Newform orbit 2340.2.de.b

• Label: 2340.2.de.b
• Level: $2340$
• Weight: $2$
• Character orbit: 2340.de
• Analytic conductor: $18.685$
• Analytic rank: $0$
• Dimension: $24$
• 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.de (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(18.6849940730\)
Analytic rank:	\(0\)
Dimension:	\(24\)
Relative dimension:	\(12\) over \(\Q(\zeta_{6})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 24 q+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
289.1		0			0			0		−2.17422	+	0.522282i		0		−1.63836	−	0.945908i		0			0			0
289.2		0			0			0		−2.17422	−	0.522282i		0		1.63836	+	0.945908i		0			0			0
289.3		0			0			0		−1.76134	−	1.37757i		0		−3.09529	−	1.78707i		0			0			0
289.4		0			0			0		−1.76134	+	1.37757i		0		3.09529	+	1.78707i		0			0			0
289.5		0			0			0		−0.412881	−	2.19762i		0		−1.40888	−	0.813416i		0			0			0
289.6		0			0			0		−0.412881	+	2.19762i		0		1.40888	+	0.813416i		0			0			0
289.7		0			0			0		0.412881	−	2.19762i		0		1.40888	+	0.813416i		0			0			0
289.8		0			0			0		0.412881	+	2.19762i		0		−1.40888	−	0.813416i		0			0			0
289.9		0			0			0		1.76134	+	1.37757i		0		−3.09529	−	1.78707i		0			0			0
289.10		0			0			0		1.76134	−	1.37757i		0		3.09529	+	1.78707i		0			0			0
289.11		0			0			0		2.17422	−	0.522282i		0		−1.63836	−	0.945908i		0			0			0
289.12		0			0			0		2.17422	+	0.522282i		0		1.63836	+	0.945908i		0			0			0
2089.1		0			0			0		−2.17422	−	0.522282i		0		−1.63836	+	0.945908i		0			0			0
2089.2		0			0			0		−2.17422	+	0.522282i		0		1.63836	−	0.945908i		0			0			0
2089.3		0			0			0		−1.76134	+	1.37757i		0		−3.09529	+	1.78707i		0			0			0
2089.4		0			0			0		−1.76134	−	1.37757i		0		3.09529	−	1.78707i		0			0			0
2089.5		0			0			0		−0.412881	+	2.19762i		0		−1.40888	+	0.813416i		0			0			0
2089.6		0			0			0		−0.412881	−	2.19762i		0		1.40888	−	0.813416i		0			0			0
2089.7		0			0			0		0.412881	+	2.19762i		0		1.40888	−	0.813416i		0			0			0
2089.8		0			0			0		0.412881	−	2.19762i		0		−1.40888	+	0.813416i		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.c	even	3	1	inner
15.d	odd	2	1	inner
39.i	odd	6	1	inner
65.n	even	6	1	inner
195.x	odd	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	2340.2.de.b	✓	24
3.b	odd	2	1	inner	2340.2.de.b	✓	24
5.b	even	2	1	inner	2340.2.de.b	✓	24
13.c	even	3	1	inner	2340.2.de.b	✓	24
15.d	odd	2	1	inner	2340.2.de.b	✓	24
39.i	odd	6	1	inner	2340.2.de.b	✓	24
65.n	even	6	1	inner	2340.2.de.b	✓	24
195.x	odd	6	1	inner	2340.2.de.b	✓	24

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
2340.2.de.b	✓	24	1.a	even	1	1	trivial
2340.2.de.b	✓	24	3.b	odd	2	1	inner
2340.2.de.b	✓	24	5.b	even	2	1	inner
2340.2.de.b	✓	24	13.c	even	3	1	inner
2340.2.de.b	✓	24	15.d	odd	2	1	inner
2340.2.de.b	✓	24	39.i	odd	6	1	inner
2340.2.de.b	✓	24	65.n	even	6	1	inner
2340.2.de.b	✓	24	195.x	odd	6	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{7}^{12} - 19T_{7}^{10} + 272T_{7}^{8} - 1449T_{7}^{6} + 5622T_{7}^{4} - 10769T_{7}^{2} + 14641 \) acting on \(S_{2}^{\mathrm{new}}(2340, [\chi])\).