Newform orbit 1760.2.l.c

• Label: 1760.2.l.c
• Level: $1760$
• Weight: $2$
• Character orbit: 1760.l
• Analytic conductor: $14.054$
• Analytic rank: $0$
• Dimension: $56$
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1760 = 2^{5} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1760.l (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(14.0536707557\)
Analytic rank:	\(0\)
Dimension:	\(56\)
Twist minimal:	no (minimal twist has level 440)
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.

\(\operatorname{Tr}(f)(q) = \) \( 56 q + 56 q^{9} + 8 q^{15} + 16 q^{25} + 16 q^{39} - 32 q^{41} - 24 q^{49} + 8 q^{55} - 32 q^{65} - 48 q^{71} + 32 q^{79} + 88 q^{81} - 16 q^{89} - 24 q^{95}+O(q^{100}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
529.1		0		−3.29264				0		−1.69658	−	1.45657i		0			−	3.97318i		0		7.84147				0
529.2		0		−3.29264				0		−1.69658	+	1.45657i		0				3.97318i		0		7.84147				0
529.3		0		−3.02021				0		−0.177003	+	2.22905i		0			−	1.23027i		0		6.12165				0
529.4		0		−3.02021				0		−0.177003	−	2.22905i		0				1.23027i		0		6.12165				0
529.5		0		−2.84044				0		2.20930	+	0.344972i		0				1.82515i		0		5.06811				0
529.6		0		−2.84044				0		2.20930	−	0.344972i		0			−	1.82515i		0		5.06811				0
529.7		0		−2.58970				0		0.464619	−	2.18727i		0				1.54883i		0		3.70654				0
529.8		0		−2.58970				0		0.464619	+	2.18727i		0			−	1.54883i		0		3.70654				0
529.9		0		−2.45029				0		−1.88833	−	1.19759i		0				4.10058i		0		3.00393				0
529.10		0		−2.45029				0		−1.88833	+	1.19759i		0			−	4.10058i		0		3.00393				0
529.11		0		−2.29285				0		−2.06667	−	0.853738i		0				0.918608i		0		2.25717				0
529.12		0		−2.29285				0		−2.06667	+	0.853738i		0			−	0.918608i		0		2.25717				0
529.13		0		−2.02800				0		1.17627	−	1.90168i		0			−	1.20527i		0		1.11278				0
529.14		0		−2.02800				0		1.17627	+	1.90168i		0				1.20527i		0		1.11278				0
529.15		0		−1.55031				0		2.09467	+	0.782535i		0				3.88217i		0		−0.596534				0
529.16		0		−1.55031				0		2.09467	−	0.782535i		0			−	3.88217i		0		−0.596534				0
529.17		0		−1.10235				0		−1.70933	−	1.44159i		0				3.87299i		0		−1.78481				0
529.18		0		−1.10235				0		−1.70933	+	1.44159i		0			−	3.87299i		0		−1.78481				0
529.19		0		−0.955334				0		2.20319	+	0.382012i		0				0.432693i		0		−2.08734				0
529.20		0		−0.955334				0		2.20319	−	0.382012i		0			−	0.432693i		0		−2.08734				0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.b	even	2	1	inner
8.b	even	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	1760.2.l.c		56
4.b	odd	2	1		440.2.l.c	✓	56
5.b	even	2	1	inner	1760.2.l.c		56
8.b	even	2	1	inner	1760.2.l.c		56
8.d	odd	2	1		440.2.l.c	✓	56
20.d	odd	2	1		440.2.l.c	✓	56
40.e	odd	2	1		440.2.l.c	✓	56
40.f	even	2	1	inner	1760.2.l.c		56

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
440.2.l.c	✓	56	4.b	odd	2	1
440.2.l.c	✓	56	8.d	odd	2	1
440.2.l.c	✓	56	20.d	odd	2	1
440.2.l.c	✓	56	40.e	odd	2	1
1760.2.l.c		56	1.a	even	1	1	trivial
1760.2.l.c		56	5.b	even	2	1	inner
1760.2.l.c		56	8.b	even	2	1	inner
1760.2.l.c		56	40.f	even	2	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T3^28 - 56*T3^26 + 1368*T3^24 - 19172*T3^22 + 170574*T3^20 - 1007388*T3^18 + 4016420*T3^16 - 10808556*T3^14 + 19407353*T3^12 - 22827564*T3^10 + 17203884*T3^8 - 8067760*T3^6 + 2245520*T3^4 - 336384*T3^2 + 20736