Newform orbit 1620.2.x.e

• Label: 1620.2.x.e
• Level: $1620$
• Weight: $2$
• Character orbit: 1620.x
• Analytic conductor: $12.936$
• Analytic rank: $0$
• Dimension: $24$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1620.x (of order \(12\), degree \(4\), not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(12.9357651274\)
Analytic rank:	\(0\)
Dimension:	\(24\)
Relative dimension:	\(6\) over \(\Q(\zeta_{12})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 24 q - 12 q^{7}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
53.1		0			0			0		−2.09212	+	0.789333i		0		−0.341151	−	0.0914111i		0			0			0
53.2		0			0			0		−1.96505	+	1.06704i		0		−3.92738	−	1.05234i		0			0			0
53.3		0			0			0		−1.09299	−	1.95074i		0		1.90251	+	0.509775i		0			0			0
53.4		0			0			0		1.09299	+	1.95074i		0		1.90251	+	0.509775i		0			0			0
53.5		0			0			0		1.96505	−	1.06704i		0		−3.92738	−	1.05234i		0			0			0
53.6		0			0			0		2.09212	−	0.789333i		0		−0.341151	−	0.0914111i		0			0			0
377.1		0			0			0		−2.19984	−	0.400874i		0		0.0735330	−	0.274429i		0			0			0
377.2		0			0			0		−1.82312	+	1.29469i		0		0.536206	−	2.00115i		0			0			0
377.3		0			0			0		−0.635536	−	2.14385i		0		−1.24371	+	4.64160i		0			0			0
377.4		0			0			0		0.635536	+	2.14385i		0		−1.24371	+	4.64160i		0			0			0
377.5		0			0			0		1.82312	−	1.29469i		0		0.536206	−	2.00115i		0			0			0
377.6		0			0			0		2.19984	+	0.400874i		0		0.0735330	−	0.274429i		0			0			0
593.1		0			0			0		−2.19984	+	0.400874i		0		0.0735330	+	0.274429i		0			0			0
593.2		0			0			0		−1.82312	−	1.29469i		0		0.536206	+	2.00115i		0			0			0
593.3		0			0			0		−0.635536	+	2.14385i		0		−1.24371	−	4.64160i		0			0			0
593.4		0			0			0		0.635536	−	2.14385i		0		−1.24371	−	4.64160i		0			0			0
593.5		0			0			0		1.82312	+	1.29469i		0		0.536206	+	2.00115i		0			0			0
593.6		0			0			0		2.19984	−	0.400874i		0		0.0735330	+	0.274429i		0			0			0
917.1		0			0			0		−2.09212	−	0.789333i		0		−0.341151	+	0.0914111i		0			0			0
917.2		0			0			0		−1.96505	−	1.06704i		0		−3.92738	+	1.05234i		0			0			0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
45.k	odd	12	1	inner
45.l	even	12	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1620.2.x.e		24
3.b	odd	2	1	inner	1620.2.x.e		24
5.c	odd	4	1		1620.2.x.f		24
9.c	even	3	1		1620.2.j.a	✓	24
9.c	even	3	1		1620.2.x.f		24
9.d	odd	6	1		1620.2.j.a	✓	24
9.d	odd	6	1		1620.2.x.f		24
15.e	even	4	1		1620.2.x.f		24
45.k	odd	12	1		1620.2.j.a	✓	24
45.k	odd	12	1	inner	1620.2.x.e		24
45.l	even	12	1		1620.2.j.a	✓	24
45.l	even	12	1	inner	1620.2.x.e		24

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
1620.2.j.a	✓	24	9.c	even	3	1
1620.2.j.a	✓	24	9.d	odd	6	1
1620.2.j.a	✓	24	45.k	odd	12	1
1620.2.j.a	✓	24	45.l	even	12	1
1620.2.x.e		24	1.a	even	1	1	trivial
1620.2.x.e		24	3.b	odd	2	1	inner
1620.2.x.e		24	45.k	odd	12	1	inner
1620.2.x.e		24	45.l	even	12	1	inner
1620.2.x.f		24	5.c	odd	4	1
1620.2.x.f		24	9.c	even	3	1
1620.2.x.f		24	9.d	odd	6	1
1620.2.x.f		24	15.e	even	4	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T7^12 + 6*T7^11 + 24*T7^10 + 52*T7^9 - 150*T7^8 - 264*T7^7 + 992*T7^6 - 3552*T7^5 + 4260*T7^4 + 3008*T7^3 + 528*T7^2 + 192*T7 + 64