Newform orbit 480.4.bh.a

• Label: 480.4.bh.a
• Level: $480$
• Weight: $4$
• Character orbit: 480.bh
• Analytic conductor: $28.321$
• Analytic rank: $0$
• Dimension: $72$
• Inner twists: $4$

Newspace parameters

Level:	$N$	$=$	$480 = 2^{5} \cdot 3 \cdot 5$
Weight:	$k$	$=$	$4$
Character orbit:	$[\chi]$	$=$	480.bh (of order $4$, degree $2$, not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$28.3209168028$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 120)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

$q$-expansion

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

$\operatorname{Tr}(f)(q) =$ $72 q - 104 q^{17} - 88 q^{25} - 912 q^{35} - 864 q^{43} + 1488 q^{51} - 1048 q^{65} - 3696 q^{67} + 1480 q^{73} - 5832 q^{81} + 5360 q^{83} - 3392 q^{91} - 328 q^{97}+O(q^{100})$

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	$a_{2}$			$a_{3}$			$a_{4}$			$a_{5}$			$a_{6}$			$a_{7}$			$a_{8}$			$a_{9}$			$a_{10}$
367.1		0		−2.12132	+	2.12132i		0		−8.21764	−	7.58092i		0		21.7697	−	21.7697i		0			−	9.00000i		0
367.2		0		−2.12132	+	2.12132i		0		8.21764	+	7.58092i		0		−21.7697	+	21.7697i		0			−	9.00000i		0
367.3		0		−2.12132	+	2.12132i		0		−0.507948	+	11.1688i		0		−17.5600	+	17.5600i		0			−	9.00000i		0
367.4		0		−2.12132	+	2.12132i		0		0.507948	−	11.1688i		0		17.5600	−	17.5600i		0			−	9.00000i		0
367.5		0		−2.12132	+	2.12132i		0		−3.59302	+	10.5873i		0		−3.55795	+	3.55795i		0			−	9.00000i		0
367.6		0		−2.12132	+	2.12132i		0		3.59302	−	10.5873i		0		3.55795	−	3.55795i		0			−	9.00000i		0
367.7		0		−2.12132	+	2.12132i		0		−8.74847	−	6.96163i		0		−1.78469	+	1.78469i		0			−	9.00000i		0
367.8		0		−2.12132	+	2.12132i		0		8.74847	+	6.96163i		0		1.78469	−	1.78469i		0			−	9.00000i		0
367.9		0		−2.12132	+	2.12132i		0		−8.64040	+	7.09531i		0		−4.53056	+	4.53056i		0			−	9.00000i		0
367.10		0		−2.12132	+	2.12132i		0		8.64040	−	7.09531i		0		4.53056	−	4.53056i		0			−	9.00000i		0
367.11		0		−2.12132	+	2.12132i		0		−11.0300	+	1.82735i		0		11.6097	−	11.6097i		0			−	9.00000i		0
367.12		0		−2.12132	+	2.12132i		0		11.0300	−	1.82735i		0		−11.6097	+	11.6097i		0			−	9.00000i		0
367.13		0		−2.12132	+	2.12132i		0		−7.39199	+	8.38800i		0		12.7938	−	12.7938i		0			−	9.00000i		0
367.14		0		−2.12132	+	2.12132i		0		7.39199	−	8.38800i		0		−12.7938	+	12.7938i		0			−	9.00000i		0
367.15		0		−2.12132	+	2.12132i		0		−4.33793	−	10.3045i		0		−15.3854	+	15.3854i		0			−	9.00000i		0
367.16		0		−2.12132	+	2.12132i		0		4.33793	+	10.3045i		0		15.3854	−	15.3854i		0			−	9.00000i		0
367.17		0		−2.12132	+	2.12132i		0		−9.87236	−	5.24752i		0		−20.3922	+	20.3922i		0			−	9.00000i		0
367.18		0		−2.12132	+	2.12132i		0		9.87236	+	5.24752i		0		20.3922	−	20.3922i		0			−	9.00000i		0
367.19		0		2.12132	−	2.12132i		0		−9.61270	+	5.70930i		0		7.34859	−	7.34859i		0			−	9.00000i		0
367.20		0		2.12132	−	2.12132i		0		9.61270	−	5.70930i		0		−7.34859	+	7.34859i		0			−	9.00000i		0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.c	odd	4	1	inner
8.d	odd	2	1	inner
40.k	even	4	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	480.4.bh.a		72
4.b	odd	2	1		120.4.v.a	✓	72
5.c	odd	4	1	inner	480.4.bh.a		72
8.b	even	2	1		120.4.v.a	✓	72
8.d	odd	2	1	inner	480.4.bh.a		72
20.e	even	4	1		120.4.v.a	✓	72
40.i	odd	4	1		120.4.v.a	✓	72
40.k	even	4	1	inner	480.4.bh.a		72

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
120.4.v.a	✓	72	4.b	odd	2	1
120.4.v.a	✓	72	8.b	even	2	1
120.4.v.a	✓	72	20.e	even	4	1
120.4.v.a	✓	72	40.i	odd	4	1
480.4.bh.a		72	1.a	even	1	1	trivial
480.4.bh.a		72	5.c	odd	4	1	inner
480.4.bh.a		72	8.d	odd	2	1	inner
480.4.bh.a		72	40.k	even	4	1	inner

Hecke kernels

This newform subspace is the entire newspace $S_{4}^{\mathrm{new}}(480, [\chi])$.