Newform orbit 3420.2.e.b

• Label: 3420.2.e.b
• Level: $3420$
• Weight: $2$
• Character orbit: 3420.e
• Analytic conductor: $27.309$
• Analytic rank: $0$
• Dimension: $24$
• 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.e (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(27.3088374913\)
Analytic rank:	\(0\)
Dimension:	\(24\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

$q$-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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
1709.1		0			0			0		−2.20595	−	0.365789i		0			−	2.31277i		0			0			0
1709.2		0			0			0		−2.20595	−	0.365789i		0			−	2.31277i		0			0			0
1709.3		0			0			0		−2.20595	+	0.365789i		0				2.31277i		0			0			0
1709.4		0			0			0		−2.20595	+	0.365789i		0				2.31277i		0			0			0
1709.5		0			0			0		−1.33763	−	1.79186i		0				0.505147i		0			0			0
1709.6		0			0			0		−1.33763	−	1.79186i		0				0.505147i		0			0			0
1709.7		0			0			0		−1.33763	+	1.79186i		0			−	0.505147i		0			0			0
1709.8		0			0			0		−1.33763	+	1.79186i		0			−	0.505147i		0			0			0
1709.9		0			0			0		−0.586990	−	2.15765i		0				2.09665i		0			0			0
1709.10		0			0			0		−0.586990	−	2.15765i		0				2.09665i		0			0			0
1709.11		0			0			0		−0.586990	+	2.15765i		0			−	2.09665i		0			0			0
1709.12		0			0			0		−0.586990	+	2.15765i		0			−	2.09665i		0			0			0
1709.13		0			0			0		0.586990	−	2.15765i		0			−	2.09665i		0			0			0
1709.14		0			0			0		0.586990	−	2.15765i		0			−	2.09665i		0			0			0
1709.15		0			0			0		0.586990	+	2.15765i		0				2.09665i		0			0			0
1709.16		0			0			0		0.586990	+	2.15765i		0				2.09665i		0			0			0
1709.17		0			0			0		1.33763	−	1.79186i		0			−	0.505147i		0			0			0
1709.18		0			0			0		1.33763	−	1.79186i		0			−	0.505147i		0			0			0
1709.19		0			0			0		1.33763	+	1.79186i		0				0.505147i		0			0			0
1709.20		0			0			0		1.33763	+	1.79186i		0				0.505147i		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.b	odd	2	1	inner
57.d	even	2	1	inner
95.d	odd	2	1	inner
285.b	even	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	3420.2.e.b	✓	24
3.b	odd	2	1	inner	3420.2.e.b	✓	24
5.b	even	2	1	inner	3420.2.e.b	✓	24
15.d	odd	2	1	inner	3420.2.e.b	✓	24
19.b	odd	2	1	inner	3420.2.e.b	✓	24
57.d	even	2	1	inner	3420.2.e.b	✓	24
95.d	odd	2	1	inner	3420.2.e.b	✓	24
285.b	even	2	1	inner	3420.2.e.b	✓	24

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
3420.2.e.b	✓	24	1.a	even	1	1	trivial
3420.2.e.b	✓	24	3.b	odd	2	1	inner
3420.2.e.b	✓	24	5.b	even	2	1	inner
3420.2.e.b	✓	24	15.d	odd	2	1	inner
3420.2.e.b	✓	24	19.b	odd	2	1	inner
3420.2.e.b	✓	24	57.d	even	2	1	inner
3420.2.e.b	✓	24	95.d	odd	2	1	inner
3420.2.e.b	✓	24	285.b	even	2	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{7}^{6} + 10T_{7}^{4} + 26T_{7}^{2} + 6 \) acting on \(S_{2}^{\mathrm{new}}(3420, [\chi])\).