Newform orbit 1760.2.f.d

• Label: 1760.2.f.d
• Level: $1760$
• Weight: $2$
• Character orbit: 1760.f
• Analytic conductor: $14.054$
• Analytic rank: $0$
• Dimension: $24$
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1760 = 2^{5} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1760.f (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(14.0536707557\)
Analytic rank:	\(0\)
Dimension:	\(24\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 24 q - 24 q^{5} - 32 q^{9} + 24 q^{25} + 32 q^{33} + 24 q^{37} + 32 q^{45} + 16 q^{49} + 8 q^{53} - 16 q^{69} + 24 q^{77} + 24 q^{81} - 24 q^{89} + 8 q^{93} + 48 q^{97}+O(q^{100}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
351.1		0			−	2.97875i		0		−1.00000				0		−4.81963				0		−5.87292				0
351.2		0				2.97875i		0		−1.00000				0		−4.81963				0		−5.87292				0
351.3		0			−	0.664406i		0		−1.00000				0		−3.22449				0		2.55856				0
351.4		0				0.664406i		0		−1.00000				0		−3.22449				0		2.55856				0
351.5		0			−	2.43031i		0		−1.00000				0		2.50020				0		−2.90640				0
351.6		0				2.43031i		0		−1.00000				0		2.50020				0		−2.90640				0
351.7		0			−	2.84742i		0		−1.00000				0		−0.280035				0		−5.10782				0
351.8		0				2.84742i		0		−1.00000				0		−0.280035				0		−5.10782				0
351.9		0			−	1.59277i		0		−1.00000				0		−1.92830				0		0.463073				0
351.10		0				1.59277i		0		−1.00000				0		−1.92830				0		0.463073				0
351.11		0			−	0.366738i		0		−1.00000				0		−1.52516				0		2.86550				0
351.12		0				0.366738i		0		−1.00000				0		−1.52516				0		2.86550				0
351.13		0			−	0.366738i		0		−1.00000				0		1.52516				0		2.86550				0
351.14		0				0.366738i		0		−1.00000				0		1.52516				0		2.86550				0
351.15		0			−	1.59277i		0		−1.00000				0		1.92830				0		0.463073				0
351.16		0				1.59277i		0		−1.00000				0		1.92830				0		0.463073				0
351.17		0			−	2.84742i		0		−1.00000				0		0.280035				0		−5.10782				0
351.18		0				2.84742i		0		−1.00000				0		0.280035				0		−5.10782				0
351.19		0			−	2.43031i		0		−1.00000				0		−2.50020				0		−2.90640				0
351.20		0				2.43031i		0		−1.00000				0		−2.50020				0		−2.90640				0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
4.b	odd	2	1	inner
11.b	odd	2	1	inner
44.c	even	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1760.2.f.d	✓	24
4.b	odd	2	1	inner	1760.2.f.d	✓	24
8.b	even	2	1		3520.2.f.m		24
8.d	odd	2	1		3520.2.f.m		24
11.b	odd	2	1	inner	1760.2.f.d	✓	24
44.c	even	2	1	inner	1760.2.f.d	✓	24
88.b	odd	2	1		3520.2.f.m		24
88.g	even	2	1		3520.2.f.m		24

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
1760.2.f.d	✓	24	1.a	even	1	1	trivial
1760.2.f.d	✓	24	4.b	odd	2	1	inner
1760.2.f.d	✓	24	11.b	odd	2	1	inner
1760.2.f.d	✓	24	44.c	even	2	1	inner
3520.2.f.m		24	8.b	even	2	1
3520.2.f.m		24	8.d	odd	2	1
3520.2.f.m		24	88.b	odd	2	1
3520.2.f.m		24	88.g	even	2	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(1760, [\chi])\):

\( T_{3}^{12} + 26T_{3}^{10} + 245T_{3}^{8} + 996T_{3}^{6} + 1588T_{3}^{4} + 672T_{3}^{2} + 64 \)

\( T_{7}^{12} - 46T_{7}^{10} + 705T_{7}^{8} - 4640T_{7}^{6} + 13392T_{7}^{4} - 14080T_{7}^{2} + 1024 \)