Newform orbit 3420.2.bj.e

• Label: 3420.2.bj.e
• Level: $3420$
• Weight: $2$
• Character orbit: 3420.bj
• Analytic conductor: $27.309$
• Analytic rank: $0$
• Dimension: $40$
• CM: no
• Inner twists: $8$

Newspace parameters

Level:	\( N \)	\(=\)	\( 3420 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3420.bj (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(27.3088374913\)
Analytic rank:	\(0\)
Dimension:	\(40\)
Relative dimension:	\(20\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 40 q+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
1189.1		0			0			0		−2.22922	+	0.174920i		0			−	3.23724i		0			0			0
1189.2		0			0			0		−2.22845	−	0.184465i		0				3.28838i		0			0			0
1189.3		0			0			0		−2.22321	−	0.239488i		0			−	1.46405i		0			0			0
1189.4		0			0			0		−1.75804	+	1.38178i		0				2.95630i		0			0			0
1189.5		0			0			0		−1.42631	+	1.72210i		0				2.19629i		0			0			0
1189.6		0			0			0		−1.31901	−	1.80561i		0				1.46405i		0			0			0
1189.7		0			0			0		−1.27397	−	1.83766i		0			−	3.28838i		0			0			0
1189.8		0			0			0		−0.963123	−	2.01802i		0				3.23724i		0			0			0
1189.9		0			0			0		−0.778229	+	2.09627i		0			−	2.19629i		0			0			0
1189.10		0			0			0		−0.317638	+	2.21339i		0			−	2.95630i		0			0			0
1189.11		0			0			0		0.317638	−	2.21339i		0			−	2.95630i		0			0			0
1189.12		0			0			0		0.778229	−	2.09627i		0			−	2.19629i		0			0			0
1189.13		0			0			0		0.963123	+	2.01802i		0				3.23724i		0			0			0
1189.14		0			0			0		1.27397	+	1.83766i		0			−	3.28838i		0			0			0
1189.15		0			0			0		1.31901	+	1.80561i		0				1.46405i		0			0			0
1189.16		0			0			0		1.42631	−	1.72210i		0				2.19629i		0			0			0
1189.17		0			0			0		1.75804	−	1.38178i		0				2.95630i		0			0			0
1189.18		0			0			0		2.22321	+	0.239488i		0			−	1.46405i		0			0			0
1189.19		0			0			0		2.22845	+	0.184465i		0				3.28838i		0			0			0
1189.20		0			0			0		2.22922	−	0.174920i		0			−	3.23724i		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
15.d	odd	2	1	inner
19.c	even	3	1	inner
57.h	odd	6	1	inner
95.i	even	6	1	inner
285.n	odd	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	3420.2.bj.e	✓	40
3.b	odd	2	1	inner	3420.2.bj.e	✓	40
5.b	even	2	1	inner	3420.2.bj.e	✓	40
15.d	odd	2	1	inner	3420.2.bj.e	✓	40
19.c	even	3	1	inner	3420.2.bj.e	✓	40
57.h	odd	6	1	inner	3420.2.bj.e	✓	40
95.i	even	6	1	inner	3420.2.bj.e	✓	40
285.n	odd	6	1	inner	3420.2.bj.e	✓	40

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
3420.2.bj.e	✓	40	1.a	even	1	1	trivial
3420.2.bj.e	✓	40	3.b	odd	2	1	inner
3420.2.bj.e	✓	40	5.b	even	2	1	inner
3420.2.bj.e	✓	40	15.d	odd	2	1	inner
3420.2.bj.e	✓	40	19.c	even	3	1	inner
3420.2.bj.e	✓	40	57.h	odd	6	1	inner
3420.2.bj.e	✓	40	95.i	even	6	1	inner
3420.2.bj.e	✓	40	285.n	odd	6	1	inner

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(3420, [\chi])\):

\( T_{7}^{10} + 37T_{7}^{8} + 519T_{7}^{6} + 3387T_{7}^{4} + 9996T_{7}^{2} + 10240 \)

\( T_{11}^{10} - 45T_{11}^{8} + 550T_{11}^{6} - 2068T_{11}^{4} + 1316T_{11}^{2} - 64 \)