Newform orbit 2205.2.g.c

• Label: 2205.2.g.c
• Level: $2205$
• Weight: $2$
• Character orbit: 2205.g
• Analytic conductor: $17.607$
• Analytic rank: $0$
• Dimension: $48$
• CM: no
• Inner twists: $8$

Newspace parameters

Level:	\( N \)	\(=\)	\( 2205 = 3^{2} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2205.g (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(17.6070136457\)
Analytic rank:	\(0\)
Dimension:	\(48\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 48 q + 48 q^{4}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
2204.1	−2.72064				0		5.40188			2.09365	+	0.785252i		0			0		−9.25529				0		−5.69607	−	2.13639i
2204.2	−2.72064				0		5.40188			−2.09365	+	0.785252i		0			0		−9.25529				0		5.69607	−	2.13639i
2204.3	−2.72064				0		5.40188			−2.09365	−	0.785252i		0			0		−9.25529				0		5.69607	+	2.13639i
2204.4	−2.72064				0		5.40188			2.09365	−	0.785252i		0			0		−9.25529				0		−5.69607	+	2.13639i
2204.5	−2.19795				0		2.83100			−2.19253	+	0.439113i		0			0		−1.82649				0		4.81907	−	0.965150i
2204.6	−2.19795				0		2.83100			2.19253	−	0.439113i		0			0		−1.82649				0		−4.81907	+	0.965150i
2204.7	−2.19795				0		2.83100			2.19253	+	0.439113i		0			0		−1.82649				0		−4.81907	−	0.965150i
2204.8	−2.19795				0		2.83100			−2.19253	−	0.439113i		0			0		−1.82649				0		4.81907	+	0.965150i
2204.9	−1.62982				0		0.656312			−1.30159	−	1.81820i		0			0		2.18997				0		2.12135	+	2.96335i
2204.10	−1.62982				0		0.656312			1.30159	+	1.81820i		0			0		2.18997				0		−2.12135	−	2.96335i
2204.11	−1.62982				0		0.656312			1.30159	−	1.81820i		0			0		2.18997				0		−2.12135	+	2.96335i
2204.12	−1.62982				0		0.656312			−1.30159	+	1.81820i		0			0		2.18997				0		2.12135	−	2.96335i
2204.13	−1.43070				0		0.0469039			1.97636	+	1.04595i		0			0		2.79430				0		−2.82757	−	1.49644i
2204.14	−1.43070				0		0.0469039			−1.97636	+	1.04595i		0			0		2.79430				0		2.82757	−	1.49644i
2204.15	−1.43070				0		0.0469039			−1.97636	−	1.04595i		0			0		2.79430				0		2.82757	+	1.49644i
2204.16	−1.43070				0		0.0469039			1.97636	−	1.04595i		0			0		2.79430				0		−2.82757	+	1.49644i
2204.17	−0.841360				0		−1.29211			−0.374684	+	2.20445i		0			0		2.76985				0		0.315244	−	1.85474i
2204.18	−0.841360				0		−1.29211			0.374684	+	2.20445i		0			0		2.76985				0		−0.315244	−	1.85474i
2204.19	−0.841360				0		−1.29211			0.374684	−	2.20445i		0			0		2.76985				0		−0.315244	+	1.85474i
2204.20	−0.841360				0		−1.29211			−0.374684	−	2.20445i		0			0		2.76985				0		0.315244	+	1.85474i

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
7.b	odd	2	1	inner
15.d	odd	2	1	inner
21.c	even	2	1	inner
35.c	odd	2	1	inner
105.g	even	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	2205.2.g.c	✓	48
3.b	odd	2	1	inner	2205.2.g.c	✓	48
5.b	even	2	1	inner	2205.2.g.c	✓	48
7.b	odd	2	1	inner	2205.2.g.c	✓	48
15.d	odd	2	1	inner	2205.2.g.c	✓	48
21.c	even	2	1	inner	2205.2.g.c	✓	48
35.c	odd	2	1	inner	2205.2.g.c	✓	48
105.g	even	2	1	inner	2205.2.g.c	✓	48

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
2205.2.g.c	✓	48	1.a	even	1	1	trivial
2205.2.g.c	✓	48	3.b	odd	2	1	inner
2205.2.g.c	✓	48	5.b	even	2	1	inner
2205.2.g.c	✓	48	7.b	odd	2	1	inner
2205.2.g.c	✓	48	15.d	odd	2	1	inner
2205.2.g.c	✓	48	21.c	even	2	1	inner
2205.2.g.c	✓	48	35.c	odd	2	1	inner
2205.2.g.c	✓	48	105.g	even	2	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{12} - 18T_{2}^{10} + 117T_{2}^{8} - 344T_{2}^{6} + 469T_{2}^{4} - 266T_{2}^{2} + 49 \) acting on \(S_{2}^{\mathrm{new}}(2205, [\chi])\).