Newform orbit 620.3.f.c

• Label: 620.3.f.c
• Level: $620$
• Weight: $3$
• Character orbit: 620.f
• Analytic conductor: $16.894$
• Analytic rank: $0$
• Dimension: $24$
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 620 = 2^{2} \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	620.f (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(16.8937763903\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 24 q - 6 q^{5} + 44 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
309.1		0		−4.99148				0		−1.47233	−	4.77831i		0				11.3647i		0		15.9149				0
309.2		0		−4.99148				0		−1.47233	+	4.77831i		0			−	11.3647i		0		15.9149				0
309.3		0		−4.48325				0		−0.219515	−	4.99518i		0			−	3.21821i		0		11.0995				0
309.4		0		−4.48325				0		−0.219515	+	4.99518i		0				3.21821i		0		11.0995				0
309.5		0		−3.03111				0		−4.60965	−	1.93678i		0			−	12.6370i		0		0.187623				0
309.6		0		−3.03111				0		−4.60965	+	1.93678i		0				12.6370i		0		0.187623				0
309.7		0		−2.79728				0		3.41250	+	3.65443i		0				9.40252i		0		−1.17522				0
309.8		0		−2.79728				0		3.41250	−	3.65443i		0			−	9.40252i		0		−1.17522				0
309.9		0		−1.59213				0		−2.32008	+	4.42913i		0			−	1.60644i		0		−6.46514				0
309.10		0		−1.59213				0		−2.32008	−	4.42913i		0				1.60644i		0		−6.46514				0
309.11		0		−0.662053				0		3.70907	+	3.35303i		0			−	8.05015i		0		−8.56169				0
309.12		0		−0.662053				0		3.70907	−	3.35303i		0				8.05015i		0		−8.56169				0
309.13		0		0.662053				0		3.70907	+	3.35303i		0			−	8.05015i		0		−8.56169				0
309.14		0		0.662053				0		3.70907	−	3.35303i		0				8.05015i		0		−8.56169				0
309.15		0		1.59213				0		−2.32008	+	4.42913i		0			−	1.60644i		0		−6.46514				0
309.16		0		1.59213				0		−2.32008	−	4.42913i		0				1.60644i		0		−6.46514				0
309.17		0		2.79728				0		3.41250	+	3.65443i		0				9.40252i		0		−1.17522				0
309.18		0		2.79728				0		3.41250	−	3.65443i		0			−	9.40252i		0		−1.17522				0
309.19		0		3.03111				0		−4.60965	−	1.93678i		0			−	12.6370i		0		0.187623				0
309.20		0		3.03111				0		−4.60965	+	1.93678i		0				12.6370i		0		0.187623				0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.b	even	2	1	inner
31.b	odd	2	1	inner
155.c	odd	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	620.3.f.c	✓	24
5.b	even	2	1	inner	620.3.f.c	✓	24
5.c	odd	4	2		3100.3.d.h		24
31.b	odd	2	1	inner	620.3.f.c	✓	24
155.c	odd	2	1	inner	620.3.f.c	✓	24
155.f	even	4	2		3100.3.d.h		24

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
620.3.f.c	✓	24	1.a	even	1	1	trivial
620.3.f.c	✓	24	5.b	even	2	1	inner
620.3.f.c	✓	24	31.b	odd	2	1	inner
620.3.f.c	✓	24	155.c	odd	2	1	inner
3100.3.d.h		24	5.c	odd	4	2
3100.3.d.h		24	155.f	even	4	2

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3}^{12} - 65T_{3}^{10} + 1524T_{3}^{8} - 15804T_{3}^{6} + 72440T_{3}^{4} - 120100T_{3}^{2} + 40000 \) acting on \(S_{3}^{\mathrm{new}}(620, [\chi])\).