 + 84 * q^77 - 256 * q^79 + 824 * q^85 - 368 * q^91 - 264 * q^93 + 104 * q^95 + 560 * 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	$a_{2}$			$a_{3}$			$a_{4}$			$a_{5}$			$a_{6}$			$a_{7}$			$a_{8}$			$a_{9}$			$a_{10}$
321.1		0		−4.93903	+	2.04581i		0		2.11756	+	5.11225i		0		5.49744	+	4.33338i		0		13.8447	−	13.8447i		0
321.2		0		−4.78162	+	1.98061i		0		0.0890392	+	0.214960i		0		−6.37258	−	2.89658i		0		12.5771	−	12.5771i		0
321.3		0		−4.68527	+	1.94070i		0		−0.107047	−	0.258435i		0		6.27527	−	3.10178i		0		11.8214	−	11.8214i		0
321.4		0		−3.76134	+	1.55800i		0		−1.16212	−	2.80560i		0		−3.19109	+	6.23033i		0		5.35633	−	5.35633i		0
321.5		0		−3.43140	+	1.42133i		0		−3.65081	−	8.81383i		0		5.54157	+	4.27680i		0		3.39035	−	3.39035i		0
321.6		0		−2.58574	+	1.07105i		0		−2.55560	−	6.16976i		0		0.327431	−	6.99234i		0		−0.825039	+	0.825039i		0
321.7		0		−2.58178	+	1.06941i		0		2.86795	+	6.92385i		0		2.88122	−	6.37954i		0		−0.842001	+	0.842001i		0
321.8		0		−2.40762	+	0.997268i		0		2.93247	+	7.07962i		0		−3.61992	+	5.99134i		0		−1.56188	+	1.56188i		0
321.9		0		−2.20277	+	0.912419i		0		−1.83455	−	4.42900i		0		−6.99574	+	0.244103i		0		−2.34425	+	2.34425i		0
321.10		0		−1.57323	+	0.651655i		0		1.10724	+	2.67312i		0		3.07101	−	6.29038i		0		−4.31355	+	4.31355i		0
321.11		0		−1.14101	+	0.472620i		0		1.67386	+	4.04105i		0		−5.26535	−	4.61260i		0		−5.28544	+	5.28544i		0
321.12		0		−0.0501663	+	0.0207796i		0		0.962011	+	2.32250i		0		4.78783	+	5.10654i		0		−6.36188	+	6.36188i		0
321.13		0		0.0501663	−	0.0207796i		0		−0.962011	−	2.32250i		0		6.99637	−	0.225364i		0		−6.36188	+	6.36188i		0
321.14		0		1.14101	−	0.472620i		0		−1.67386	−	4.04105i		0		−6.98477	−	0.461559i		0		−5.28544	+	5.28544i		0
321.15		0		1.57323	−	0.651655i		0		−1.10724	−	2.67312i		0		−2.27644	+	6.61950i		0		−4.31355	+	4.31355i		0
321.16		0		2.20277	−	0.912419i		0		1.83455	+	4.42900i		0		−4.77413	−	5.11934i		0		−2.34425	+	2.34425i		0
321.17		0		2.40762	−	0.997268i		0		−2.93247	−	7.07962i		0		1.67684	−	6.79619i		0		−1.56188	+	1.56188i		0
321.18		0		2.58178	−	1.06941i		0		−2.86795	−	6.92385i		0		−2.47369	+	6.54835i		0		−0.842001	+	0.842001i		0
321.19		0		2.58574	−	1.07105i		0		2.55560	+	6.16976i		0		−4.71280	+	5.17586i		0		−0.825039	+	0.825039i		0
321.20		0		3.43140	−	1.42133i		0		3.65081	+	8.81383i		0		6.94264	+	0.894325i		0		3.39035	−	3.39035i		0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
7.b	odd	2	1	inner
17.d	even	8	1	inner
119.l	odd	8	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	476.3.x.a	✓	96
7.b	odd	2	1	inner	476.3.x.a	✓	96
17.d	even	8	1	inner	476.3.x.a	✓	96
119.l	odd	8	1	inner	476.3.x.a	✓	96

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
476.3.x.a	✓	96	1.a	even	1	1	trivial
476.3.x.a	✓	96	7.b	odd	2	1	inner
476.3.x.a	✓	96	17.d	even	8	1	inner
476.3.x.a	✓	96	119.l	odd	8	1	inner

Hecke kernels

This newform subspace is the entire newspace $S_{3}^{\mathrm{new}}(476, [\chi])$.