Newform orbit 1360.2.bn.b

• Label: 1360.2.bn.b
• Level: $1360$
• Weight: $2$
• Character orbit: 1360.bn
• Analytic conductor: $10.860$
• Analytic rank: $0$
• Dimension: $64$
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1360 = 2^{4} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1360.bn (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(10.8596546749\)
Analytic rank:	\(0\)
Dimension:	\(64\)
Relative dimension:	\(32\) over \(\Q(i)\)
Twist minimal:	yes
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.

\(\operatorname{Tr}(f)(q) = \) \( 64 q - 8 q^{13} + 64 q^{21} + 24 q^{25} - 56 q^{33} - 32 q^{41} - 24 q^{45} + 64 q^{53} + 64 q^{57} - 16 q^{61} + 40 q^{65} + 56 q^{73} - 40 q^{77} - 176 q^{81} - 104 q^{93} - 16 q^{97}+O(q^{100}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
783.1		0		−2.31479	+	2.31479i		0		1.46598	+	1.68846i		0		0.128431	+	0.128431i		0			−	7.71653i		0
783.2		0		−2.30888	+	2.30888i		0		0.0693728	−	2.23499i		0		−2.72720	−	2.72720i		0			−	7.66182i		0
783.3		0		−2.07229	+	2.07229i		0		−1.97965	+	1.03971i		0		−2.03728	−	2.03728i		0			−	5.58873i		0
783.4		0		−2.04074	+	2.04074i		0		1.96591	−	1.06545i		0		0.352171	+	0.352171i		0			−	5.32927i		0
783.5		0		−1.88050	+	1.88050i		0		−2.14494	−	0.631845i		0		3.05902	+	3.05902i		0			−	4.07260i		0
783.6		0		−1.48210	+	1.48210i		0		−1.67948	−	1.47627i		0		−2.15811	−	2.15811i		0			−	1.39324i		0
783.7		0		−1.30895	+	1.30895i		0		−0.435207	+	2.19331i		0		−0.618757	−	0.618757i		0			−	0.426688i		0
783.8		0		−1.23944	+	1.23944i		0		−2.23562	+	0.0446591i		0		−1.02188	−	1.02188i		0			−	0.0724006i		0
783.9		0		−1.17914	+	1.17914i		0		1.34637	−	1.78530i		0		2.63836	+	2.63836i		0				0.219276i		0
783.10		0		−0.937094	+	0.937094i		0		2.07857	+	0.824358i		0		−2.11676	−	2.11676i		0				1.24371i		0
783.11		0		−0.760463	+	0.760463i		0		2.15930	−	0.580879i		0		−3.49050	−	3.49050i		0				1.84339i		0
783.12		0		−0.742888	+	0.742888i		0		1.64465	+	1.51496i		0		2.47515	+	2.47515i		0				1.89624i		0
783.13		0		−0.552078	+	0.552078i		0		−1.19559	−	1.88960i		0		−0.0505973	−	0.0505973i		0				2.39042i		0
783.14		0		−0.386153	+	0.386153i		0		0.586384	+	2.15781i		0		1.19970	+	1.19970i		0				2.70177i		0
783.15		0		−0.124060	+	0.124060i		0		−2.20593	+	0.365900i		0		2.34724	+	2.34724i		0				2.96922i		0
783.16		0		−0.0370416	+	0.0370416i		0		0.559877	−	2.16484i		0		−0.355339	−	0.355339i		0				2.99726i		0
783.17		0		0.0370416	−	0.0370416i		0		0.559877	−	2.16484i		0		0.355339	+	0.355339i		0				2.99726i		0
783.18		0		0.124060	−	0.124060i		0		−2.20593	+	0.365900i		0		−2.34724	−	2.34724i		0				2.96922i		0
783.19		0		0.386153	−	0.386153i		0		0.586384	+	2.15781i		0		−1.19970	−	1.19970i		0				2.70177i		0
783.20		0		0.552078	−	0.552078i		0		−1.19559	−	1.88960i		0		0.0505973	+	0.0505973i		0				2.39042i		0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
4.b	odd	2	1	inner
5.c	odd	4	1	inner
20.e	even	4	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1360.2.bn.b	✓	64
4.b	odd	2	1	inner	1360.2.bn.b	✓	64
5.c	odd	4	1	inner	1360.2.bn.b	✓	64
20.e	even	4	1	inner	1360.2.bn.b	✓	64

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
1360.2.bn.b	✓	64	1.a	even	1	1	trivial
1360.2.bn.b	✓	64	4.b	odd	2	1	inner
1360.2.bn.b	✓	64	5.c	odd	4	1	inner
1360.2.bn.b	✓	64	20.e	even	4	1	inner