Newform orbit 4032.2.v.e

• Label: 4032.2.v.e
• Level: $4032$
• Weight: $2$
• Character orbit: 4032.v
• Analytic conductor: $32.196$
• Analytic rank: $0$
• Dimension: $40$
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 4032 = 2^{6} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4032.v (of order \(4\), degree \(2\), not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(32.1956820950\)
Analytic rank:	\(0\)
Dimension:	\(40\)
Relative dimension:	\(20\) over \(\Q(i)\)
Twist minimal:	no (minimal twist has level 1008)
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.

\(\operatorname{Tr}(f)(q) = \) \( 40 q - 40 q^{7} - 24 q^{13} + 32 q^{19} - 8 q^{37} - 32 q^{43} + 40 q^{49} - 48 q^{55} - 24 q^{61} + 64 q^{85} + 24 q^{91} + 64 q^{97}+O(q^{100}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
1583.1		0			0			0		−2.96859	−	2.96859i		0		−1.00000				0			0			0
1583.2		0			0			0		−2.62814	−	2.62814i		0		−1.00000				0			0			0
1583.3		0			0			0		−2.51504	−	2.51504i		0		−1.00000				0			0			0
1583.4		0			0			0		−2.12043	−	2.12043i		0		−1.00000				0			0			0
1583.5		0			0			0		−1.65702	−	1.65702i		0		−1.00000				0			0			0
1583.6		0			0			0		−1.17902	−	1.17902i		0		−1.00000				0			0			0
1583.7		0			0			0		−0.925496	−	0.925496i		0		−1.00000				0			0			0
1583.8		0			0			0		−0.667815	−	0.667815i		0		−1.00000				0			0			0
1583.9		0			0			0		−0.111394	−	0.111394i		0		−1.00000				0			0			0
1583.10		0			0			0		−0.0893433	−	0.0893433i		0		−1.00000				0			0			0
1583.11		0			0			0		0.0893433	+	0.0893433i		0		−1.00000				0			0			0
1583.12		0			0			0		0.111394	+	0.111394i		0		−1.00000				0			0			0
1583.13		0			0			0		0.667815	+	0.667815i		0		−1.00000				0			0			0
1583.14		0			0			0		0.925496	+	0.925496i		0		−1.00000				0			0			0
1583.15		0			0			0		1.17902	+	1.17902i		0		−1.00000				0			0			0
1583.16		0			0			0		1.65702	+	1.65702i		0		−1.00000				0			0			0
1583.17		0			0			0		2.12043	+	2.12043i		0		−1.00000				0			0			0
1583.18		0			0			0		2.51504	+	2.51504i		0		−1.00000				0			0			0
1583.19		0			0			0		2.62814	+	2.62814i		0		−1.00000				0			0			0
1583.20		0			0			0		2.96859	+	2.96859i		0		−1.00000				0			0			0

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	4032.2.v.e		40
3.b	odd	2	1	inner	4032.2.v.e		40
4.b	odd	2	1		1008.2.v.e	✓	40
12.b	even	2	1		1008.2.v.e	✓	40
16.e	even	4	1		1008.2.v.e	✓	40
16.f	odd	4	1	inner	4032.2.v.e		40
48.i	odd	4	1		1008.2.v.e	✓	40
48.k	even	4	1	inner	4032.2.v.e		40

    

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

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(4032, [\chi])\):

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