Newform orbit 2340.2.bc.a

• Label: 2340.2.bc.a
• Level: $2340$
• Weight: $2$
• Character orbit: 2340.bc
• Analytic conductor: $18.685$
• Analytic rank: $0$
• Dimension: $56$
• CM: no
• Inner twists: $8$

Newspace parameters

Level:	\( N \)	\(=\)	\( 2340 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2340.bc (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 dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 56 q+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
629.1		0			0			0		−2.22721	−	0.198795i		0		−1.01960	+	1.01960i		0			0			0
629.2		0			0			0		−2.21980	+	0.269206i		0		−0.644393	+	0.644393i		0			0			0
629.3		0			0			0		−2.17955	+	0.499581i		0		3.20502	−	3.20502i		0			0			0
629.4		0			0			0		−2.10597	+	0.751602i		0		−0.282581	+	0.282581i		0			0			0
629.5		0			0			0		−1.90513	−	1.17067i		0		1.63133	−	1.63133i		0			0			0
629.6		0			0			0		−1.82913	+	1.28619i		0		−2.70086	+	2.70086i		0			0			0
629.7		0			0			0		−1.73294	−	1.41312i		0		−2.28851	+	2.28851i		0			0			0
629.8		0			0			0		−1.41312	−	1.73294i		0		2.28851	−	2.28851i		0			0			0
629.9		0			0			0		−1.28619	+	1.82913i		0		2.70086	−	2.70086i		0			0			0
629.10		0			0			0		−1.17067	−	1.90513i		0		−1.63133	+	1.63133i		0			0			0
629.11		0			0			0		−0.751602	+	2.10597i		0		0.282581	−	0.282581i		0			0			0
629.12		0			0			0		−0.499581	+	2.17955i		0		−3.20502	+	3.20502i		0			0			0
629.13		0			0			0		−0.269206	+	2.21980i		0		0.644393	−	0.644393i		0			0			0
629.14		0			0			0		−0.198795	−	2.22721i		0		1.01960	−	1.01960i		0			0			0
629.15		0			0			0		0.198795	+	2.22721i		0		1.01960	−	1.01960i		0			0			0
629.16		0			0			0		0.269206	−	2.21980i		0		0.644393	−	0.644393i		0			0			0
629.17		0			0			0		0.499581	−	2.17955i		0		−3.20502	+	3.20502i		0			0			0
629.18		0			0			0		0.751602	−	2.10597i		0		0.282581	−	0.282581i		0			0			0
629.19		0			0			0		1.17067	+	1.90513i		0		−1.63133	+	1.63133i		0			0			0
629.20		0			0			0		1.28619	−	1.82913i		0		2.70086	−	2.70086i		0			0			0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
5.b	even	2	1	inner
13.d	odd	4	1	inner
15.d	odd	2	1	inner
39.f	even	4	1	inner
65.g	odd	4	1	inner
195.n	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.bc.a	✓	56
3.b	odd	2	1	inner	2340.2.bc.a	✓	56
5.b	even	2	1	inner	2340.2.bc.a	✓	56
13.d	odd	4	1	inner	2340.2.bc.a	✓	56
15.d	odd	2	1	inner	2340.2.bc.a	✓	56
39.f	even	4	1	inner	2340.2.bc.a	✓	56
65.g	odd	4	1	inner	2340.2.bc.a	✓	56
195.n	even	4	1	inner	2340.2.bc.a	✓	56

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
2340.2.bc.a	✓	56	1.a	even	1	1	trivial
2340.2.bc.a	✓	56	3.b	odd	2	1	inner
2340.2.bc.a	✓	56	5.b	even	2	1	inner
2340.2.bc.a	✓	56	13.d	odd	4	1	inner
2340.2.bc.a	✓	56	15.d	odd	2	1	inner
2340.2.bc.a	✓	56	39.f	even	4	1	inner
2340.2.bc.a	✓	56	65.g	odd	4	1	inner
2340.2.bc.a	✓	56	195.n	even	4	1	inner

Hecke kernels

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