Newform orbit 2240.2.l.c

• Label: 2240.2.l.c
• Level: $2240$
• Weight: $2$
• Character orbit: 2240.l
• Analytic conductor: $17.886$
• Analytic rank: $0$
• Dimension: $24$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 2240 = 2^{6} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2240.l (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(17.8864900528\)
Analytic rank:	\(0\)
Dimension:	\(24\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 24 q - 4 q^{5} + 12 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
1569.1		0		−3.11575				0		−0.660542	−	2.13628i		0				1.00000i		0		6.70793				0
1569.2		0		−3.11575				0		−0.660542	+	2.13628i		0			−	1.00000i		0		6.70793				0
1569.3		0		−2.41750				0		−1.94498	−	1.10320i		0			−	1.00000i		0		2.84431				0
1569.4		0		−2.41750				0		−1.94498	+	1.10320i		0				1.00000i		0		2.84431				0
1569.5		0		−1.58895				0		1.82232	−	1.29582i		0				1.00000i		0		−0.475223				0
1569.6		0		−1.58895				0		1.82232	+	1.29582i		0			−	1.00000i		0		−0.475223				0
1569.7		0		−1.29255				0		0.437032	−	2.19294i		0			−	1.00000i		0		−1.32931				0
1569.8		0		−1.29255				0		0.437032	+	2.19294i		0				1.00000i		0		−1.32931				0
1569.9		0		−1.09381				0		−2.20510	−	0.370875i		0				1.00000i		0		−1.80358				0
1569.10		0		−1.09381				0		−2.20510	+	0.370875i		0			−	1.00000i		0		−1.80358				0
1569.11		0		−0.236390				0		1.55127	+	1.61046i		0			−	1.00000i		0		−2.94412				0
1569.12		0		−0.236390				0		1.55127	−	1.61046i		0				1.00000i		0		−2.94412				0
1569.13		0		0.236390				0		1.55127	−	1.61046i		0			−	1.00000i		0		−2.94412				0
1569.14		0		0.236390				0		1.55127	+	1.61046i		0				1.00000i		0		−2.94412				0
1569.15		0		1.09381				0		−2.20510	+	0.370875i		0				1.00000i		0		−1.80358				0
1569.16		0		1.09381				0		−2.20510	−	0.370875i		0			−	1.00000i		0		−1.80358				0
1569.17		0		1.29255				0		0.437032	+	2.19294i		0			−	1.00000i		0		−1.32931				0
1569.18		0		1.29255				0		0.437032	−	2.19294i		0				1.00000i		0		−1.32931				0
1569.19		0		1.58895				0		1.82232	+	1.29582i		0				1.00000i		0		−0.475223				0
1569.20		0		1.58895				0		1.82232	−	1.29582i		0			−	1.00000i		0		−0.475223				0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
4.b	odd	2	1	inner
40.e	odd	2	1	inner
40.f	even	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	2240.2.l.c	✓	24
4.b	odd	2	1	inner	2240.2.l.c	✓	24
5.b	even	2	1		2240.2.l.d	yes	24
8.b	even	2	1		2240.2.l.d	yes	24
8.d	odd	2	1		2240.2.l.d	yes	24
20.d	odd	2	1		2240.2.l.d	yes	24
40.e	odd	2	1	inner	2240.2.l.c	✓	24
40.f	even	2	1	inner	2240.2.l.c	✓	24

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
2240.2.l.c	✓	24	1.a	even	1	1	trivial
2240.2.l.c	✓	24	4.b	odd	2	1	inner
2240.2.l.c	✓	24	40.e	odd	2	1	inner
2240.2.l.c	✓	24	40.f	even	2	1	inner
2240.2.l.d	yes	24	5.b	even	2	1
2240.2.l.d	yes	24	8.b	even	2	1
2240.2.l.d	yes	24	8.d	odd	2	1
2240.2.l.d	yes	24	20.d	odd	2	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(2240, [\chi])\):

\( T_{3}^{12} - 21T_{3}^{10} + 151T_{3}^{8} - 463T_{3}^{6} + 628T_{3}^{4} - 320T_{3}^{2} + 16 \)

\( T_{13}^{6} + T_{13}^{5} - 33T_{13}^{4} + 3T_{13}^{3} + 260T_{13}^{2} - 124T_{13} - 356 \)