Newform orbit 1360.2.bn.a

• Label: 1360.2.bn.a
• Level: $1360$
• Weight: $2$
• Character orbit: 1360.bn
• Analytic conductor: $10.860$
• Analytic rank: $0$
• Dimension: $32$
• 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:	\(32\)
Relative dimension:	\(16\) 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.

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

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		−2.19121	+	2.19121i		0		1.49569	+	1.66220i		0		2.96099	+	2.96099i		0			−	6.60283i		0
783.2		0		−1.79808	+	1.79808i		0		−0.494871	−	2.18062i		0		0.552628	+	0.552628i		0			−	3.46620i		0
783.3		0		−1.75921	+	1.75921i		0		0.152427	+	2.23087i		0		−3.52764	−	3.52764i		0			−	3.18965i		0
783.4		0		−1.62263	+	1.62263i		0		1.74625	−	1.39664i		0		−1.20200	−	1.20200i		0			−	2.26589i		0
783.5		0		−1.11416	+	1.11416i		0		−2.20290	+	0.383718i		0		0.0454135	+	0.0454135i		0				0.517277i		0
783.6		0		−0.708995	+	0.708995i		0		−1.24756	+	1.85569i		0		1.80520	+	1.80520i		0				1.99465i		0
783.7		0		−0.656289	+	0.656289i		0		1.83824	+	1.27314i		0		0.769074	+	0.769074i		0				2.13857i		0
783.8		0		−0.250928	+	0.250928i		0		−1.28728	−	1.82836i		0		3.34453	+	3.34453i		0				2.87407i		0
783.9		0		0.250928	−	0.250928i		0		−1.28728	−	1.82836i		0		−3.34453	−	3.34453i		0				2.87407i		0
783.10		0		0.656289	−	0.656289i		0		1.83824	+	1.27314i		0		−0.769074	−	0.769074i		0				2.13857i		0
783.11		0		0.708995	−	0.708995i		0		−1.24756	+	1.85569i		0		−1.80520	−	1.80520i		0				1.99465i		0
783.12		0		1.11416	−	1.11416i		0		−2.20290	+	0.383718i		0		−0.0454135	−	0.0454135i		0				0.517277i		0
783.13		0		1.62263	−	1.62263i		0		1.74625	−	1.39664i		0		1.20200	+	1.20200i		0			−	2.26589i		0
783.14		0		1.75921	−	1.75921i		0		0.152427	+	2.23087i		0		3.52764	+	3.52764i		0			−	3.18965i		0
783.15		0		1.79808	−	1.79808i		0		−0.494871	−	2.18062i		0		−0.552628	−	0.552628i		0			−	3.46620i		0
783.16		0		2.19121	−	2.19121i		0		1.49569	+	1.66220i		0		−2.96099	−	2.96099i		0			−	6.60283i		0
1327.1		0		−2.19121	−	2.19121i		0		1.49569	−	1.66220i		0		2.96099	−	2.96099i		0				6.60283i		0
1327.2		0		−1.79808	−	1.79808i		0		−0.494871	+	2.18062i		0		0.552628	−	0.552628i		0				3.46620i		0
1327.3		0		−1.75921	−	1.75921i		0		0.152427	−	2.23087i		0		−3.52764	+	3.52764i		0				3.18965i		0
1327.4		0		−1.62263	−	1.62263i		0		1.74625	+	1.39664i		0		−1.20200	+	1.20200i		0				2.26589i		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.a	✓	32
4.b	odd	2	1	inner	1360.2.bn.a	✓	32
5.c	odd	4	1	inner	1360.2.bn.a	✓	32
20.e	even	4	1	inner	1360.2.bn.a	✓	32

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
1360.2.bn.a	✓	32	1.a	even	1	1	trivial
1360.2.bn.a	✓	32	4.b	odd	2	1	inner
1360.2.bn.a	✓	32	5.c	odd	4	1	inner
1360.2.bn.a	✓	32	20.e	even	4	1	inner