Newform orbit 2340.2.bn.a

• Label: 2340.2.bn.a
• Level: $2340$
• Weight: $2$
• Character orbit: 2340.bn
• Analytic conductor: $18.685$
• Analytic rank: $0$
• Dimension: $56$
• Inner twists: $8$

Newspace parameters

Level:	\( N \)	\(=\)	\( 2340 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2340.bn (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(18.6849940730\)
Analytic rank:	\(0\)
Dimension:	\(56\)
Relative dimension:	\(28\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 56 q + 12 q^{13} + 16 q^{43} - 32 q^{55} - 48 q^{61}+O(q^{100}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
233.1		0			0			0		−2.21982	−	0.269090i		0		−0.661260	−	0.661260i		0			0			0
233.2		0			0			0		−2.21982	−	0.269090i		0		0.661260	+	0.661260i		0			0			0
233.3		0			0			0		−2.14455	−	0.633154i		0		0.0901279	+	0.0901279i		0			0			0
233.4		0			0			0		−2.14455	−	0.633154i		0		−0.0901279	−	0.0901279i		0			0			0
233.5		0			0			0		−1.82617	+	1.29039i		0		3.01029	+	3.01029i		0			0			0
233.6		0			0			0		−1.82617	+	1.29039i		0		−3.01029	−	3.01029i		0			0			0
233.7		0			0			0		−1.72541	−	1.42231i		0		−2.73050	−	2.73050i		0			0			0
233.8		0			0			0		−1.72541	−	1.42231i		0		2.73050	+	2.73050i		0			0			0
233.9		0			0			0		−0.940412	+	2.02870i		0		−1.11300	−	1.11300i		0			0			0
233.10		0			0			0		−0.940412	+	2.02870i		0		1.11300	+	1.11300i		0			0			0
233.11		0			0			0		−0.860921	−	2.06369i		0		3.53976	+	3.53976i		0			0			0
233.12		0			0			0		−0.860921	−	2.06369i		0		−3.53976	−	3.53976i		0			0			0
233.13		0			0			0		−0.189234	+	2.22805i		0		−0.518144	−	0.518144i		0			0			0
233.14		0			0			0		−0.189234	+	2.22805i		0		0.518144	+	0.518144i		0			0			0
233.15		0			0			0		0.189234	−	2.22805i		0		−0.518144	−	0.518144i		0			0			0
233.16		0			0			0		0.189234	−	2.22805i		0		0.518144	+	0.518144i		0			0			0
233.17		0			0			0		0.860921	+	2.06369i		0		3.53976	+	3.53976i		0			0			0
233.18		0			0			0		0.860921	+	2.06369i		0		−3.53976	−	3.53976i		0			0			0
233.19		0			0			0		0.940412	−	2.02870i		0		−1.11300	−	1.11300i		0			0			0
233.20		0			0			0		0.940412	−	2.02870i		0		1.11300	+	1.11300i		0			0			0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
5.c	odd	4	1	inner
13.b	even	2	1	inner
15.e	even	4	1	inner
39.d	odd	2	1	inner
65.h	odd	4	1	inner
195.s	even	4	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	2340.2.bn.a	✓	56
3.b	odd	2	1	inner	2340.2.bn.a	✓	56
5.c	odd	4	1	inner	2340.2.bn.a	✓	56
13.b	even	2	1	inner	2340.2.bn.a	✓	56
15.e	even	4	1	inner	2340.2.bn.a	✓	56
39.d	odd	2	1	inner	2340.2.bn.a	✓	56
65.h	odd	4	1	inner	2340.2.bn.a	✓	56
195.s	even	4	1	inner	2340.2.bn.a	✓	56

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
2340.2.bn.a	✓	56	1.a	even	1	1	trivial
2340.2.bn.a	✓	56	3.b	odd	2	1	inner
2340.2.bn.a	✓	56	5.c	odd	4	1	inner
2340.2.bn.a	✓	56	13.b	even	2	1	inner
2340.2.bn.a	✓	56	15.e	even	4	1	inner
2340.2.bn.a	✓	56	39.d	odd	2	1	inner
2340.2.bn.a	✓	56	65.h	odd	4	1	inner
2340.2.bn.a	✓	56	195.s	even	4	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(2340, [\chi])\).