Newform orbit 3420.2.bj.d

• Label: 3420.2.bj.d
• Level: $3420$
• Weight: $2$
• Character orbit: 3420.bj
• Analytic conductor: $27.309$
• Analytic rank: $0$
• Dimension: $32$
• Inner twists: $4$

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:	\(32\)
Relative dimension:	\(16\) over \(\Q(\zeta_{6})\)
Twist minimal:	no (minimal twist has level 1140)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) 32 * q + 4 * q^11 + 12 * q^19 - 12 * q^25 - 22 * q^29 - 56 * q^31 + 2 * q^35 + 16 * q^41 - 88 * q^49 - 14 * q^55 + 86 * q^59 + 6 * q^61 - 36 * q^65 - 10 * q^71 + 50 * q^79 + 30 * q^85 - 34 * q^89 + 4 * q^91 - 46 * q^95

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		−2.04519	+	0.903992i		0				0.920170i		0			0			0
1189.2		0			0			0		−1.97786	−	1.04311i		0			−	1.20000i		0			0			0
1189.3		0			0			0		−1.60262	+	1.55936i		0			−	4.44246i		0			0			0
1189.4		0			0			0		−1.54855	+	1.61307i		0				3.05973i		0			0			0
1189.5		0			0			0		−1.18735	−	1.89478i		0				0.635261i		0			0			0
1189.6		0			0			0		−0.842697	−	2.07120i		0				4.65052i		0			0			0
1189.7		0			0			0		−0.622684	+	2.14762i		0			−	3.05973i		0			0			0
1189.8		0			0			0		−0.589297	−	2.15702i		0			−	4.17007i		0			0			0
1189.9		0			0			0		−0.549131	+	2.16759i		0				4.44246i		0			0			0
1189.10		0			0			0		0.239714	+	2.22318i		0			−	0.920170i		0			0			0
1189.11		0			0			0		0.886302	−	2.05292i		0				2.68244i		0			0			0
1189.12		0			0			0		1.33473	−	1.79402i		0			−	2.68244i		0			0			0
1189.13		0			0			0		1.89229	+	1.19132i		0				1.20000i		0			0			0
1189.14		0			0			0		2.16268	−	0.568163i		0				4.17007i		0			0			0
1189.15		0			0			0		2.21506	−	0.305802i		0			−	4.65052i		0			0			0
1189.16		0			0			0		2.23460	+	0.0808834i		0			−	0.635261i		0			0			0
2629.1		0			0			0		−2.04519	−	0.903992i		0			−	0.920170i		0			0			0
2629.2		0			0			0		−1.97786	+	1.04311i		0				1.20000i		0			0			0
2629.3		0			0			0		−1.60262	−	1.55936i		0				4.44246i		0			0			0
2629.4		0			0			0		−1.54855	−	1.61307i		0			−	3.05973i		0			0			0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.b	even	2	1	inner
19.c	even	3	1	inner
95.i	even	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.d		32
3.b	odd	2	1		1140.2.bg.c	✓	32
5.b	even	2	1	inner	3420.2.bj.d		32
15.d	odd	2	1		1140.2.bg.c	✓	32
19.c	even	3	1	inner	3420.2.bj.d		32
57.h	odd	6	1		1140.2.bg.c	✓	32
95.i	even	6	1	inner	3420.2.bj.d		32
285.n	odd	6	1		1140.2.bg.c	✓	32

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
1140.2.bg.c	✓	32	3.b	odd	2	1
1140.2.bg.c	✓	32	15.d	odd	2	1
1140.2.bg.c	✓	32	57.h	odd	6	1
1140.2.bg.c	✓	32	285.n	odd	6	1
3420.2.bj.d		32	1.a	even	1	1	trivial
3420.2.bj.d		32	5.b	even	2	1	inner
3420.2.bj.d		32	19.c	even	3	1	inner
3420.2.bj.d		32	95.i	even	6	1	inner

Hecke kernels

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

T7^16 + 78*T7^14 + 2391*T7^12 + 36400*T7^10 + 286487*T7^8 + 1104414*T7^6 + 1788673*T7^4 + 1169476*T7^2 + 246016

\( T_{11}^{8} - T_{11}^{7} - 44T_{11}^{6} - 6T_{11}^{5} + 524T_{11}^{4} + 428T_{11}^{3} - 1020T_{11}^{2} - 204T_{11} + 256 \)