Newform orbit 1008.2.v.e

• Label: 1008.2.v.e
• Level: $1008$
• Weight: $2$
• Character orbit: 1008.v
• Analytic conductor: $8.049$
• Analytic rank: $0$
• Dimension: $40$
• Inner twists: $4$

Newspace parameters

Level:	$N$	$=$	$1008 = 2^{4} \cdot 3^{2} \cdot 7$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	1008.v (of order $4$, degree $2$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$8.04892052375$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
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.

$\operatorname{Tr}(f)(q) =$ 40 * q + 40 * q^7 + 48 * q^10 - 24 * q^13 + 12 * q^16 - 32 * q^19 - 8 * q^22 - 56 * q^34 - 8 * q^37 + 32 * q^43 - 52 * q^46 + 40 * q^49 - 8 * q^52 + 48 * q^55 + 56 * q^58 - 24 * q^61 + 48 * q^64 + 48 * q^70 - 24 * q^76 - 64 * q^82 + 64 * q^85 - 120 * q^88 - 24 * q^91 - 128 * q^94 + 64 * 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	$a_{2}$			$a_{3}$			$a_{4}$			$a_{5}$			$a_{6}$			$a_{7}$			$a_{8}$			$a_{9}$			$a_{10}$
323.1	−1.40729	−	0.139782i		0		1.96092	+	0.393427i	−1.17902	−	1.17902i		0		1.00000			−2.70459	−	0.827766i		0		1.49442	+	1.82403i
323.2	−1.39680	+	0.221233i		0		1.90211	−	0.618037i	−2.51504	−	2.51504i		0		1.00000			−2.52014	+	1.28408i		0		4.06942	+	2.95660i
323.3	−1.37088	−	0.347400i		0		1.75863	+	0.952488i	0.111394	+	0.111394i		0		1.00000			−2.07997	−	1.91669i		0		−0.114009	−	0.191406i
323.4	−1.13420	−	0.844744i		0		0.572816	+	1.91622i	2.12043	+	2.12043i		0		1.00000			0.969023	−	2.65725i		0		−0.613769	−	4.19620i
323.5	−1.11731	+	0.866958i		0		0.496766	−	1.93732i	0.925496	+	0.925496i		0		1.00000			1.12454	+	2.59527i		0		−1.83643	−	0.231700i
323.6	−0.890883	−	1.09833i		0		−0.412656	+	1.95697i	−1.65702	−	1.65702i		0		1.00000			2.51702	−	1.29019i		0		−0.343745	+	3.29617i
323.7	−0.614527	+	1.27372i		0		−1.24471	−	1.56547i	−2.62814	−	2.62814i		0		1.00000			2.75887	−	0.623393i		0		4.96257	−	1.73245i
323.8	−0.579268	+	1.29014i		0		−1.32890	−	1.49467i	−0.667815	−	0.667815i		0		1.00000			2.69811	−	0.848644i		0		1.24842	−	0.474728i
323.9	−0.351970	−	1.36971i		0		−1.75223	+	0.964197i	2.96859	+	2.96859i		0		1.00000			1.93741	+	2.06069i		0		3.02127	−	5.11098i
323.10	−0.153718	−	1.40583i		0		−1.95274	+	0.432203i	0.0893433	+	0.0893433i		0		1.00000			0.907777	+	2.67879i		0		0.111868	−	0.139335i
323.11	0.153718	+	1.40583i		0		−1.95274	+	0.432203i	−0.0893433	−	0.0893433i		0		1.00000			−0.907777	−	2.67879i		0		0.111868	−	0.139335i
323.12	0.351970	+	1.36971i		0		−1.75223	+	0.964197i	−2.96859	−	2.96859i		0		1.00000			−1.93741	−	2.06069i		0		3.02127	−	5.11098i
323.13	0.579268	−	1.29014i		0		−1.32890	−	1.49467i	0.667815	+	0.667815i		0		1.00000			−2.69811	+	0.848644i		0		1.24842	−	0.474728i
323.14	0.614527	−	1.27372i		0		−1.24471	−	1.56547i	2.62814	+	2.62814i		0		1.00000			−2.75887	+	0.623393i		0		4.96257	−	1.73245i
323.15	0.890883	+	1.09833i		0		−0.412656	+	1.95697i	1.65702	+	1.65702i		0		1.00000			−2.51702	+	1.29019i		0		−0.343745	+	3.29617i
323.16	1.11731	−	0.866958i		0		0.496766	−	1.93732i	−0.925496	−	0.925496i		0		1.00000			−1.12454	−	2.59527i		0		−1.83643	−	0.231700i
323.17	1.13420	+	0.844744i		0		0.572816	+	1.91622i	−2.12043	−	2.12043i		0		1.00000			−0.969023	+	2.65725i		0		−0.613769	−	4.19620i
323.18	1.37088	+	0.347400i		0		1.75863	+	0.952488i	−0.111394	−	0.111394i		0		1.00000			2.07997	+	1.91669i		0		−0.114009	−	0.191406i
323.19	1.39680	−	0.221233i		0		1.90211	−	0.618037i	2.51504	+	2.51504i		0		1.00000			2.52014	−	1.28408i		0		4.06942	+	2.95660i
323.20	1.40729	+	0.139782i		0		1.96092	+	0.393427i	1.17902	+	1.17902i		0		1.00000			2.70459	+	0.827766i		0		1.49442	+	1.82403i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
16.f	odd	4	1	inner
48.k	even	4	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1008.2.v.e	✓	40
3.b	odd	2	1	inner	1008.2.v.e	✓	40
4.b	odd	2	1		4032.2.v.e		40
12.b	even	2	1		4032.2.v.e		40
16.e	even	4	1		4032.2.v.e		40
16.f	odd	4	1	inner	1008.2.v.e	✓	40
48.i	odd	4	1		4032.2.v.e		40
48.k	even	4	1	inner	1008.2.v.e	✓	40

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
1008.2.v.e	✓	40	1.a	even	1	1	trivial
1008.2.v.e	✓	40	3.b	odd	2	1	inner
1008.2.v.e	✓	40	16.f	odd	4	1	inner
1008.2.v.e	✓	40	48.k	even	4	1	inner
4032.2.v.e		40	4.b	odd	2	1
4032.2.v.e		40	12.b	even	2	1
4032.2.v.e		40	16.e	even	4	1
4032.2.v.e		40	48.i	odd	4	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{2}^{\mathrm{new}}(1008, [\chi])$:

T5^40 + 784*T5^36 + 224304*T5^32 + 29085120*T5^28 + 1705059168*T5^24 + 39939500288*T5^20 + 309073644288*T5^16 + 746491278336*T5^12 + 418162118912*T5^8 + 363667456*T5^4 + 65536

T11^40 + 3664*T11^36 + 4437680*T11^32 + 2045565248*T11^28 + 297547122016*T11^24 + 14249609883392*T11^20 + 256269727085312*T11^16 + 1533931048213504*T11^12 + 3396101795115264*T11^8 + 2189103463530496*T11^4 + 426337261060096