Newform orbit 2340.2.de.c

• Label: 2340.2.de.c
• Level: $2340$
• Weight: $2$
• Character orbit: 2340.de
• Analytic conductor: $18.685$
• Analytic rank: $0$
• Dimension: $32$
• CM: no
• Inner twists: $4$

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:	\(32\)
Relative dimension:	\(16\) over \(\Q(\zeta_{6})\)
Twist minimal:	no (minimal twist has level 780)
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.

\(\operatorname{Tr}(f)(q) = \) \( 32 q+O(q^{10}) \)

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		−2.08837	+	0.799202i		0		1.22448	+	0.706955i		0			0			0
289.2		0			0			0		−2.08837	−	0.799202i		0		−1.22448	−	0.706955i		0			0			0
289.3		0			0			0		−1.92732	+	1.13378i		0		3.95650	+	2.28429i		0			0			0
289.4		0			0			0		−1.92732	−	1.13378i		0		−3.95650	−	2.28429i		0			0			0
289.5		0			0			0		−0.878409	+	2.05631i		0		−3.96186	−	2.28738i		0			0			0
289.6		0			0			0		−0.878409	−	2.05631i		0		3.96186	+	2.28738i		0			0			0
289.7		0			0			0		−0.562170	−	2.16425i		0		2.51027	+	1.44931i		0			0			0
289.8		0			0			0		−0.562170	+	2.16425i		0		−2.51027	−	1.44931i		0			0			0
289.9		0			0			0		−0.0904816	+	2.23424i		0		2.69460	+	1.55573i		0			0			0
289.10		0			0			0		−0.0904816	−	2.23424i		0		−2.69460	−	1.55573i		0			0			0
289.11		0			0			0		1.71544	−	1.43431i		0		−2.34579	−	1.35434i		0			0			0
289.12		0			0			0		1.71544	+	1.43431i		0		2.34579	+	1.35434i		0			0			0
289.13		0			0			0		1.76371	−	1.37453i		0		−1.63668	−	0.944936i		0			0			0
289.14		0			0			0		1.76371	+	1.37453i		0		1.63668	+	0.944936i		0			0			0
289.15		0			0			0		2.06759	−	0.851510i		0		−0.952150	−	0.549724i		0			0			0
289.16		0			0			0		2.06759	+	0.851510i		0		0.952150	+	0.549724i		0			0			0
2089.1		0			0			0		−2.08837	−	0.799202i		0		1.22448	−	0.706955i		0			0			0
2089.2		0			0			0		−2.08837	+	0.799202i		0		−1.22448	+	0.706955i		0			0			0
2089.3		0			0			0		−1.92732	−	1.13378i		0		3.95650	−	2.28429i		0			0			0
2089.4		0			0			0		−1.92732	+	1.13378i		0		−3.95650	+	2.28429i		0			0			0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.b	even	2	1	inner
13.c	even	3	1	inner
65.n	even	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.c		32
3.b	odd	2	1		780.2.bx.a	✓	32
5.b	even	2	1	inner	2340.2.de.c		32
13.c	even	3	1	inner	2340.2.de.c		32
15.d	odd	2	1		780.2.bx.a	✓	32
15.e	even	4	1		3900.2.q.q		16
15.e	even	4	1		3900.2.q.r		16
39.i	odd	6	1		780.2.bx.a	✓	32
65.n	even	6	1	inner	2340.2.de.c		32
195.x	odd	6	1		780.2.bx.a	✓	32
195.bl	even	12	1		3900.2.q.q		16
195.bl	even	12	1		3900.2.q.r		16

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
780.2.bx.a	✓	32	3.b	odd	2	1
780.2.bx.a	✓	32	15.d	odd	2	1
780.2.bx.a	✓	32	39.i	odd	6	1
780.2.bx.a	✓	32	195.x	odd	6	1
2340.2.de.c		32	1.a	even	1	1	trivial
2340.2.de.c		32	5.b	even	2	1	inner
2340.2.de.c		32	13.c	even	3	1	inner
2340.2.de.c		32	65.n	even	6	1	inner
3900.2.q.q		16	15.e	even	4	1
3900.2.q.q		16	195.bl	even	12	1
3900.2.q.r		16	15.e	even	4	1
3900.2.q.r		16	195.bl	even	12	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T7^32 - 74*T7^30 + 3293*T7^28 - 95134*T7^26 + 2025634*T7^24 - 32000846*T7^22 + 391421493*T7^20 - 3700014186*T7^18 + 27484519410*T7^16 - 157898268002*T7^14 + 703860634765*T7^12 - 2349278824894*T7^10 + 5910960394721*T7^8 - 10506121271000*T7^6 + 13445770750000*T7^4 - 10437750000000*T7^2 + 5062500000000