Newform orbit 5220.2.b.f

• Label: 5220.2.b.f
• Level: $5220$
• Weight: $2$
• Character orbit: 5220.b
• Analytic conductor: $41.682$
• Analytic rank: $0$
• Dimension: $24$
• Inner twists: $8$

Newspace parameters

Level:	\( N \)	\(=\)	\( 5220 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5220.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(41.6819098551\)
Analytic rank:	\(0\)
Dimension:	\(24\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 24 q + 48 q^{25} - 104 q^{49} - 80 q^{91}+O(q^{100}) \)

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		−2.10485	−	0.754717i		0				1.11057i		0			0			0
289.2		0			0			0		−2.10485	−	0.754717i		0				1.11057i		0			0			0
289.3		0			0			0		−2.10485	+	0.754717i		0			−	1.11057i		0			0			0
289.4		0			0			0		−2.10485	+	0.754717i		0			−	1.11057i		0			0			0
289.5		0			0			0		−1.90448	−	1.17173i		0				3.55878i		0			0			0
289.6		0			0			0		−1.90448	−	1.17173i		0				3.55878i		0			0			0
289.7		0			0			0		−1.90448	+	1.17173i		0			−	3.55878i		0			0			0
289.8		0			0			0		−1.90448	+	1.17173i		0			−	3.55878i		0			0			0
289.9		0			0			0		−1.56286	−	1.59920i		0			−	4.48349i		0			0			0
289.10		0			0			0		−1.56286	−	1.59920i		0			−	4.48349i		0			0			0
289.11		0			0			0		−1.56286	+	1.59920i		0				4.48349i		0			0			0
289.12		0			0			0		−1.56286	+	1.59920i		0				4.48349i		0			0			0
289.13		0			0			0		1.56286	−	1.59920i		0				4.48349i		0			0			0
289.14		0			0			0		1.56286	−	1.59920i		0				4.48349i		0			0			0
289.15		0			0			0		1.56286	+	1.59920i		0			−	4.48349i		0			0			0
289.16		0			0			0		1.56286	+	1.59920i		0			−	4.48349i		0			0			0
289.17		0			0			0		1.90448	−	1.17173i		0			−	3.55878i		0			0			0
289.18		0			0			0		1.90448	−	1.17173i		0			−	3.55878i		0			0			0
289.19		0			0			0		1.90448	+	1.17173i		0				3.55878i		0			0			0
289.20		0			0			0		1.90448	+	1.17173i		0				3.55878i		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
29.b	even	2	1	inner
87.d	odd	2	1	inner
145.d	even	2	1	inner
435.b	odd	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	5220.2.b.f	✓	24
3.b	odd	2	1	inner	5220.2.b.f	✓	24
5.b	even	2	1	inner	5220.2.b.f	✓	24
15.d	odd	2	1	inner	5220.2.b.f	✓	24
29.b	even	2	1	inner	5220.2.b.f	✓	24
87.d	odd	2	1	inner	5220.2.b.f	✓	24
145.d	even	2	1	inner	5220.2.b.f	✓	24
435.b	odd	2	1	inner	5220.2.b.f	✓	24

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
5220.2.b.f	✓	24	1.a	even	1	1	trivial
5220.2.b.f	✓	24	3.b	odd	2	1	inner
5220.2.b.f	✓	24	5.b	even	2	1	inner
5220.2.b.f	✓	24	15.d	odd	2	1	inner
5220.2.b.f	✓	24	29.b	even	2	1	inner
5220.2.b.f	✓	24	87.d	odd	2	1	inner
5220.2.b.f	✓	24	145.d	even	2	1	inner
5220.2.b.f	✓	24	435.b	odd	2	1	inner

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(5220, [\chi])\):

\( T_{7}^{6} + 34T_{7}^{4} + 295T_{7}^{2} + 314 \)

\( T_{17}^{6} - 74T_{17}^{4} + 1569T_{17}^{2} - 8164 \)

\( T_{37}^{6} - 122T_{37}^{4} + 2692T_{37}^{2} - 832 \)