Newform orbit 1840.2.m.g

• Label: 1840.2.m.g
• Level: $1840$
• Weight: $2$
• Character orbit: 1840.m
• Analytic conductor: $14.692$
• Analytic rank: $0$
• Dimension: $40$
• Inner twists: $8$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1840 = 2^{4} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1840.m (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(14.6924739719\)
Analytic rank:	\(0\)
Dimension:	\(40\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 40 q + 80 q^{9} - 24 q^{25} + 24 q^{41} - 16 q^{49} + 80 q^{69} + 40 q^{81} - 8 q^{85}+O(q^{100}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
1839.1		0		−3.28652				0		1.54120	+	1.62009i		0				2.73174i		0		7.80121				0
1839.2		0		−3.28652				0		−1.54120	+	1.62009i		0				2.73174i		0		7.80121				0
1839.3		0		−3.28652				0		−1.54120	−	1.62009i		0			−	2.73174i		0		7.80121				0
1839.4		0		−3.28652				0		1.54120	−	1.62009i		0			−	2.73174i		0		7.80121				0
1839.5		0		−2.49894				0		−2.19676	+	0.417445i		0			−	3.04922i		0		3.24468				0
1839.6		0		−2.49894				0		2.19676	+	0.417445i		0			−	3.04922i		0		3.24468				0
1839.7		0		−2.49894				0		2.19676	−	0.417445i		0				3.04922i		0		3.24468				0
1839.8		0		−2.49894				0		−2.19676	−	0.417445i		0				3.04922i		0		3.24468				0
1839.9		0		−2.20329				0		1.71768	−	1.43163i		0				0.642617i		0		1.85447				0
1839.10		0		−2.20329				0		−1.71768	+	1.43163i		0			−	0.642617i		0		1.85447				0
1839.11		0		−2.20329				0		−1.71768	−	1.43163i		0				0.642617i		0		1.85447				0
1839.12		0		−2.20329				0		1.71768	+	1.43163i		0			−	0.642617i		0		1.85447				0
1839.13		0		−1.49850				0		0.689327	+	2.12716i		0			−	4.18735i		0		−0.754490				0
1839.14		0		−1.49850				0		−0.689327	−	2.12716i		0				4.18735i		0		−0.754490				0
1839.15		0		−1.49850				0		−0.689327	+	2.12716i		0			−	4.18735i		0		−0.754490				0
1839.16		0		−1.49850				0		0.689327	−	2.12716i		0				4.18735i		0		−0.754490				0
1839.17		0		−0.924187				0		0.611037	−	2.15096i		0			−	1.51428i		0		−2.14588				0
1839.18		0		−0.924187				0		−0.611037	−	2.15096i		0			−	1.51428i		0		−2.14588				0
1839.19		0		−0.924187				0		−0.611037	+	2.15096i		0				1.51428i		0		−2.14588				0
1839.20		0		−0.924187				0		0.611037	+	2.15096i		0				1.51428i		0		−2.14588				0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
4.b	odd	2	1	inner
5.b	even	2	1	inner
20.d	odd	2	1	inner
23.b	odd	2	1	inner
92.b	even	2	1	inner
115.c	odd	2	1	inner
460.g	even	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1840.2.m.g	✓	40
4.b	odd	2	1	inner	1840.2.m.g	✓	40
5.b	even	2	1	inner	1840.2.m.g	✓	40
20.d	odd	2	1	inner	1840.2.m.g	✓	40
23.b	odd	2	1	inner	1840.2.m.g	✓	40
92.b	even	2	1	inner	1840.2.m.g	✓	40
115.c	odd	2	1	inner	1840.2.m.g	✓	40
460.g	even	2	1	inner	1840.2.m.g	✓	40

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
1840.2.m.g	✓	40	1.a	even	1	1	trivial
1840.2.m.g	✓	40	4.b	odd	2	1	inner
1840.2.m.g	✓	40	5.b	even	2	1	inner
1840.2.m.g	✓	40	20.d	odd	2	1	inner
1840.2.m.g	✓	40	23.b	odd	2	1	inner
1840.2.m.g	✓	40	92.b	even	2	1	inner
1840.2.m.g	✓	40	115.c	odd	2	1	inner
1840.2.m.g	✓	40	460.g	even	2	1	inner

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(1840, [\chi])\):

\( T_{3}^{10} - 25T_{3}^{8} + 220T_{3}^{6} - 835T_{3}^{4} + 1303T_{3}^{2} - 628 \)

\( T_{7}^{10} + 37T_{7}^{8} + 457T_{7}^{6} + 2232T_{7}^{4} + 3636T_{7}^{2} + 1152 \)