Newform orbit 1620.3.o.g

• Label: 1620.3.o.g
• Level: $1620$
• Weight: $3$
• Character orbit: 1620.o
• Analytic conductor: $44.142$
• Analytic rank: $0$
• Dimension: $32$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1620.o (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(44.1418028264\)
Analytic rank:	\(0\)
Dimension:	\(32\)
Relative dimension:	\(16\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 32 q - 8 q^{7}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
701.1		0			0			0		−1.93649	−	1.11803i		0		−2.26486	−	3.92285i		0			0			0
701.2		0			0			0		−1.93649	−	1.11803i		0		5.78429	+	10.0187i		0			0			0
701.3		0			0			0		−1.93649	−	1.11803i		0		−0.973755	−	1.68659i		0			0			0
701.4		0			0			0		−1.93649	−	1.11803i		0		3.57283	+	6.18832i		0			0			0
701.5		0			0			0		−1.93649	−	1.11803i		0		−3.54568	−	6.14130i		0			0			0
701.6		0			0			0		−1.93649	−	1.11803i		0		−6.81144	−	11.7978i		0			0			0
701.7		0			0			0		−1.93649	−	1.11803i		0		3.48846	+	6.04219i		0			0			0
701.8		0			0			0		−1.93649	−	1.11803i		0		−1.24985	−	2.16480i		0			0			0
701.9		0			0			0		1.93649	+	1.11803i		0		3.48846	+	6.04219i		0			0			0
701.10		0			0			0		1.93649	+	1.11803i		0		−1.24985	−	2.16480i		0			0			0
701.11		0			0			0		1.93649	+	1.11803i		0		−6.81144	−	11.7978i		0			0			0
701.12		0			0			0		1.93649	+	1.11803i		0		3.57283	+	6.18832i		0			0			0
701.13		0			0			0		1.93649	+	1.11803i		0		−3.54568	−	6.14130i		0			0			0
701.14		0			0			0		1.93649	+	1.11803i		0		5.78429	+	10.0187i		0			0			0
701.15		0			0			0		1.93649	+	1.11803i		0		−0.973755	−	1.68659i		0			0			0
701.16		0			0			0		1.93649	+	1.11803i		0		−2.26486	−	3.92285i		0			0			0
1241.1		0			0			0		−1.93649	+	1.11803i		0		−2.26486	+	3.92285i		0			0			0
1241.2		0			0			0		−1.93649	+	1.11803i		0		5.78429	−	10.0187i		0			0			0
1241.3		0			0			0		−1.93649	+	1.11803i		0		−0.973755	+	1.68659i		0			0			0
1241.4		0			0			0		−1.93649	+	1.11803i		0		3.57283	−	6.18832i		0			0			0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
9.c	even	3	1	inner
9.d	odd	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1620.3.o.g		32
3.b	odd	2	1	inner	1620.3.o.g		32
9.c	even	3	1		1620.3.g.c	✓	16
9.c	even	3	1	inner	1620.3.o.g		32
9.d	odd	6	1		1620.3.g.c	✓	16
9.d	odd	6	1	inner	1620.3.o.g		32

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
1620.3.g.c	✓	16	9.c	even	3	1
1620.3.g.c	✓	16	9.d	odd	6	1
1620.3.o.g		32	1.a	even	1	1	trivial
1620.3.o.g		32	3.b	odd	2	1	inner
1620.3.o.g		32	9.c	even	3	1	inner
1620.3.o.g		32	9.d	odd	6	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T7^16 + 4*T7^15 + 258*T7^14 + 512*T7^13 + 46349*T7^12 + 108708*T7^11 + 3508258*T7^10 + 11250064*T7^9 + 198230175*T7^8 + 684910540*T7^7 + 6159686170*T7^6 + 24464622840*T7^5 + 144431792234*T7^4 + 430655189624*T7^3 + 1134980174724*T7^2 + 1477835376952*T7 + 1509541505956